SlideShare a Scribd company logo
Master of Science Thesis
Wake Dynamics Study of an H-type Vertical
Axis Wind Turbine
Chenguang He
August 12, 2013
Faculty of Aerospace Engineering · Delft University of Technology
MSc_Thesis_Wake_Dynamics_Study_of_an_H-type_Vertical_Axis_Wind_Turbine
Wake Dynamics Study of an H-type Vertical
Axis Wind Turbine
Master of Science Thesis
For obtaining the degree of Master of Science in Aerospace Engineering
at Delft University of Technology
Chenguang He
August 12, 2013
Faculty of Aerospace Engineering · Delft University of Technology
Copyright c Chenguang He
All rights reserved.
Delft University Of Technology
Department Of
Aerodynamics and Wind Energy
The undersigned hereby certify that they have read and recommend to the Faculty of Aerospace
Engineering for acceptance a thesis entitled “Wake Dynamics Study of an H-type Vertical
Axis Wind Turbine” by Chenguang He in partial fulfillment of the requirements for the
degree of Master of Science.
Dated: August 12, 2013
Head of department:
Prof. dr. G.J.W. van Bussel
Supervisor:
Dr. ir. C.J. Simao Ferreira
Reader:
Dr. Daniele Ragni
Reader:
Dr. Marios Kotsonis
MSc_Thesis_Wake_Dynamics_Study_of_an_H-type_Vertical_Axis_Wind_Turbine
Summary
Recent developments in wind energy have identified vertical axis wind turbines as a favored
candidate for megawatt-scale offshore systems. Compared with the direct horizontal axis
competitors they poss higher potentials for scalability and mechanical simplicity.
The wake dynamics of an H-type vertical axis wind turbine is investigated using Particle Image
Velocimetry (PIV). The experiments are conducted in an open jet wind tunnel with a turbine
model of 1 m diameter constituted of 2 straight blades generated from a NACA0018. The
turbine model is operated at a tip speed ratio of 4.5 and at a maximum chord Reynolds of
210,000. Two-component planar PIV measurements at the mid-span plane focus on vorticity
shedding and horizontal wake expansion. Stereoscopic PIV measurements at 7 cross-stream
vertical planes are performed to study tip vortex dynamics and evolution of 3D wake structures.
Measurement at the turbine mid-span plane shows that the roll-up of shed vortex is triggered
by wake interactions. Vorticity decay is asymmetrical with the faster decay rate at the leeward
side. The faster windward wake expansion is attributed to the windward deflection of the
tower wake. Wake recovery has not been observed in the horizontal measurement plane up
to 4R downstream of the rotor.
Experimental results on the vertical planes show that the tip vortex is stronger than the shed
vortex in the horizontal plane. The strongest tip vortex is produced near the turbine axial
plane (y/R = 0), and the in-rotor vorticity decay accounts for 60% - 90% of the overall decay.
Near y/R = 0, tip vortices move inboard behind the rotor, whereas the turbine tower and
the horizontal struts obstruct the inboard motion within the rotor swept volume. The rate
of inboard motion is proportional to the vorticity strength. Due to weak vortex strength and
strong blade blockage, tip vortices move outboard at two sides of the rotor primarily towards
the windward side. Roll-over of vortex pairs contributes to the breakdown of vortical structure
behind the rotor. Vertical wake recovery begins 4R downstream of the rotor, and the fastest
recovery is observed near y/R = 0.
v
MSc_Thesis_Wake_Dynamics_Study_of_an_H-type_Vertical_Axis_Wind_Turbine
Acknowledgements
Hereby, I would express my sincere gratitude to my supervisor Dr. Carlos Sim˜ao Ferreira for
your continuous support and encouragement throughout the project. Also I would like to
thank my daily supervisors Dr. Daniele Ragni, Giuseppe Tescione and Dr. Artur Palha. Your
guidances and supports were vital to the success of this project. Thanks Prof. Fulvio Scarano
for your valuable suggestions on my thesis work. I would also like to thank the members of
my graduation committee, Prof. Gerard van Bussel and Dr. Marios Kotsonis for your helpful
advice and suggestions in general.
Thanks to my office roommates, Chidam, Lento, Mark, Rob for the laugh we shared in the past
ten months. And thanks to all my Chinese and International friends for being the surrogate
family during my five years of stay in Holland, and making me feel at home thousands miles
away from China.
Finally a sincere thanks to my girlfriend Nuo, and my families. Without your understanding,
great patience and endless love I would not be able to accomplish all these.
vii
MSc_Thesis_Wake_Dynamics_Study_of_an_H-type_Vertical_Axis_Wind_Turbine
Contents
List of Figures xii
List of Tables xiii
Nomenclature xv
1 Project Outline 1
2 Vertical Axis Wind Turbine - A Brief Introduction 3
2.1 VAWT vs. HAWT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 Fundamental Aspects of VAWT Wake Aerodynamics 7
3.1 Definitions and Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
3.2 Generation of Vorticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.3 Vorticity and Energy Considerations . . . . . . . . . . . . . . . . . . . . . . 11
4 Particle Image Velocimetry 13
4.1 Fundamentals of 2C-PIV . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.2 Stereoscopic PIV (SPIV) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2.1 Working principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.2.2 Translational and rotational configurations . . . . . . . . . . . . . . . 16
4.2.3 Image reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 18
5 Experimental Set-up and Image Processing 19
5.1 Wind Tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
5.2 Turbine Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5.3 Operational Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5.4 PIV Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.5 PIV Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5.6 System of Reference and Field of View . . . . . . . . . . . . . . . . . . . . . 23
5.7 Image Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
ix
x Contents
6 2D Wake Dynamics 27
6.1 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.3 In-rotor Vorticity Shedding . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.3.1 Evaluation method . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.3.2 On path tracking of wake circulation . . . . . . . . . . . . . . . . . . 32
6.4 Blade-wake and Wake-wake Interaction . . . . . . . . . . . . . . . . . . . . . 34
6.5 Vortex Dynamics Along the Wake Boundary . . . . . . . . . . . . . . . . . . 36
6.5.1 Determination of vortex core position and peak vorticity . . . . . . . 36
6.5.2 Vortex trajectory and vortex pitch distance . . . . . . . . . . . . . . . 38
6.5.3 Evolution of peak vorticity . . . . . . . . . . . . . . . . . . . . . . . 39
6.6 Wake Circulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
6.7 Wake Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6.8 Induction and Wake Velocity Profile . . . . . . . . . . . . . . . . . . . . . . 43
6.8.1 Stream-wise velocity profiles . . . . . . . . . . . . . . . . . . . . . . 43
6.8.2 Cross-stream velocity profiles . . . . . . . . . . . . . . . . . . . . . . 45
7 3D Wake Dynamics 47
7.1 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
7.2 Tip Vortex Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
7.2.1 Azimuthal variation of tip vortex circulation . . . . . . . . . . . . . . 53
7.2.2 Determination of tip vortex core position and peak vorticity . . . . . 56
7.2.3 Tip vortex motions in the xz-plane . . . . . . . . . . . . . . . . . . . 57
7.2.4 Stream-wise evolution of tip vorticity . . . . . . . . . . . . . . . . . . 60
7.3 3D Wake Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
7.3.1 Wake geometry in the xy-plane . . . . . . . . . . . . . . . . . . . . . 63
7.3.2 Wake geometry in the yz-plane . . . . . . . . . . . . . . . . . . . . . 63
7.4 Stream-wise Wake Velocity Profiles . . . . . . . . . . . . . . . . . . . . . . . 63
8 Uncertainty Analysis 67
8.1 Free-stream Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
8.2 Model Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
8.2.1 Model imperfections . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
8.2.2 Operational conditions . . . . . . . . . . . . . . . . . . . . . . . . . 70
8.3 Measurement Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
8.4 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
9 Conclusions and Recommendations 73
9.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
9.1.1 2D wake dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
9.1.2 3D wake dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
9.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
References 77
A Image stitching Function 81
List of Figures
2.1 Examples of VAWT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3.1 Schematic of 2D VAWT division . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 CP -TSR diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3.3 Free body diagram of inflow vector . . . . . . . . . . . . . . . . . . . . . . . 9
3.4 2D characteristics, without induction . . . . . . . . . . . . . . . . . . . . . . 10
3.5 2D characteristics, with induction . . . . . . . . . . . . . . . . . . . . . . . 11
3.6 Schematic of tip vortex release along blade trajectory . . . . . . . . . . . . . 12
3.7 Schematics of wake vortex sheets . . . . . . . . . . . . . . . . . . . . . . . . 12
4.1 Schematics of PIV set-up [35] . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.2 Multi-pass vs. single-pass . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
4.3 Schematics of stereo camera arrangement . . . . . . . . . . . . . . . . . . . 16
4.4 Configurations PIV systems [31] . . . . . . . . . . . . . . . . . . . . . . . . 17
4.5 Effect of Scheimpflug adapter [1] . . . . . . . . . . . . . . . . . . . . . . . . 17
4.6 Multi-level Calibration Plate [32] . . . . . . . . . . . . . . . . . . . . . . . . 18
5.1 Schematics of OJF [3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
5.2 Lift characteristics of the airfoil . . . . . . . . . . . . . . . . . . . . . . . . . 20
5.3 Configuration of horizontal measurements . . . . . . . . . . . . . . . . . . . 22
5.4 Configuration of vertical measurements . . . . . . . . . . . . . . . . . . . . . 22
5.5 Schematics of measurement windows of horizontal plane . . . . . . . . . . . 23
5.6 Schematics of measurement windows of vertical planes . . . . . . . . . . . . 24
5.7 Example of raw images and processed image . . . . . . . . . . . . . . . . . . 25
6.1 Contour of wake velocity and wake vorticity, 2D phase-locked experimental
results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
6.2 Contour of wake velocity and wake vorticity, 2D phase-locked simulation results 30
6.3 Change of bound circulation vs. vorticity shedding . . . . . . . . . . . . . . . 31
6.4 Schematics of integration window . . . . . . . . . . . . . . . . . . . . . . . . 31
6.5 Sensitivity analysis of box length . . . . . . . . . . . . . . . . . . . . . . . . 32
xi
xii List of Figures
6.6 On path circulation tracking . . . . . . . . . . . . . . . . . . . . . . . . . . 32
6.7 Maximum circulation position . . . . . . . . . . . . . . . . . . . . . . . . . . 33
6.8 Illustration of Blade-Wake Interaction . . . . . . . . . . . . . . . . . . . . . 35
6.9 Vorticity strengthening due to wake-wake interaction . . . . . . . . . . . . . 35
6.10 Velocity distribution at vortex core . . . . . . . . . . . . . . . . . . . . . . . 36
6.11 Vorticity distribution at vortex core . . . . . . . . . . . . . . . . . . . . . . . 37
6.12 Schematics of vortex core center . . . . . . . . . . . . . . . . . . . . . . . . 38
6.13 Vortex pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6.14 RMS of absolute velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
6.15 Peak vorticity distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
6.16 Wake circulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6.17 Schematics of the wake geometry . . . . . . . . . . . . . . . . . . . . . . . . 42
6.18 Wake geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
6.19 Phase-locked stream-wise velocity profile . . . . . . . . . . . . . . . . . . . . 44
6.20 Peak velocity deficit of horizontal mid-span plane . . . . . . . . . . . . . . . 44
6.21 Schematic of wake stream-wise velocity distribution . . . . . . . . . . . . . . 45
6.22 Schematics 3D induction due to tip vortex . . . . . . . . . . . . . . . . . . . 45
6.23 Simulated wake development until 16R downwind of the turbine . . . . . . . 46
6.24 Cross-stream velocity profile . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
7.1 Contour of wake velocity and wake vorticity, 3D phase-locked experimental
results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
7.2 Illustration of the influence of misalignment angle on uy . . . . . . . . . . . 52
7.3 Illustration of bound circulation of a skewed measurement plane . . . . . . . 53
7.4 Sensitivity analysis of the background cutoff criteria . . . . . . . . . . . . . . 55
7.5 Azimuthal variation of tip vortex strength . . . . . . . . . . . . . . . . . . . 56
7.6 Vorticity distribution at the vortex core . . . . . . . . . . . . . . . . . . . . . 57
7.7 Vorticity distribution away from the vortex core . . . . . . . . . . . . . . . . 57
7.8 Tip vortex trajectory in the xz-plane . . . . . . . . . . . . . . . . . . . . . . 58
7.9 Schematics of vortex inboard motion . . . . . . . . . . . . . . . . . . . . . . 59
7.10 Illustration of vortex pair roll-over, y/R = 0 . . . . . . . . . . . . . . . . . . 60
7.11 Stream-wise variation of tip vorticity . . . . . . . . . . . . . . . . . . . . . . 61
7.12 Decay of tip vorticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
7.13 Wake geometry in the xy-plane . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.14 Wake geometry in the yz-plane . . . . . . . . . . . . . . . . . . . . . . . . . 64
7.15 Wake velocity profile in xy-plane . . . . . . . . . . . . . . . . . . . . . . . . 65
7.16 Peak velocity deficit of 3D vertical planes . . . . . . . . . . . . . . . . . . . 66
8.1 Convergence of the mean flow . . . . . . . . . . . . . . . . . . . . . . . . . 68
8.2 Schematic of blade deformation (exaggerated) . . . . . . . . . . . . . . . . . 70
A.1 Standard window alignment patterns . . . . . . . . . . . . . . . . . . . . . . 81
A.2 Possible window alignment patterns . . . . . . . . . . . . . . . . . . . . . . 82
A.3 Standard window alignment patterns . . . . . . . . . . . . . . . . . . . . . . 82
List of Tables
8.1 Uncertainty of image calibration . . . . . . . . . . . . . . . . . . . . . . . . 71
A.1 Converting operation to standard window alignment pattern . . . . . . . . . 83
xiii
MSc_Thesis_Wake_Dynamics_Study_of_an_H-type_Vertical_Axis_Wind_Turbine
Nomenclature
Latin Symbols
B Number of blade [-]
CPmax maximum power coefficient [-]
c Blade chord [m]
H Blade span [m]
N Number of samples [-]
p∞ Static pressure [pa]
R Rotor radius [m]
t0 Vortex core radius [m]
Rec Chord based Reynolds number [-]
Rconst specific gas constant [J/(kg·K)]
t Vortex age [s]
T Temperature [K]
u Velocity vector [m/s]
ub Blade velocity [m/s]
ures Local inflow velocity [m/s]
uv Vorticity sheet convective velocity [m/s]
u∞ Free-stream velocity [m/s]
w Width of vorticity sheet [m]
xv
xvi Nomenclature
Greek Symbols
α Angle of attack [rad]
Γ Blade circulation [m2/s]
˙γ Pitching rate [rad/s]
θ Blade azimuthal angle [deg]
λ Tip speed ratio [-]
ρ Density [kg/m3]
σ Blade solidity [-]
ψ Misalignment angle [rad]
ω Vorticity vector [1/s]
Acronyms
2D Two dimensional
3D Three dimensional
2C-PIV Two Components PIV
AoA Angle of Attack
BWI Blade-Wake Interaction
CFD Computational Fluid Dynamics
DUWIND Wind Energy Research Group
HAWT Horizontal Axis Wind Turbine
OJF Open Jet Facility
PTU Processing Time Unit
PIV Particle Image Velocimetry
SPIV Stereoscopic PIV
TSR Tip Speed Ratio
TU Delft Delft University of Technology
VAWT Vertical Axis Wind Turbine
WWI Wake-Wake Interaction
xvii
MSc_Thesis_Wake_Dynamics_Study_of_an_H-type_Vertical_Axis_Wind_Turbine
Chapter 1
Project Outline
The re-merging interests on Vertical Axis Wind Turbine (VAWT) for urban or off-shore appli-
cations require an improved understanding of rotor aerodynamics for performance optimization
and wind farm design. The present project investigated the wake development of an H-type
VAWT using Particle Image Velocimetry (PIV). Phase-locked flow properties were measured
at a fixed tip speed ratio of 4.5. Two types of PIV measurements were conducted: a two-
component planar PIV measurement at the horizontal mid-span plane, and a three-component
stereoscopic PIV measurement at vertical measurement planes (aligned with free-stream). The
study aims to:
• Identifying main characteristics of three dimensional (3D) wake development of an H-
type VAWT, both in detailed vortex scale and in global wake scale.
• Validating the two dimensional (2D) unsteady inviscid panel code using measurement
results at turbine mid-span plane.
Based on the obtained measurement data, detailed flow analyses were performed with the
focus on following aspects.
At horizontal mid-span plane:
• Circulation of wake vorticity sheets.
• Blade-wake interaction and wake-wake interaction, investigating the triggering mecha-
nism of vortical structures roll-up.
• Shed vortex dynamics along wake shear layer, focusing on vortex convective trajectory
and vorticity evolution.
• Wake geometry at mid-span position, with specific attention to asymmetrical wake
expansion.
• Induction field and stream-wise evolution of wake velocity profiles.
At vertical measurement planes:
1
2 Project Outline
• Azimuthal variation of tip vortex strength.
• Tip vortex motion in vertical planes, focusing on the cross-stream variation of vortex
motions and vortex pair roll-over behind the rotor swept volume.
• Stream-wise vorticity decay, with a comparison with simple theoretical vortex model.
• 3D wake geometry.
• Evolution of stream-wise velocity profile in vertical planes.
Chapter 2
Vertical Axis Wind Turbine - A Brief
Introduction
Based on the alignment of rotational axis, two types of wind turbines are distinguished:
Horizontal Axis Wind Turbine (HAWT) with rotational axis lying parallel to the ground, and
Vertical Axis Wind Turbine (VAWT) with rotational axis standing vertically. Besides their
different appearances, the underlying working principle is same. Wind turbine extracts kinetic
energy from the wind, converting it into mechanical energy in the form of rotational motion;
through built-in electricity generator, the mechanical energy is converted into electric energy
which is delivered to electric networks.
VAWTs are divided into two streams: drag-driven type and lift-driven type. The drag-driven
type is propelled by the drag difference between the upstream and the downstream part of
rotor blade. A famous example of drag-driven VAWT is the Savonius rotor (Figure 2.1(a))
named after Finish engineer Sigurd Savonius who invented it in 1925 [34]. Structural simplicity
and relatively high reliability make drag-driven VAWTs particularly suitable for applications
such as wind-anemometers and Flettner Ventilators. The former ones are commonly seen on
the building rooftop whereas the latter ones are typically used as the cooling system of road
vehicles. Despite their simplicity, the Savonius rotors, as with other variants of drag-driven
VAWTs, have generally low operational efficiency (CPmax =0.17) when compared with their
horizontal axis competitors (CPmax =0.59).
Another Typology of VAWT is driven by lift. One famous example is the so-called Darrieus
turbine (Figure 2.1(b)) patented by American Engineer Georges Darrieus in 1931 [29]. In
theory Darrieus turbines are the most efficient VAWT, achieving an optimal power coefficient
of CP =0.42 [26]. Since turbine blades are curved into an egg-beater shape (to reduce the
stress induced by centrifugal force), Darrieus turbines are also known as the egg-beater rotors.
In 1970s and 1980s, this configuration was extensively studied in Canada and the United
States. In particular, the research work at Sandia National Laboratories proved the feasibility
of large scale Darrieus turbines [30]. In 1984, the completion of Eole C (Figure 2.1(b)), the
largest VAWT ever built [11], marked the culmination of a decade research efforts. In the
3
4 Vertical Axis Wind Turbine - A Brief Introduction
end of 1980s, the shrinkage of North America market cut down research funding, resulting
in a research stop for almost 15 years. In the following decades commercial development
took over, companies like FloWind launched massive implementations of Darrieus turbines. In
its full development during 1987, the power output of all FloWind VAWTs could supply the
electricity use of nearly 20,000 California families. However, the glorious commercial success
was not sustained as series of fatigue-related failures finally dragged down FloWind at the end
of 2004 [17][30][39].
To overcome the structural deficiency of Darrieus turbines, a number of design concepts were
explored since 1980s. Among them, the H-type VAWT or H-rotor (Figure 2.1(c)) stand out for
its simplicity and efficiency. The use of straight blade reduces the difficulty of manufacturing
curved blade; and the use of inherent blade stall characteristic removes the need of speed-
break mechanism [30]. H-rotor researches during 1980s produced famous prototypes like
VAWT-850, which is the largest H-rotor in Europe [27]. In 1990s, years of research efforts
were transformed into commercial developments. Companies like Solwind of New Zealand,
Ropatec of Italy, Neuh¨aususer of Germany designed and produced a range of H-rotors [16].
(a) Savonius type VAWT [5] (b) Darrieus turbines (Eole C) [30]
(c) H-rotor [30]
Figure 2.1: Examples of VAWT
2.1 VAWT vs. HAWT 5
2.1 VAWT vs. HAWT
As an omni-directional machine, VAWT eliminates the need of pitching system hence reduces
mechanical complexity [22]. VAWTs are generally quieter than HAWTs, making them suit-
able for densely populated areas [19]. The ground-based equipment (e.g. transmission and
electrical generation, etc.) makes VAWTs lighter, and easier for maintenance [12]. In offshore
applications, low center of gravity allows an enhanced floating stability and a reduced gravi-
tational load. The possibility of under-water electric generator further decreases the size and
cost of the floating support structure.
VAWTs have great potentials in wind farm operations. As the power output of a wind turbine
is proportional to blade swept area, growing demand of power output has pushed the size
of HAWTs to limit. Larger wind turbine size results in higher centrifugal force and bending
stresses. Longer turbine blade requires larger turbine spacing hence lower wind farm density
[30]. On the other hand, the size of VAWT can be extended vertically without a significant
increase of occupied area. Recent researches showed that the wake recovery of a VAWT is
faster, allowing for clustered array and increases wind farm power output [12][25].
However VAWT has its problems. Besides the well-known self-starting problem, the occurrence
of dynamics stall at low rotational speed also shortens the turbine life. The inherent rotor
asymmetry and unsteady operation of VAWTs lead to complicated blade loading and flow
phenomena, which challenge blade designs and flow analyses [10].
MSc_Thesis_Wake_Dynamics_Study_of_an_H-type_Vertical_Axis_Wind_Turbine
Chapter 3
Fundamental Aspects of VAWT
Wake Aerodynamics
The wake of a VAWT is inherently unsteady. The unsteadiness originates from periodical
change of local Angle of Attack (AoA) at the blade level and from blade-wake interactions
at the rotor level. Flow phenomena due to this unsteadiness include time varying vorticity
shedding, unsteady wake evolution, blade vortex interaction, etc. Wake dynamics of VAWTs
is further complicated by the strong asymmetry between the advancing and receding sides of
the rotor [36]. Decades of research discontinuity leads to a limited understanding of these
complicated phenomena.
In the past few years, wake aerodynamics of an H-rotor was extensively studied in the
Wind Energy Research Group (DUWIND) of Delft University of Technology (TU Delft). An
inviscid unsteady panel code has been developed to simulate time dependent wake evolution
[14]. Recently, the development of hybrid code has started, coupling Computational Fluid
Dynamics (CFD) solver at turbine blades and vortex method at turbine wakes. Both methods
are grid-free, making them insensitive to numerical dissipation hence well suitable for vortical
flow simulation. In parallel to the numerical works, a range of experimental studies (e.g. smoke
visualization, hot-wire and PIV measurement, etc.) were performed to validate numerical
codes [36][37][38].
This chapter addresses fundamental aspects of the H-rotor wake dynamics, focusing on the
generation and spatial distribution of vorticity within the rotor swept volume. The evolution
of the vortical structures downstream of the rotor will be discussed in Chapter 6 and Chapter 7
in combined with the discussion of experimental results.
3.1 Definitions and Notations
The wake of a VAWT can be divided into a region within the rotor swept volume and a region
behind the rotor. Traditional momentum-based streamtube models treated a turbine rotor as
7
8 Fundamental Aspects of VAWT Wake Aerodynamics
two half cups to adapty classical momentum theories [28]. Although this division accurately
predicts integral forces, its capability in capturing the details of vortex dynamics is limited.
The inefficiency lies in its incomplete treatment of the regions between upwind and downwind
half of the rotor. These two regions, commonly referred to as the windward and the leeward,
are essential to vorticity shedding and energy extraction of a VAWT. A better way of rotor
division is proposed in [36]:
• Upwind 45◦ < θ < 135◦
• Leeward 135◦ < θ < 225◦
• Downwind 225◦ < θ < 315◦
• Windward 315◦ < θ < 360◦ ∪ 0◦ < θ < 45◦
With θ being the azimuthal angle and θ = 90◦ being the most upwind. Figure 3.1 display a
schematics of this division. The Cartesian reference system is origined at the turbine center,
x-axis directs positively downwind of the turbine, y-axis points windward and z-axis points
upwards. Counter-clockwise rotation is defined positive seen from above.
In the following context, x-direction is referred to as the stream-wise direction and y-direction
is referred to as the cross-stream directions. The turbine axial plane is the plane y/R = 0.
In the horizontal direction, inboard refers to the direction of decreasing |y/R|, and outboard
refers to the direction of increasing |y/R|. In the vertical direction, inboard refers to the
direction of decreasing |z/H|, and outboard refers the direction of increasing |z/H|.
x
y
R
θ = 0˚
θ = 45˚
θ = 270˚θ = 90˚
θ = 180˚
θ = 135˚ θ = 225˚
θ = 315˚
u∞ ω
Upwind
Windward
Leeward
Downwind
Figure 3.1: Schematic of 2D VAWT division
Like other rotational machines, two parameters are important for VAWTs. Blade Solidity σ
describes the percentage of the rotor area covered by solid blades:
σ =
Bc
R
(3.1)
Where B is the number of blade, c blade chord and R rotor radius. Large blade solidity creates
strong rotor blockage hence large flow induction. The Tip Speed Ratio (TSR) λ determines
3.2 Generation of Vorticity 9
turbine rotational frequency and is crucial to the power output:
λ =
ωR
u∞
(3.2)
Where ω is the rotor angular velocity in radius per second and u∞ is the free-stream velocity.
According to a typical CP -TSR diagram (Figure 3.2) the peak power is found at the medium
range of TSR. Low TSR tends to trigger dynamic stall, which postpones the occurrence of
normal stall but intensifies unsteady blade loading, whereas high TSR results in low AoA, both
compromising turbine efficiency.
1 2 3 4 5 6 7 8
0
0.1
0.2
0.3
0.4
TSR
C
P
Re=150,000
Re=300,000
Figure 3.2: CP -TSR diagram
3.2 Generation of Vorticity
The wake of VAWTs consist of shed and trailed vorticities. Due to unsteady blade motions,
the release and distribution of vorticity are time dependent.
x
y
R
u∞
λu∞ ueff ω
θ
u∞
Figure 3.3: Free body diagram of inflow vector
Based on the schematics of Figure 3.3, the geometrical AoA α can be derived as a function
10 Fundamental Aspects of VAWT Wake Aerodynamics
of blade azimuthal angle θ:
α = tan−1 − cos θ
λ − sin θ
(3.3)
Time variations of AoA and inflow velocity lead to a periodically varying bound circulation,
which, according to the Kelvin’s theorem [23] generates shed vorticity proportional to the
negative change rate of bound circulation Γ:
ωshed (t, z) = −
∂Γ (t, z)
∂t
(3.4)
The bound circulation can be derived using the unsteady formulation of the KuttaJoukowski
theorem [23]:
Γ = Γinflow + Γpitching
= cπ uresα +
c
2
1
2
− a ˙γ
(3.5)
Where ures the local inflow velocity, a the distance from rotation center to the leading edge
of airfoil, and ˙γ the pitching rate. The first right-hand-side term measures the circulation due
to inflow velocity, and the second term specifies the additional circulation of blade pitching
motions.
The magnitude of trailed vorticity is determined by the spatial gradient of bound circulation
in the z-direction:
ωtrailed (t, z) = −
∂Γ (t, z)
∂z
(3.6)
Shed vorticity aligns with the blade trailing edge, and trailed vorticity is orientated perpen-
dicular to the blade trailing edge. Two types of vorticity have a phase difference of 90◦.
0 45 90 135 180 225 270 315 360
−30
−20
−10
0
10
20
30
θ°
α°
λ = 3
λ = 4
λ = 5
(a) Geometrical AoA
0 45 90 135 180 225 270 315 360
−1
−0.5
0
0.5
1
θ°
Γ/Γ
θ=90
°
,λ=3
λ = 3
λ = 4
λ = 5
(b) Normalized bound circulation
0 45 90 135 180 225 270 315 360
−1
−0.5
0
0.5
1
θ°
ω/ω
θ=0
°
,λ=5
λ = 3
λ = 4
λ = 5
(c) Normalized shed vorticity
Figure 3.4: 2D characteristics, without induction
Figure 3.4 displays the azimuthal variation of the geometrical AoA, bound circulation and
vorticity shedding at three TSRs. The greatest AoAs are found at the leeward side around
θ = 130◦ and θ = 230◦ (varying with TSR). Increasing TSR causes a drop of AoA, which
reduces the likelihood of dynamics stall. Result shows that bound circulation is independent
of TSR. The strongest circulations are observed at the most upwind and downwind sides of
the rotor; whereas the greatest changes rate of bound circulation (i.e. the strongest vorticity
3.3 Vorticity and Energy Considerations 11
shedding) occurs at the most windward and leeward sides. Shed vorticity plot (Figure 3.4(c))
shows that vorticity shedding increases with TSR since the change rate of bound circulation
becomes higher.
The analysis so far has not considered the effect of flow induction. In reality, vorticity distribu-
tion is non-symmetrical at two sides of the rotor. This is primary due to the asymmetrical flow
induction as the windward advancing blade has different inflow conditions from the leeward
receding blade. In the stream-wise direction, wake induction of the upwind blade passage re-
duces the inflow velocity hence vorticity shedding downwind of the rotor, therefore the global
wake dynamics is mainly determined by the wake generated at the upwind half of the rotor.
Figure 3.5 displays the effective AoA and vorticity shedding from 2D simulation.
0 45 90 135 180 225 270 315 360
−5
0
5
10
15
20
θ°
α
°
(a) Effective AoA
0 45 90 135 180 225 270 315 360
−1
−0.5
0
0.5
1
θ°
ω/ωmax
(b) Normalized shed vorticity
Figure 3.5: 2D characteristics, with induction
Trailed vortex is generated along the finite span of a 3D VAWT. The strongest trailed vortex,
known as the tip vortex, is released at the blade tip where the spatial gradient of the circulation
is the highest. Neglecting ground effects and gravitational forces, the distribution of tip vortex
is symmetrical with respect to the turbine axial plane y/R = 0. Figure 3.6 shows a schematic
of tip vortex releasing along blade trajectory. Curved arrow represents the direction of vortex
roll-up; plus and minus signs indicate pressure and suction sides of the blade. Tip vorticity
changes its orientation at the most windward and leeward sides of the rotor, as a result of the
sign change of bound circulation (Figure 3.4(b)). The production of trailed vorticity is weaker
at the downwind part of the rotor due to reduced bound circulation. As shedding vorticity
is determined by the time variation of bound circulation, the strongest vorticity shedding
concentrates at the turbine mid-span where bound circulation is usually the highest.
3.3 Vorticity and Energy Considerations
Assuming the energy extraction of a wind turbine can be measured by the Bernoulli constant
∇H, it can be shown that ∇H is determined by the local flow velocity u and the vorticity
field ω [23]:
∇H = ρ (u × ω) (3.7)
12 Fundamental Aspects of VAWT Wake Aerodynamics
+ -
-+
0˚
180˚
90˚ 270˚
u∞
Figure 3.6: Schematic of tip vortex release along blade trajectory
where vorticity is related to the curl of blade force by:
Dω
Dt
=
1
ρ
∇ × f
=
1
ρ
∂fx
∂z
j −
∂fx
∂y
k
(3.8)
For 2D VAWT spatial derivatives and force terms in z-direction are omitted, implying vorticity
shedding and energy exchange occur at azimuthal positions where
∂fy
∂x − ∂fx
∂y is non-zero.
To extract power in 3D, both shed and trailed vorticity are essential. Figure 3.7 shows a
simplified schematic of a VAWT wake consisting of an array of vortex sheets. Shed vortices
form the red sheets perpendicular to the inflow direction, and trailed vortices form the blue
sheets parallel to the incoming flow. Two types of vortex sheet form a square wake tube which
deforms along its convection.
u∞
(a) Shedding vorticity sheets
u∞
(b) Trailing vorticity sheets
Figure 3.7: Schematics of wake vortex sheets
Chapter 4
Particle Image Velocimetry
Particle Image Velocimetry (PIV) is a non-intrusive flow diagnostic technique allowing flow
field measurements. Comparing with intrusive flow measurement techniques like hot wire
anemometer or pressure tube, PIV eliminates the need of instrumental intrusions by using
non-intrusive laser light and tracer particles. Using Two Components PIV (2C-PIV) technique
two velocity components within a planar interrogation window are obtained, and by using
Stereoscopic PIV (SPIV) a third velocity component normal to the measurement plane can
be resolved. Recently, the development of Tomographic PIV [15] extends the measurement
range to a 3D volume.
Fundamentals of 2C-PIV measurements are discussed in Section 4.1. A brief introduction to
SPIV technique is presented in Section 4.2. If not stated otherwise, the content of 2C-PIV
is based on the lecture notes of the course Flow Measurement Techniques of TU Delft [35],
PIV lecture slides of A. James Clark School of Engineering, University of Maryland [24] and
the book Particle Image Velocimetry - A Practical Guide [32]. The content of SPIV is based
on the paper of Arroyo and Greated [8] and the review paper of Prasad [31].
4.1 Fundamentals of 2C-PIV
A typical 2C-PIV set-up consists of following components: a laser generator producing light
sheet for particle illumination, a camera capturing the particle scattered light, and a PIV
software for image acquisition and data processing. Figure 4.1 shows a basic PIV set-up. Key
components are discussed in the following context.
Tracer particles
PIV measures flow velocity by cross correlating tracer particle positions of two consecutive
image frames. Tracer particles must be small enough to faithfully trace the fluid motion;
in the meanwhile, the size of the tracer particle should be large enough to scatter adequate
13
14 Particle Image Velocimetry
Figure 4.1: Schematics of PIV set-up [35]
light. The contradictory requirements make it non-trivial to select a proper particle size. Small
particles are excellent flow tracer (due to low mass inertia) but are not good scatter (due to
limited size); whereas the situation is opposite for large particles. For micro-metric particles
used in PIV measurements, light scattering occurs at Mie regime where particle diameter is
comparable or larger than the laser wavelength. In this regime, the strongest scattering occurs
at 0◦ and 180◦ with respect to the incoming light, while the weakest scattering concentrates
in the direction normal to the camera viewing direction. Since the contrast of PIV image is
strongly determined by the scattering intensity, it is preferred to use the largest possible tracer
particles without interfering flow properties. The diameter of typical tracer particles is about
1-3 µm in air flow measurement.
Integration window
Average particle displacement of interrogation window is derived using cross correlation. For
statistically significant results, it is important to have a sufficient number of tracer particles;
in the meanwhile over-seeding should also be avoided to prevent multi-phase flow. Typically,
a desired particle concentration lie within the range from 109 to 1012 particles/m3 and each
integration window should contain at least 10 particles.
If large velocity variation presents in the measurement domain, the selection of a proper
window size becomes difficult. A small window tends to cause particle loss, whereas large
window size inevitably averages out flow details. To overcome this difficulty, the so-called
multi-pass technique is developed. Starting with large window, this approach pre-shifts smaller
interrogation windows (of the next pass) by using the distance estimated at the current pass.
This process continues until the smallest window size is reached. Figure 4.2 demonstrates an
example of applying single pass and multi-pass operations to a same measurement area. It is
4.2 Stereoscopic PIV (SPIV) 15
clear that multi-pass operation is capable of resolving flow field with large velocity contrast
between the vortex region and the background free-stream region, which is impossible by using
single-pass operation.
Single-pass
window size 24×24
Multi-pass
min. window size 24×24
Figure 4.2: Multi-pass vs. single-pass
Overlap between neighboring interrogation windows is often preferred to increase the use of
measurement data. Since particles near the edge of windows are less likely to be captured
in both frames, the processed image tends to be less accurate around window edges. By
overlapping, these data are replaced by the data of neighboring window which does not lies
at the edge. 20-30% overlap is common in practice.
PIV acquisition and processing software
The complicity of PIV measurement requires a real-time control of mutual dependent sub-
systems. Modern PIV softwares (e.g. LaVision, PIVtec, TSI, etc) integrate control of various
sub-systems (e.g. laser, cameras, etc.) into a central control unit which supports online
processing in parallel to measurements.
4.2 Stereoscopic PIV (SPIV)
4.2.1 Working principle
Stereoscopic PIV determines the velocity component normal to the measurement plane by
using two synchronized cameras viewing from different angles. In a single camera set-up
(Figure 4.4(a)), out-of-plane velocity is projected onto the object plane causing perspective
errors. Using two off-axis cameras, the perspective error is converted into information about
out-of-plane velocity components.
Figure 4.3 shows the 2D schematic of a stereoscopic camera arrangement. Velocity compo-
16 Particle Image Velocimetry
u
ux
ux1
ux2
uz
CAM1 CAM2
α1
α2
X
z
Y
Object plane
Figure 4.3: Schematics of stereo camera arrangement
nents in x-, y- and z- directions can be derived as:
ux =
ux1 tan α2 + ux2 tan α1
tan α1 + tan α2
uy =
uy1 tan β2 + uy2 tan β1
tan β1 + tan β2
uz =
ux1 − ux2
tan α1 + tan α2
=
uy1 − uy2
tan β1 + tan β2
(4.1)
Where α and β represent camera viewing angle with respect to yz- and xz-plane. To avoid
singularity as α and β approaches zero, Equation 4.1 can be modified to:
ux =
ux1 + ux2
2
+
uz
2
(tan α1 − tan α2)
uy =
uy1 + uy2
2
+
uz
2
(tan β1 − tan β2)
(4.2)
4.2.2 Translational and rotational configurations
Based on camera arrangements, two SPIV configurations are distinguished. A translational
configuration consists of two parallel standing cameras with lens axes normal to the light sheet
(Figure 4.4(b)). This configuration allows for uniform magnification and good image focus,
but its resolution is restricted by viewing angle θ (or camera off-axis angle). It can be shown
that the accuracy of out-of-plane displacement is inversely proportional to viewing angle [43]:
σ∆z
σ∆x
=
1
tan α
(4.3)
Where σ∆z and σ∆x represent the errors of out-of-plane and in-plane velocity components.
With increasing viewing angle, the viewing axis deviates from lens design specification, causing
substantial performance decay.
The restriction on viewing angle is removed with a rotational configuration (Figure 4.4(c)).
Since lens axes align with the viewing directions, the viewing angle can be increased without
4.2 Stereoscopic PIV (SPIV) 17
104
(a) Planar PIV (b) SPIV - Translational system
(c) SPIV - Rotational system
Figure 4.4: Configurations PIV systems [31]
(a) Before using Scheimpug
adapter
(b) After using Scheimpug
adapter
Figure 4.5: Effect of Scheimpflug adapter [1]
18 Particle Image Velocimetry
compromising lens performance, thereby allowing higher accuracy of out-of-plane velocity
components. Rotating cameras bring the drawback of non-uniform image magnification. To
retrieve uniform magnification cameras have to be mounted according to the Scheimpflug
condition [6], which requires a co-linear alignment of object plane, lens plane and image
plane. Without proper alignment the resulting image has only a narrow band of focused
region as shown in Figure 4.5(a). A practical solution is to add a Scheimpug adapter between
lens and CCD chip. By manually adjusting the orientation of Scheimpug adapter, a broader
focus range can be achieved as shown in Figure 4.5(b) [1].
Although increasing off-axis angle improves measurement accuracy, an excessively large angle
should be avoided to prevent strongly distorted image. In practice, the optimal measurement
quality is obtained as camera opening angle approaches 90◦.
4.2.3 Image reconstruction
To obtain displacement vectors in the object plane, the data of image plane is projected back
using mapping function. This process is known as image reconstruction.
If the complete geometry of PIV system is known, geometrical reconstruction can be used
to link the image plane data x to the object plane data X. Since this approach requires a
complete knowledge of imaging parameters, its practical use is limited.
A more useful method, known as calibration-based reconstruction, reconstructs the mapping
function through a calibration process. A typical mapping function reads:
x = f (X) (4.4)
Where f is usually a polynomial function with undetermined coefficients. Since the number
of calibration points often exceeds the number of unknown coefficients, the polynomial coef-
ficients are commonly determined using least square approximations. Calibration is performed
using a calibration target, typically a rectangular metal plate with prescribed grid marker
(cross, dots, etc.). For the calibration of a 2C-PIV set-up, a single image of the calibration
plate is sufficient; for the calibration of a SPIV set-up, a second image is required at a known
distance offset the laser sheet. Most commonly, a multi-level calibration plate (Figure 4.6) is
used for the calibration of SPIV configuration.
Figure 4.6: Multi-level Calibration Plate [32]
Chapter 5
Experimental Set-up and Image
Processing
5.1 Wind Tunnel
The PIV experiments have been performed in the Open Jet Facility (OJF) of TU Delft. The
OJF is a closed-circuit, open-jet wind tunnel with an octagonal cross-section of 2.85 × 2.85
m2 and a contraction ratio of 3:1. The tunnel jet is free to expand in a 13.7 × 6.6 × 8.2 m3
test section. Driven by a 500 kW electric motor, the OJF delivers free stream velocity range
from 3 m/s to 34 m/s with a flow uniformity of ±0.5% and a turbulence level of 0.24% [2].
A 350 kW heat exchanger maintains a constant temperature of 20◦C in the test section. A
schematic of the wind tunnel is shown in Figure 5.1.
Figure 5.1: Schematics of OJF [3]
19
20 Experimental Set-up and Image Processing
5.2 Turbine Model
The testing model is a two bladed H-type VAWT (H-rotor) with a rotor radius of 0.5 m. The
rotor blades are generated by straight extrusion of a NACA0018 airfoil to 1 m span and 6 cm
chord. Both sides of the blade are tripped with span-wise zig zag tapes, approximately 10%
chord from the blade leading edge. Each blade is supported by two aerodynamically profiled
struts (0.5 m) mounted at 0.2R inboard of blade tips, giving an aspect ratio of 1.8 and a
blade solidity of 0.11. The entire turbine model, including blades, struts and supporting shaft
is painted in black to reduce laser reflections.
The wind turbine is supported by a 3 m steel shaft connected to a Faulhaber R
brushless
DC Motor at the bottom. With the maximum output power of 202 W, this motor drives the
turbine at low wind speeds and maintains constant rotational speed. A Faulhaber gearbox with
5:1 gear ratio is coupled to the electrical engine to obtain sufficient torque at the operating
regimes. An optical trigger is mounted on the shaft to synchronize the PIV system for the
phased-lock acquisition.
5.3 Operational Conditions
The turbine was operated at a fixed TSR of λ =4.5. The operational TSR was determined
by a CP -TSR diagram similar to the one of Figure 3.2. Simulation shows λ = 4.5 yields the
optimal power output (CP = 0.4) for the testing turbine.
At a rotational speed of 800 RPM, the chord-based Reynolds Rec number is computed:
Rec =
ρωRc
µ
= 175, 000
Considering free-stream velocity and flow inductions, the actual chord-based Reynolds number
varied between 130, 000 to 210, 000.
0 5 10 15
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Angle of attack α
°
CL
NACA0018, Re=∞
NACA0018, Re=130,000
NACA0018, Re=210,000
NACA0003, Re=∞
αmax
=12.5o
(a) Lift polar
0 5 10 15
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Angle of attack α°
dCL
/dα
NACA0018, Re=∞
NACA0018, Re=130,000
NACA0018, Re=210,000
NACA0003, Re=∞
αmax
=12.5o
(b) Slope of lift polar
Figure 5.2: Lift characteristics of the airfoil
5.4 PIV Equipment 21
Both lift coefficient and lift slope are important for VAWTs. The former one specifies the
magnitude of bound circulation hence the strength of tip vortex, whereas the latter one
determines unsteady vorticity shedding hence the power efficiency of the turbine. Since one
of objectives is to validate vorticity shedding at the mid-span plane of the 2D simulation,
it is more important to use an airfoil with comparable lift slope as the viscous NACA0018
airfoil used in the experiment. The lift polar and lift slope of a NACA0018 airfoil are given
in Figure 5.2. Since the lift slope reduces in viscous flow, a thinner airfoil (NACA0003,
dCL
dα = 0.1) was used in the inviscid simulation to ensure the same performance of VAWT.
Noted although the lift characteristics of inviscid NACA0003 airfoil are closer to the viscous
NACA0018 airfoil, its higher lift slope is still an important cause of discrepancies in latter
comparisons. Neglecting flow inductions, the maximum angle of attack of 12.5◦ is highlighted
by the vertical dashed line in Figure 5.2.
5.4 PIV Equipment
The tracer particle was produced by a SAFEX R
twin fog generator placed downstream of
the rotor. This generator produces Diethyl glycol-based seeding particles of 1 µm median
diameter with a relaxation time of less than 1 µs [33]. Uniform mixing in the test section was
ensured by the wind tunnel closed loop.
A Quantel Evergreen R
double pulsed Nd:YAG laser system was used as the light source.
With the emitting power of 200 mJ per pulse, this system provides green light of wavelength
532 nm creating laser sheet of approximately 2 mm width and 40×30 cm2 illuminating area.
The pulsed laser energy, repetition rate and time delay between pulses were controlled by a
Processing Time Unit (PTU) and a sychnozation box called the Standford box.
Two LaVision R
Imager pro LX 16M cameras were used for image acquisition. The cameras
have a resolution of 4870×3246 pixels2 with the pixel size of 7.4×7.4 µm2. Each camera was
equipped with a Nikon R
lens with focal length varying with desired Field of View (FOV) and
image resolution (see Section 5.5 for details). Day light filter was added to reduce ambient
light. Camera acquisition was synchronized to the laser shooting using the DaVis acquisition
software.
5.5 PIV Set-up
The measurements were conducted with PIV system in two set-ups: a 2C-PIV measurements
at the horizontal plane and a SPIV measurements at the vertical planes.
The first set-up investigated horizontal measurement plane at the rotor mid-span position
(Figure 5.3). Given vertical symmetry of the rotor and that no relevant out of plane velocity
component has been detected across the mid-span plane, a planar PIV setup has been used
by combining two cameras into a single field of view. These two cameras were mounted on an
horizontal beam, side by side at 1.3 m beneath the horizontal laser sheet. Each camera was
equipped with an f = 105 mm Nikon lens, with a measuring aperture of f/4 and magnification
factor of M = 0.09. The Field of View (FOV) of single camera was 266 × 399 mm2, and the
combined FOV was 266 × 755 mm2 with an overlap of 44 mm in the y-direction.
22 Experimental Set-up and Image Processing
In the second set-up, measurements were taken in the vertical planes of 7 cross-stream posi-
tions (Figure 5.4). The SPIV set-up had two rotational cameras at two ends of a horizontal
beam; a laser generator in middle of the beam produced vertical laser sheet to illuminate the
measurement region. The cameras, mounted about d = 2.0 m from the measurement plane,
were equipped with f = 180 mm Nikon lenses (f/4) with a relative viewing angle of δ = 96◦
and a magnification factor of M = 0.07. The resulting FOV was 365 × 430 mm2.
Figure 5.3: Configuration of horizontal measurements
Figure 5.4: Configuration of vertical measurements
5.6 System of Reference and Field of View 23
5.6 System of Reference and Field of View
To synchronize the motion of cameras and laser, a two degrees-of-freedom traversing system
was used, providing a stream-wise range of 1.4 m and a cross-stream range of 1.0 m.
The horizontal measurements covers the rotor swept area and the wake region up to 4R
downstream of the rotor. The positions of measurement window were optimized to minimize
blade and tower shadows. To cover the target measurement domain, the traversing system
was placed at two stream-wise positions. The first traversing system position covered the
measurement range of x/R = [−1.88, 1.38], y/R = [−1.34, 1.35] and the second position
covers the range of x/R = [1.13, 4.43], y/R = [−1.77, 1.77]. Figure 5.5 shows a schematic
of the measurement domain. Each interrogation window is labeled with a unique ID, with
the first digit indicating the number of traversing system position and the second alphabet
indicating the window sequence. In the stream-wise direction windows were overlap by 7.1%
to 19.9% of window width, in the cross-stream direction window overlap was constant and
equaled to 21.6%. Between the first and second traversing system positions, two overlapped
windows (1N, 2H) were measured for alignment. Convergence of the averaged phase-locked
velocity was ensured with 150 images taken at θ = 90◦.
0 3 4
0
wind
Figure 5.5: Schematics of measurement windows of horizontal plane
The vertical measurements covered the stream-wise range from x/R = −1.10 to x/R = 6.00
at 7 cross-stream positions, y/R = -1.0, -0.8, -0.4, 0, +0.4, +0.8, +1.0. Measurement
windows were placed at three height of z/H = 0.18, 0.50, 0.75, capturing flow behaviors in
the vertical range from z/H = −0.07 to z/H = 1.01. Figure 5.6 shows the side view and
the top view of the measurement domain. The stream-wise window overlap ranged from
19.0-43.6% of the window size. Between neighboring traversing system positions, overlapped
windows were measured to determine their relative positions. To reduce blade shadows, phase-
locked measurements were performed at θ = 0◦, with 150 images taken at each interrogation
window.
24 Experimental Set-up and Image Processing
0 2 3 4 5 6 7
0 TS4TS4TS4
4H
TS4
4I
TS4
4L
TS4
TS6TS6TS6TS6TS6TS6TS6
TS7TS7TS7TS7TS7TS7TS7
TS5TS5TS5TS5TS5TS5TS5
TS9TS9TS9
wind
x/R
z/H
(a) Side view
0 2 3 4 5 6 7
0 y/R=0
wind
x/R
y/R
(b) Top view
Figure 5.6: Schematics of measurement windows of vertical planes
5.7 Image Processing
LaVision R
Davis software was used for image processing. Data processing includes 3 major
steps: pre-processing, processing and post-processing.
In the pre-processing phase, background noise was removed by subtracting the minimum
average; a 3 × 3 Gaussian filter was used to ensure Gaussian profile shape and to reduce the
effect of peak locking; spatial disparities of image intensity were excluded by removing the
sliding background.
The images were processed with a multi-pass correlation with the minimal window size of
32 × 32 pixels2 and an overlap ratio of 50%. The cross-correlation was sped up with built-in
GPU mode of DaVis, using NVIDIA GeForce R
GTX 570 GPU (480 cores, 1405.4 GFlops in
double precision and 152.0 GB/s memory bandwidth) [4].
In the post-processing phase outliers of cross-correlation results were removed by applying
a median filter. Final results were exported as DAT-files, which includes the following scale
quantities:
• Velocity field: ux, uy, uz, |u|
• Standard deviation: σux , σuy , σuz , σ|u|
• Reynold stress: τxy, τxz, τyz, τxx, τyy, τzz
5.7 Image Processing 25
Figure 5.7 gives an example of a raw image and the corresponding pre-processed and processed
images.
(a) Raw image (b) Pre-processed image (c) Processed image
Figure 5.7: Example of raw images and processed image
Since the DaVis exported data is based on local coordinates, it is essential to stitch individual
images using global coordinates. Details of the stitching function can be found in Appendix A.
At overlap regions, the interrogation window with better image quality was used. Averaging
or image interpolation was not applied.
MSc_Thesis_Wake_Dynamics_Study_of_an_H-type_Vertical_Axis_Wind_Turbine
Chapter 6
2D Wake Dynamics
The study of 2D wake dynamics at the turbine mid-span plane focuses on 6 aspects:
• Vorticity shedding within the rotor swept area (Section 6.3)
• Blade-wake and wake-wake interaction (Section 6.4)
• Vortex dynamics along the wake boundary (Section 6.5)
• Wake circulation behind the rotor swept area (Section 6.6)
• Wake geometry (Section 6.7)
• Wake induction and velocity profiles (Section 6.8)
Experimental and simulation results are displayed in Section 6.1 and Section 6.2. Detailed
analyses based on these results are presented from Section 6.3 to Section 6.8.
6.1 Experimental Results
Measurement results of the mid-span plane are presented in Figure 6.1. Figure 6.1(a) and
Figure 6.1(b) show the contour plots of stream-wise velocity ux and cross-stream velocity
uy, respectively. Figure 6.1(c) shows the out-of-plane vorticity contour ωz. The results were
averaged over a phased-locked sampling of 150 images when blades were at the most upwind
and downwind positions. Spatial coordinates are non-dimensionalized with the turbine radius
R; velocity components are non-dimensionalized with the free-stream velocity u∞ and vorticity
is non-dimensionalized with u∞
c . The wind came from the left and the turbine rotated in the
counter-clockwise direction. Turbine blades, its trajectory, supporting struts and turbine tower
are indicated in black, while the shadow blocked areas are blanked.
Experimental results show asymmetrical wake expansion with faster expansion at the windward
side. Velocity deficit induced by energy extraction is visible in the stream-wise velocity plot.
The highest velocity gradients are observed in the most upwind and downwind blade positions,
27
28 2D Wake Dynamics
(a) Non-dimensionalized stream-wise velocity
(b) Non-dimensionalized cross-stream velocity
(c) Non-dimensionalized out-of-plane vorticity
Figure 6.1: Contour of wake velocity and wake vorticity, 2D phase-locked experimental
results
6.2 Simulation Results 29
when blade circulation is respectively maximum in positive (counter clockwise) and negative
(clockwise) signs.
Due to periodic blades motion, shed vorticity sheets follow curved trajectories. The down-
stream convection of the curved vorticity sheets form a U-shape wake geometry (Figure 6.1(c)).
Defining vorticity sheet released over one turbine period as a complete wake cycle, each wake
cycle consists of a convex upwind segment and a downwind concave segment. Wake geometry
at the mid-span xy-plane is characterized by downstream transport of convex wake segments
within the rotor swept area and downstream transport of concave wake segments behind the
rotor. Windward and leeward counter-rotating vortical structure resemble a K´arm´an vortex
street behind a cylinder. Near wake vortex roll-ups and interactions with neighboring vortices
cause vortex deformation along its convection. Further downstream, vorticity strength reduces
under diffusion and the concentrated vortex spreads to a broader area.
6.2 Simulation Results
Results presented in this section are produced by the 2D version of the in-house developed
unsteady inviscid free wake panel code. In the simulation, two airfoil are discretized using
constant sources and doublet elements, with their strengths are determined by the Kutta
condition imposed at trailing edges. The wake is modeled as a lattice of straight vortex
filament and is free to evolve under mutual inductions. Direct computation of wake induction
is accelerated by parallelization on GPU. Vortex elements are modeled as Rankine-type vortex,
representing free vortex at the outer radius (potential flow) and rigid body rotation at the
inner radius. Viscous diffusion is not accounted in the current version of the simulation code.
An Adam-Bashforth second order time scheme is used for time marching.
To investigate fully developed wake flow, the simulation ran until the convergence of integral
force parameter (e.g. CT ), which corresponded to 15 rotations with a wake extension of 25R
downstream of the turbine. The phase-locked results shown in Figure 6.2 were obtained by
averaging instantaneous flow fields of 1◦ azimuthal step over 10 turbine rotations.
6.3 In-rotor Vorticity Shedding
Vorticity shedding is a result of unsteady aerodynamics at the blade level, and is crucial to wake
development and energy extraction of an H-rotor. Examining the vorticity sheet emanating
from the blade (Figure 6.1(c)), counter-rotating vorticity sheets are clearly visible as a result
of non-sharp trailing edge.
6.3.1 Evaluation method
According to the Kelvin’s theorem [23], the magnitude of shed vorticity equals to the negative
change rate of blade bound circulation Γ. Deriving vorticity using this relation requires a
time sequence of measurements over a blade enclosed domain. Unfortunately light blockages
30 2D Wake Dynamics
(a) Normalized stream-wise velocity
(b) Normalized cross-stream velocity
(c) Normalized out-of-plane vorticity
Figure 6.2: Contour of wake velocity and wake vorticity, 2D phase-locked simulation results
6.3 In-rotor Vorticity Shedding 31
of rotor blades and other supporting structures often result in discontinuous measurement
contour.
An alternative way of determining the magnitude of the shed vorticity is by considering a finite
domain near the blade trailing edge. As shown in Figure 6.3, the vorticity ω that are released
in infinitesimal time interval δt is related to the change in bound circulation δΓ by:
δΓ = ω · (wδs′
)
Where δs′
= δsb − δsv = (ub − uv)δt
(6.1)
Where w is the local width of vorticity sheet, ub is the velocity of blade motion and uv is the
convective velocity of the vorticity sheet.
δsb
δsv
Γ
t
t+δt
Γ+δΓ
u
Figure 6.3: Change of bound circulation vs. vorticity shedding
l
d
wt
Figure 6.4: Schematics of integration window
Although the underlying principle is straightforward, the aforementioned method is difficult
in practice. First, the finite window length implicitly introduces uncertainties by summing up
the vorticity released at earlier time instances. To reduce this uncertainty, it is preferred to
minimize the window length l, and to shorten the distance between the window and the blade
trailing edge d. However, it is difficult to have the domain very close to the blade trailing
edge as blade edge laser reflections often leads to a larger masked area than the actual size of
the blade. Also an excessively small domain size cannot guarantee improved accuracy. Strong
velocity gradient confined within the thin layer of vorticity sheet makes precise capturing
difficult using standard multi-pass correlation. Assuming the wake sheet just emanated from
the blade is 1 mm wide (comparable to the thickness of blade trailing edge), and considering
the camera scale is approximately 10 pixels/mm, the resulting resolution in the direction of
wake width is only 10 vectors. This is apparently insufficient to resolve dynamic flow behavior
within the wake sheet. Second, a precise estimation of vorticity convective distance δsv is
often difficult due to the non-uniform convective velocity of vorticity sheets. A sensitivity
analysis near blade trailing edge shows that the computed circulation varies significantly with
the change of domain size, therefore it is not feasible to use this approach to the wake sheets
just released from the blade.
32 2D Wake Dynamics
6.3.2 On path tracking of wake circulation
Although the experimental resolution does not allow to resolve the vorticity release close to the
blade trailing edge, the method outlined in the last section is applicable to the wake segment
further away from the blade. Viscous diffusion and wake sheet expansion reduce sharp velocity
gradients, making the application less sensitive to the size of integration window.
0 0.02 0.04 0.06 0.08
−0.8
−0.75
−0.7
−0.65
−0.6
−0.55
Box length
ωc/u∞
Figure 6.5: Sensitivity analysis of box length
The on path circulation is computed using integration windows along the wake sheet. Each
window is orientated such that the window length l (short edge) aligns with tangential direction
of the vorticity sheet. Window lengths are non-uniform and are determined based on a similar
sensitive analysis as shown Figure 6.5. Results show that an overly small window length results
in large fluctuations due to the the uncertainty on image processing. The smallest length that
produces steady circulation is chosen as the window length. Window widths w (long edge)
vary along the wake curve. In order to eliminate the influence of background vorticity, window
width is chosen to be the local width of vorticity sheet t (Figure 6.4).
0 0.5 1 1.5 2 2.5
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
s/R
Γ/Lu∞
EXP
SIM, NACA0018
SIM, NACA0003
(a) Wake of upwind blade
0.511.522.5
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
s/R
Γ/Lu∞
EXP
SIM, NACA0018
SIM, NACA0003
(b) Wake of downwind blade
Figure 6.6: On path circulation tracking
Figure 6.6 displays the results of on path wake circulation. Horizontal axis represents the path
coordinate along the wake, with the origin defined at the blade trailing edge (Figure 6.7);
6.3 In-rotor Vorticity Shedding 33
vertical axis measures the circulation per unit length, which is non-dimensionalized by the free-
stream velocity u∞. The y-axis of Figure 6.6(a) and the x-axis of Figure 6.6(b) are reversed
for easy comparison. Comparing two simulation results shows that the wake circulation trailed
from a NACA0018 airfoil is stronger due to the larger lift slope, as expected in Section 5.3.
Figure 6.6(a) compares the measured windward wake circulation with the result of 2D simu-
lation. Simulation predicted circulations are generally higher owing to the higher lift slopes.
Agreement between the measurement and the simulation is reasonable from s/R = 0 to
s/R = 1.5. Assuming limited wake convection, this part of wake corresponds to the vorticity
shed from θ = 0◦ to θ = 90◦, where the decreasing change rate of bound circulation results
in a steady decline of wake strength towards the upwind side of the rotor. Both simulation
and experimental results observe two circulation peaks with the measured peaks lying more
upwind. The measured upwind peak (at around s/R = 1.4) is partially blocked by the tower
shadow. The positions of peak circulation are highlighted by black circles in Figure 6.7. Wake
circulation reduces dramatically downstream of the peaks due the induction of upwind wakes.
Fluctuations of the measured result might result from a number of factors including variations
of data quality, sensitivity of integration window sizes and residual background noises.
s/R
s/R
(a) Experiments
s/R
s/R
(b) Simulation, NACA0018
s/R
s/R
(c) Simulation, NACA0003
Figure 6.7: Maximum circulation position
The wake strength at the leeward side of the rotor is presented in Figure 6.6(b). The experi-
mental circulation shows an increase from the large s/R (upwind part), climbing to its peak
values (leeward part) in the middle range of s/R and drops drastically from the peak onward
(downwind part). Although the simulation predicts a similar trend, the discrepancies in detail
are different. First, the simulation predicted upwind circulation is much higher. Second, three
local peaks are are observed in the simulation results, whereas only one peak is observed in the
measured results. In contrast to the windward side, the measured leeward peak shifts down-
wind with respect to the simulation results. In average the leeward observed peak circulation
is 20% higher than the peak circulation at the windward wake.
The variation of wake circulation is determined by three factors:
• Strength of newly released wake
• Vorticity convection along the curved wake segment
• Vorticity strengthening due to wake interactions
34 2D Wake Dynamics
The convection velocity of the vorticity sheets is determined by viscous blade dragging and
local velocity field. In general vorticity convection along the path is relatively slower than
the downstream wake transport. Since wake interactions only causes local modifications of
wake circulation, the global difference of upwind circulation is most likely attributed to the
circulation difference just released from the blade. It seems that the numerical simulation
predicts the windward wake circulation reasonably well, whereas it tends to overestimate at
the leeward side. Comparing with a nominal shed vorticity distribution (Figure 3.5(b)), the
increase of circulation presented in Figure 6.6 is more abrupt. Since most circulation peaks
correspond to the positions of wake crossing, the strengthening of local vorticity field is most
likely caused by wake interactions which also shift the position of the peak circulation. Detailed
effects of wake interaction are discussed in the next section.
6.4 Blade-wake and Wake-wake Interaction
Blade-Wake Interaction (BWI) arise when a downwind turbine blade crosses the wake segments
generated by the other blades or generated by the blade itself during previous revolutions.
Wake-Wake Interaction (WWI) occur when different wake segments cross each other. For
VAWTs, BWI and WWI have two major implications:
• On blades: BWI changes the local velocity field, which alters pressure distribution and
blade loading of downwind blades.
• On wakes: BWI and WWI cause local change of wake vorticity, which triggers the roll-up
of vortical structure.
Using moving interrogation windows the phenomenon of BWI and WWI were captured. Fig-
ure 6.8(a) displays the flow field at three time instances separated by 25◦ azimuthal angles
(corresponding to 5.2 ms). Blade crossing occurs at approximately θ = 185◦ and the box
in the bottom image highlights the wake segment influenced by the interaction. Different
wake segment can be distinguished by locations and intensities. Corresponding 2D simulation
results are presented in Figure 6.8(b). Comparing the location of the boxes shows that the
measured influenced region is more downwind and more inboard of the rotor.
To understand how BWI and WWI triggers the roll-up of vortical flow structure, the on path
circulation is computed. Figure 6.9 presents the results in 3D: the vorticity contour lies on
the 2D plane; the lower curve indicates the trajectory on which the circulation is evaluated;
and the height between the upper and lower curve represents the circulation strength. The
evaluation method is similar to the one introduced in Section 6.3.1.
Results show that circulation increase at the position of BWI. At the crossing point the
vorticity is transferred from the newly released vorticity sheet to the weaker wake segment,
creating a region of higher vorticity gradients. In case of BWI, the examined wake segment of
Figure 6.9 corresponds to the weak one. After crossing, the strengthened local vorticity field
leads to a counter-clockwise flow rotation, which rolls up the wake segment into large vortical
structures (i.e. shed vortices). The mechanism of WWI is similar although the intensity of
wake interaction is lower due to more diffused vorticity content.
6.4 Blade-wake and Wake-wake Interaction 35
(a) Experimental result (b) Numerical result
Figure 6.8: Illustration of Blade-Wake Interaction
Γ/(L u∞
)=0.63
Γ/(L u∞
)=0.25
(a) Experimental result
Γ/(L u∞
)=0.84
Γ/(L u∞
)=0.42
Γ/(L u∞
)=0.61
Γ/(L u∞
)=0.23
(b) Numerical result
Figure 6.9: Vorticity strengthening due to wake-wake interaction
36 2D Wake Dynamics
The measured circulation is generally lower than the simulation prediction, coherently with the
observations in Section 6.3. Simulation predicts multiple circulation peaks induced by BWI
or WWI, while the WWI induced circulation peak is almost undetectable in the measurement
results. This difference might be explained by the effect of viscous diffusion which reduces
wake strength and intensity of wake interaction. Moreover, the effect of diffusion tends
to remove strong vorticity gradients (results from wake interaction), leading to flattened
circulation peaks.
The number of circulation peaks has substantial impacts on the vortex roll-up downwind of the
rotor. Single circulation peak triggers single vortex roll-up, which produces concentrated shed
vortex in the experimental result (Figure 6.1(c)); in contrast, multiple peaks trigger vortex
roll-up at multiple spatial locations, which gives rise to a more scattered vortical structure in
the simulation result (Figure 6.2(c)).
6.5 Vortex Dynamics Along the Wake Boundary
Shed vortices are generated by BWIs and WWIs discussed in the last section. The down-
stream convections of the vortical structure have strong influences on the wake development
at horizontal planes. Vortex trajectory defines wake geometry, and induction of shed vorticity
is crucial to wake velocity field.
6.5.1 Determination of vortex core position and peak vorticity
(a) The cuts
1.1 1.15 1.2 1.25 1.3 1.35 1.4
−0.1
0
0.1
0.2
0.3
0.4
x/R
u
y
/u
∞
(b) uy along horizontal cut
1 1.1 1.2 1.3 1.4
−0.6
−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
y/R
ux
/u∞
(c) ux along vertical cut
Figure 6.10: Velocity distribution at vortex core
Important vortex properties include vortex core position, vortex core radius, vorticity distri-
bution, and vortex circulation strength. For studying time varying vortex properties, flow
measurements at different phase angles are required. With available phase-locked results, we
exploit the periodical wake characteristic to bypass the difficulty of not having phase varying
data. Assuming wake flow repeats itself every integer numbers of turbine rotational period T,
studying consecutive released vortices can be considered equivalent to the tracking of single
vortex over a sequence of time instances separated by T. Although this approach works well
with isolated vortex, it becomes less capable when connected vortices are encountered (see for
instance Figure 6.1(c) and Figure 6.2(c)). Interference of neighboring vortices makes the anal-
ysis sensitive to the definition of vortex domain. Consequently, the following analysis would
6.5 Vortex Dynamics Along the Wake Boundary 37
not focus on domain dependent properties such as vortex core radius and circulation strength,
instead, domain independent properties such as peak vorticity and vortex core position are
discussed.
Studying peak vorticity evolution allows a quantitative measurement of the change rate of
shed vorticity. An accurate determination of peak vorticity is, however, impeded by low
particle densities at the vortex core (due to centrifugal forces). To evaluate the effect of
reduced particles, velocity distributions is plot along a vertical cut and a horizontal cut passing
through the vortex core. The orthogonal cuts and corresponding velocity profiles are displayed
in Figure 6.10. Both profiles show continuous velocity distribution in the region between
velocity peaks, implying data quality of the vortex core is not significantly affected by the
reduction of particle density (probably due to relatively low vorticity). Similar results are
observed at other vortices.
1.1 1.15 1.2 1.25 1.3 1.35 1.4
−1.5
−1
−0.5
0
0.5
1
xpeak
x/R
ωz
c/u∞
(a) ωz along horizontal cut
1 1.1 1.2 1.3 1.4
−1.5
−1
−0.5
0
0.5
ypeak
y/R
ω
z
c/u
∞
ypeak
(b) ωz along vertical cut
Figure 6.11: Vorticity distribution at vortex core
Since vorticity is the strongest at vortex core, the vortex core location is assumed identical to
the location of the peak vorticity. Two methods are used to determine the location of the peak
vorticity. The first method makes use of the vorticity plot along the cuts of Figure 6.10(a).
Although the vorticity field is more oscillating, comparable oscillation amplitude between the
vortex core and the surrounding flow region suggests that the observed fluctuations are not a
result of low data quality but are induced by flow unsteadiness. Since it is difficult to match
the observed asymmetrical vorticity field with an axial-symmetrical vortex model, the vorticity
profile is fitted with a polynomial function (dashed line). The stream-wise and cross-stream
positions of the maximum vorticity correspond to the locations of peak vorticity in the x- and
y-direction. The second method determines the vortex core position (¯x, ¯y) by using weighted
average over an iso-vorticity contour:
¯x =
xi,jωi,jdA
ωi,jdA
, ¯y =
yi,jωi,jdA
ωi,jdA
(6.2)
Where ωi,j is the vorticity of vortex particle, xi,j and yi,j are spatial coordinates of the vortex
particle and dA is the pixel size.
In order to examine the sensitivity of the cutoff limit, different cutoff limits are tested. Results
show that the difference between two methods are negligible (maximum 1.6%). For simplicity,
the first method was used.
38 2D Wake Dynamics
Peak vorticity is determined by averaging the (absolute) maximum vorticity along two orthog-
onal cuts which pass through the vortex core.
6.5.2 Vortex trajectory and vortex pitch distance
Figure 6.12 displays a schematic of shed vortex positions downstream of the rotor. Two groups
of vortices are distinguished: the 1st, 3th and 5th vortices are released from one blade and the
2nd, 4th and 6th vortices are generated by the other blade. The × signs and ⋆ signs indicate the
position of vortex core in the windward and leeward sides respectively. Non-dimensionalized
vorticity field with an absolute cutoff limit of 0.3 is added to the background for reference.
Vortices of the same ID number show one-to-one correspondences between the simulation and
measured results. As discussed in Section 6.4, the simulated vorticity field is less concentrated
due to multiple vortex roll-ups.
−1 0 1 2 3 4
−1.5
−1
−0.5
0
0.5
1
1.5
wind
x/R
y/R
ωz
c/u∞
−1.2
−0.8
−0.4
0
0.4
0.8
1.2
2 3 4 5 6
2
43
1
5 6
(a) Experimental results
−1 0 1 2 3 4
−1.5
−1
−0.5
0
0.5
1
1.5
wind
x/R
y/R
ωz
c/u∞
−1.2
−0.8
−0.4
0
0.4
0.8
1.2
21 3 4 5
21
3 4 65
(b) Simulation results
Figure 6.12: Schematics of vortex core center
Vortex convective velocity is measured by the variation of vortex pitch, which is defined
as the distance that a vortex is transported during one blade rotation. Assuming vortices
released from two blades are identical, the average distances of neighboring vortices are used
to compute vortex pitch in half rotation. The vortex pitches are plotted at the midpoints
of neighboring vortices (Figure 6.13). The measured vortex pitches are comparable at two
sides of the rotor, whereas the simulation predicted vortex pitches are larger at the windward
side. Higher wake velocity (see Section 6.8.1) yields the simulation predicted pitch distance
generally larger than the measured one.
The plot of cross-stream vortex pitch (Figure 6.13(b)) shows that the outboard vortex motion
is faster at the windward side. With increasing downstream distance, the pitch distance
reduces with the slowing down of wake expansion. Results show reasonable agreement between
the measurement and the simulation at the leeward side, while the discrepancy is large at
the windward side. Stronger windward expansion explains the larger pitch distance in the
experimental results.
6.5 Vortex Dynamics Along the Wake Boundary 39
1 1.5 2 2.5 3 3.5 4
0.4
0.5
0.6
0.7
0.8
x/R
ux
/u∞ windward, EXP
leeward, EXP
windward, SIM
leeward, SIM
(a) Stream-wise pitch
1 1.5 2 2.5 3 3.5 4
−0.2
−0.1
0
0.1
0.2
x/R
u
y
/u
∞
windward, EXP
leeward, EXP
windward, SIM
leeward, SIM
(b) Cross-wise pitch
Figure 6.13: Vortex pitch
6.5.3 Evolution of peak vorticity
The vorticity variation is determined by the combined effect of vortex roll-up and viscous. In
the near wake, the roll-up of inboard released vortex particles locally strengthens the vortex
circulation; but the roll-up does not necessarily increase the vorticity of individual vortex par-
ticle. For instance, if weaker vortex particle is rolled into the vortex core, the total circulation
will increase but the mean vorticity will decrease. In the meanwhile, strong velocity gradients
are removed by viscosity, resulting in a reduced vorticity peak and an expanded vortex core.
Vorticity is further reduced by the turbulent diffusion through flow mixing and kinetic energy
cascade. The growing magnitude of turbulent diffusion is demonstrated in the standard devi-
ation plot of Figure 6.14. As shown, the influence of turbulence is low in the near wake but
grows rapidly with increasing x/R. Comparing two sides of the rotor, the turbulence induced
uncertainty is stronger at the windward side. Although turbulence diffusion scheme is not
explicitly included in the simulation, the propagation of small numerical error resembles the
growing effect of turbulence diffusion.
Figure 6.14: RMS of absolute velocity
Figure 6.15 illustrates the variation of peak vorticity in the stream-wise direction. Negative
40 2D Wake Dynamics
windward vorticity is shown in red and the positive leeward vorticity is shown in blue. The error
bars represent the uncertainty in estimating the phase-averaged results using instantaneous
measurements (based on Figure 6.14).
The windward and leeward measured shed vorticity have comparable strength just released
from the rotor, but their downstream evolution becomes different. Vorticity of windward side
increases from x/R = 1.5 to x/R = 2.3, suggesting viscous diffusion is locally overcome by
vortex roll-up. Further downstream, the roll-up strength decreases and vorticity decays under
diffusion. Overall, peak vorticity reduces to 30% of its original strength (at x/R = 1.3) at
3.6R behind the rotor. The decay of leeward vorticity is almost linear, resulting in a total
vorticity decrease of 70% at 3.5R behind the rotor. Interestingly, decay rate downstream of
x/R = 2.3 is approximately the same between the windward and the leeward sides.
0.5 1 1.5 2 2.5 3 3.5 4
−2.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
2.5
x/R
Peakvorticityωz
c/u∞
windward, EXP
leeward, EXP
windward, SIM
leeward, SIM
Figure 6.15: Peak vorticity distribution
The differences between experimental and simulation results are large. At the windward side
the simulation predicted peak vorticity is in average 40% lower than the measured result;
whereas at the leeward side the simulation overestimates the vorticity by 15%. This discrep-
ancy might be explained by different wake expansion pattern that will be discussed in detail in
Section 6.7. In the experiment, the windward deflected wake squeezes the shear layer along the
wake boundary, resulting in an increased velocity gradient hence a locally enhanced vorticity
field; conversely, the stretched leeward shear layer causes a decrease of vorticity. Examining
Figure 6.1(a) it is clear that the windward shear layer is thinner than the leeward one. Since
the simulation predicts an opposite wake expansion pattern, the squeezing and stretching
effects are reversed.
As shown in Figure 6.15, the rate of vorticity decay are almost identical at the two sides of
the rotor. The numerical simulation underestimates the decay rate by 10%, which might be
traced back to the absence of diffusion scheme.
6.6 Wake Circulation
Due to the difficulty of specifying vortex domains, circulations of a bound vortex contour is
not computed; instead, the circulation of equally spaced sub-domains moving downstream is
6.7 Wake Geometry 41
evaluated. Circulation at windward (y/R > 0) and leeward (y/R < 0) regions are derived
separately.
Figure 6.16(a) displays the wake circulation as a function of the stream-wise position x/R.
Results show strong fluctuations near vortex cores, which reduces with increasing downstream
distance. Detailed differences between the experimental and the simulation results (e.g. the
shift of stream-wise peak circulation, etc.) are consistent with the discussion of vortex dy-
namics in the last section.
To reduce vortex induced fluctuations, accumulated circulation is plotted. In Figure 6.16(b),
the value at a certain x/R corresponds to the total circulation summed over all sub-domains
upstream of this position. Linear circulation increase are observed at both sides of the rotor,
which implies the total circulation is conserved. Results from the 2D simulation show a similar
evolution trend but it overestimates the circulation by 10%.
Summing up the windward and leeward wake circulation, the total circulation is represented
by the black curves in Figure 6.16(b). As seen, the total wake circulation is conserved and
equals to zero. Since the circulation of the complete rotor system (rotor+wake) is zero, this
observation implies the circulation of the rotor is zero.
1 1.5 2 2.5 3 3.5 4
−2.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
2.5
x/R
Γ
z
/Lu
∞
windward, EXP
leeward, EXP
windward, SIM
leeward, SIM
(a) Circulation
1 1.5 2 2.5 3 3.5 4
−1.5
−1
−0.5
0
0.5
1
1.5
x/R
Γz
/Lu∞
windward, EXP
leeward, EXP
windward+leeward, EXP
windward, SIM
leeward, SIM
windward+leeward, SIM
(b) Accumulated circulation
Figure 6.16: Wake circulation
6.7 Wake Geometry
Wake geometry defines global wake shape and provides important reference scale for wind
farm designs. Conventionally wake geometry is defined by using streamline that corresponds
to certain velocity cutoff or by using vortex trajectory [41]. Determining streamlines requires
time-averaged results which are not available to the current study, thus the following context
analyzes the horizontal wake geometry based on the convective trajectory of shed vortices.
Figure 6.17 displays the wake geometry obtained by least square fitting of vortex core positions.
For reference the streamline that corresponds to 99% free-stream velocity of time-averaged
simulation results is added to the plot. Both experimental and simulation results show the
42 2D Wake Dynamics
−1 0 1 2 3 4
−1.5
−1
−0.5
0
0.5
1
1.5
x/R
y/R
wind
Exp
SIM
SIM, 99% u
∞
streamline
Figure 6.17: Schematics of the wake geometry
horizontal wake expansion as a result of energy extraction. In comparison the experiment
observes a faster expansion at the windward side while the simulation predicts a more sym-
metrical expansion. In average the measured wake expansion angle is 8◦ at the windward side
and 5◦ at the leeward side. The corresponding simulation predicted expansion angles are 4◦
and 5◦ respectively.
Comparing with the wake geometry defined by the streamline, the geometry obtained using
vortex trajectory lies slightly inboard since vortex induction increases the stream-wise velocity
outboard of the vortex core.
The asymmetrical wake expansion is also demonstrated in the wake centerline plot of Fig-
ure 6.18(a). The measured wake centerline lies around y/R = 0.1 and moves towards the
windward side with an angle of circa 0.7◦. In contrast the simulation predicted wake center-
line, which lies close to y/R = 0, shifts windward with an angle of 0.3◦. This observation is
consistent with the asymmetric wake expansion discussed above.
The presence of the turbine tower is probably the main cause of measured asymmetrical
wake expansion. In Figure 6.1(a), tower wake is represented by the yellow expanding region
behind the turbine tower. With flow passing the rotating tower, a leeward pointing lift force
is generated; the reaction of this force deflects the tower wake to the windward side of the
rotor, which steers the expansion of turbine wake to the same side.
To analyze global wake expansion, the cross-stream wake diameter Dw is computed. As
shown in Figure 6.18(b), the measured wake diameter increases 41% at 3.5R downstream of
the turbine, whereas the wake diameter predicted by the simulation increases 35% at the same
downstream distance. Since wake expansion is a direct consequence of energy extraction, the
faster measured wake expansion is most probably attributed to the larger velocity deficit that
will be discussed in the next section.
6.8 Induction and Wake Velocity Profile 43
1.5 2 2.5 3 3.5
−0.4
−0.2
0
0.2
0.4
x/R
Wakecenterlinepositiony/R
EXP
SIM
(a) Wake centerline position
1 1.5 2 2.5 3 3.5
1
1.2
1.4
x/R
WakediameterDw
/2R
EXP
SIM
(b) Wake diameter
Figure 6.18: Wake geometry
6.8 Induction and Wake Velocity Profile
Knowledge of wake inductions and wake velocity profiles is crucial to the understanding of
wake recovery of a wind turbine. According to Kinze [25], VAWTs exhibit favorable velocity
recovery characteristics in comparison to similar sized HAWTs. In the following section,
we testify this statement by investigating stream-wise wake velocity profiles in the mid-span
plane of the turbine model. The cross-stream velocity profile is also discussed to facilitate the
understanding of asymmetrical wake expansion.
Comparing with time-averaged results the phase-locked wake velocity profiles are more im-
portant for VAWTs. First, cyclic blade loading and extreme loading conditions of downwind
rotors are determined by the instantaneous wake velocity of upwind rotors. Second, the kinetic
energy perceived by the downwind rotor is time varying. Decomposition the time dependent
flow into mean, periodic and randomly fluctuating components [21], it can be shown that
the kinetic energy of the time dependent flow is usually higher than the kinetic energy of the
mean flow.
6.8.1 Stream-wise velocity profiles
Figure 6.19(a) shows the stream-wise wake velocity profiles at 6 positions x/R =1.5, 2.0, 2.5,
3.0, 3.5, and 4.0. The results of phase-locked 2D simulation are plotted in Figure 6.19(b).
The measured stream-wise velocity profiles are non-symmetric with respect to y/R = 0. Faster
windward expansion shifts the velocity profiles to the windward side. Between y/R = −0.7
and y/R = 0.9, velocity deficits are high and velocity gradients dux
dy are low; outboard of this
region ux increases rapidly. The shapes of the phase-locked velocity profile are similar to all
stream-wise positions. Along the shed vortex trajectory, vortex induced fluctuations are visible
at the windward region from y/R = 0.5 to y/R = 1.2 and leeward region from y/R = −0.8
to y/R = −1.0. In the stream-wise direction, the influence of vortex induction diminishes and
the velocity profiles become smoother with increasing x/R.
The simulation result shows a more symmetrical profile. The maximum velocity deficit is
found at y/R = −0.2 and remains at this position with increasing downstream distance.
The peak velocity deficit, a non-dimensional number defined by 1 − uxmin /u∞, is presented
in Figure 6.20. The figure shows no indication of wake recovery until 4R downstream of the
44 2D Wake Dynamics
0 0.2 0.4 0.6 0.8 1
−1.5
−1
−0.5
0
0.5
1
1.5
u
x
/u
∞
y/R
x/R=1.5
x/R=2.0
x/R=2.5
x/R=3.0
x/R=3.5
x/R=4.0
(a) Experimental results
0 0.2 0.4 0.6 0.8 1
−1.5
−1
−0.5
0
0.5
1
1.5
u
x
/u
∞
y/R
x/R=1.5
x/R=2.0
x/R=2.5
x/R=3.0
x/R=3.5
x/R=4.0
(b) Simulation results
Figure 6.19: Phase-locked stream-wise velocity profile
turbine. The peak deficits predicted by the 2D simulation are in average 20% lower than the
experimental observed values.
1.5 2 2.5 3 3.5 4
50
60
70
80
90
100
x/R
Peakvelocitydeficit[100%]
EXP
SIM
Figure 6.20: Peak velocity deficit of horizontal mid-span plane
To understand aforementioned observations, the variation of wake velocity behind a generalized
wind turbine is plotted in Figure 6.21. Immediately behind the rotor, wake velocity decreases
as a result of energy extraction. Wake velocity reaches its minimum of (1 − 2a)u∞ at xcrit,
with a being the flow induction factor. Further downstream, flow re-energirization takes place
and the wake velocity starts to recover. The observed growing wake deficit suggests that wake
recovery has not yet started until x/R = 4.0.
The discrepancy of the measured and the simulation results might be traced to two possible
sources:
• Wake of the turbine tower
• Absence of tip vortex induction in 2D simulation
As already mentioned in Section 6.7, the presence of the rotating turbine tower is an important
cause of wake asymmetry, thus it also contributes to the asymmetrical velocity distribution
in Figure 6.19(a). Additionally, the downwind transport of the tower wake also reduces the
wake velocity along its path.
6.8 Induction and Wake Velocity Profile 45
x
ux
xcrit
Turbine
plane
(1-2a)u∞
Figure 6.21: Schematic of wake stream-wise velocity distribution
In the 2D simulations, the wake velocity at the mid-span horizontal plane is solely determined
by the induction of in-plane shed vorticity. In reality the wake velocity is also influenced by the
induction of tip vortex in the vertical direction. Tip vortex induction within the rotor swept
area has been discussed in [36], demonstrating it a main cause of stronger velocity deficit
in 3D. Behind the rotor, the situation is similar. As will be discussed in Section 7.3.1, tip
vortices are distributed along convex and concave vortex tubes as shown in Figure 6.22; the
induction of these tubes produces negative components of stream-wise induction, leading to
larger velocity deficit at the turbine mid-span plane.
Concave tip
vortex tube
Convex tip
vortex tube
H-rotor
Induction
ω
Figure 6.22: Schematics 3D induction due to tip vortex
Although wake recovery is not observed at the turbine mid-span plane, the other span-wise
positions might experience a different flow recovery rate. Wake recovery in the vertical di-
rection might also be different due to the inherent rotor asymmetry (Section 7.4). 2D wake
simulation until 16R downwind of the rotor (Figure 6.23) shows that wake expansion stops
at approximately x/R = 6, which implies wake recovery starts after this distance.
6.8.2 Cross-stream velocity profiles
Figure 6.24 shows the phase-locked velocity profiles of cross-stream velocity uy. Comparing
with the stream-wise velocity profiles, velocity fluctuations are stronger; the strongest fluctu-
ations are found at the most upstream station of x/R = 1.5 and the fluctuations magnitude
decrease with increasing x/R. Velocity fluctuations 4R behind the rotor are almost negligible.
46 2D Wake Dynamics
Figure 6.23: Simulated wake development until 16R downwind of the turbine
It is visible that the positive uy dominates the windward region with its influence further
extended to the leeward region; small regions of negative uy is only observed to the most
leeward side of the rotor. The cross-stream position of zero uy shifts windward due to non-
symmetrical wake expansion. With increasing x/R, the magnitude of cross-stream induction
reduces.
The velocity distribution is more asymmetrical in the simulation result. Zero cross-stream
velocity is observed near the turbine axial plane at y/R = 0.1. Comparing the velocity profiles
at the most downstream position of x/R = 4.0 shows that the simulation predicted uy is
lower at the windward side and is higher at the leeward side, which is consistent with the
cross-stream vortex pitch discussed in Section 6.5.2.
−0.15 −0.1 −0.05 0 0.05 0.1 0.15
−1.5
−1
−0.5
0
0.5
1
1.5
uy
/u∞
y/R
x/R=1.5
x/R=2.0
x/R=2.5
x/R=3.0
x/R=3.5
x/R=4.0
(a) Experimental results
−0.15 −0.1 −0.05 0 0.05 0.1 0.15
−1.5
−1
−0.5
0
0.5
1
1.5
uy
/u∞
y/R
x/R=1.5
x/R=2.0
x/R=2.5
x/R=3.0
x/R=3.5
x/R=4.0
(b) Simulation results
Figure 6.24: Cross-stream velocity profile
Chapter 7
3D Wake Dynamics
The release and downstream convection of tip vortices are crucial to the 3D wake development
of an H-type VAWT. Tip vortex motions in the xz-plane define wake geometry in the vertical
direction, whereas the variations of tip vorticity, among other factors, determine induction
fields in 3D. Blade-vortex interactions at the downwind blade passage cause unsteady blade
loading and are important sources of noise generation. In this chapter, we examine 3D wake
dynamics with the focus on tip vortex dynamics and non-symmetric wake distribution. The
following aspects are addressed:
• Azimuthal variation of tip vortex strength (section 7.2.1)
• Tip vortex motion in the vertical xz-plane (section 7.2.3)
• Stream-wise tip vorticity decay (section 7.2.4)
• 3D wake geometry (section 7.3)
• Stream-wise wake velocity profile in the xz-plane (section 7.4)
The experimental results and preliminary observations are presented in Section 7.1.
7.1 Experimental Results
Figure 7.1 shows the 3D phase-locked measurement results at 7 cross-stream positions of
y/R=+1.0, +0.8, +0.4, 0, -0.4, -0.8, -1.0. To minimize light blockage, velocity fields were
acquired with the blades at the most windward/leeward positions. Figure 7.1(a), Figure 7.1(b)
and Figure 7.1(c) display the contour plots of stream-wise velocity ux , cross-stream velocity uy
and span-wise velocity uz respectively, all defined according to Figure 3.1. The vorticity con-
tour ωy is presented in Figure 7.1(d). Spatial coordinates x, y and z are non-dimensionalized
using rotor radius R or blade span H; velocity and vorticity are non-dimensionalized similar
to the 2D results. Blades, struts and tower are indicated in black, and shadow-blocked areas
are blanked.
47
48 3D Wake Dynamics
Wind
Wind
Wind
Wind
Wind
Wind
Wind
(a) Non-dimensionalized stream-wise velocity
7.1 Experimental Results 49
Wind
Wind
Wind
Wind
Wind
Wind
Wind
(b) Non-dimensionalized cross-stream velocity
50 3D Wake Dynamics
Wind
Wind
Wind
Wind
Wind
Wind
Wind
(c) Non-dimensionalized vertical velocity
7.1 Experimental Results 51
Wind
Wind
Wind
Wind
Wind
Wind
Wind
(d) Non-dimensionalized cross-stream vorticity
Figure 7.1: Contour of wake velocity and wake vorticity, 3D phase-locked experimental
results
52 3D Wake Dynamics
Tip vortices are represented by the deep blue regions in Figure 7.1(d). Almost circular tip
vortices are observed close to the turbine axial plane; moving outboard tip vortex is stretched
due to increasing misalignment between the axis of the vortex core and the normal of the
measurement plane. The vorticity plot clearly shows inboard tip vortex motions near y/R = 0
and outboard tip vortex motions at two sides of the rotor. At y/R=+0.4, 0, -0.4, -0.8, the
release and roll-up of the downwind tip vortice are visible. Both upwind and the downwind tip
vortices have negative vorticity, rotating clock-wisely seen from the leeward side. Tip vortex
deforms along its downstream convection.
The previously mentioned misalignment also influences the observed cross-stream velocity
(Figure 7.1(b)). Considering a windward vortex tube at the upwind part (Figure 7.2), due to
the misalignment angle ψ, the induced velocity on the top side of the tube has a negative
y-component, and the induced velocity at the bottom side has a positive y-component. At
the windward side (y/R = +1.0, +0.8, +0.4), these two velocity components result in a blue
region on the top and an orange region at the bottom. At the leeward side, the situation is
reversed. Since the velocity component in the y-direction increases with misalignment angle,
the deepest blue and the deepest orange vortex regions are observed at the most windward and
leeward sides of the rotor. The sign of vertical velocity uz alternates due to vortex induction.
x
y
x
y
yx
z
u+y
u-y
y
z
u+y
u+y
u-y
u-y
x
xz
y
u+y
u-y
xz
y
Windward
Leeward
ψ
ψ
Figure 7.2: Illustration of the influence of misalignment angle on uy
The cross-stream velocity plot (Figure 7.1(b)) also shows the wake of vertical turbine blades
and horizontal struts. The blade wake is represented by the red vertical wake segments behind
the blade, and the struts wake corresponds to the horizontal wake region released around the
struts height (z/H = 0.3).
7.2 Tip Vortex Dynamics 53
7.2 Tip Vortex Dynamics
Before detailed discussion, some common terminologies are introduced to ease the discussion.
Vortex tube is defined as a stream tube consisting of streamlines bound in the vortex region.
The orientation of the vortex tube, or vortex tube axis, aligns with the convective velocity of
vortex tube and axial velocity is referred to as the velocity component along the vortex axis.
The cross-section plane normal to the vortex axis is referred to as vortex plane.
7.2.1 Azimuthal variation of tip vortex circulation
In SPIV measurements, the misalignment between the axis of vortex tube and the normal of
the measurement plane leads to the derived flow properties (e.g. out-of-plane vorticity) being
just the component projected in the normal direction of the measurement plane.
φV
φH
φH
φv
Vind-H
Vind-V
XZ
Y
A
B
DE
C
H
Lcosθ
Isometric view Front view
X
Z
Y L
H
Measurement plane
Normal plane
of the vortex tube
Vortex tube
Γ
ψ
Figure 7.3: Illustration of bound circulation of a skewed measurement plane
Fortunately, the misalignment does not affect the estimation of bound circulation. Consider a
straight vortex line of constant circulation Γ in the left plot of Figure 7.3. The measurement
plane, an H height L long solid line rectangular, is misaligned with the dashed vortex plane
(normal to the vortex tube) by an angle ψ around the y-axis. Misalignment around the
x-axis is zero. In the front view of the vortex tube (right plot of Figure 7.3), the rotated
measurement plane is projected onto the normal plane of the vortex tube. The circulation of
the measurement plane can be derived using following two formulas:
uθ =
Γ
2πr
Γ =
∂Ω
udl
(7.1)
The first formula computes the vortex induced velocity uθ at a distance |r| away from the
vortex core center. uθ is the tangential velocity perpendicular to the radius vector r. The
54 3D Wake Dynamics
second formula calculates the bound circulation using line integral of the velocity vector along
the contour boundary ∂Ω. On the vertical boundaries of the rotated measurement plane, the
circulation is calculated as:
AB =
L
2
cos ψ, AC =
L
2
2
cos2 ψ + y2, cos φV =
AB
AC
ΓV = 2
H
2
− H
2
VindV
(y) cos φV dy =
2Γ
2π
H
2
− H
2
L
2
cos ψ
L
2
2
cos2 ψ + y2
dy
=
Γ
π
tan−1 y
2L cos ψ
|
H
2
− H
2
=
2Γ
π
tan−1 H
L cos ψ
(7.2)
Similarly, the circulation of the horizontal boundaries can be derived as:
AD =
H
2
, AE =
H
2
2
+ y2, cos φH =
AD
AE
ΓH = 2
L
2
− L
2
VindH
(x) cos φHdx =
2Γ
2π
L
2
− L
2
H
2
cos ψ
H
2
2 + x2
dx
=
Γ
π
tan−1 x
2H
|
L
2
− L
2
cos ψ =
2Γ
π
tan−1 L cos ψ
H
(7.3)
Using the trigonometric property tan−1 x + tan−1 1
x = π
2 , we obtain the total circulation:
Γtot = ΓV + ΓH =
2Γ
π
tan−1 H
L cos ψ
+
2Γ
π
tan−1 L cos ψ
H
= Γ (7.4)
Equation 7.4 demonstrates that the measured circulation is independent of the misalignment
angle ψ. The proof on the misalignment around x-axis is similar. Using this property, vortex
strength can be evaluated.
In 3D, the strength of tip vortex is determined by the span-wise circulation gradient at blade
tips. The time varying AoA leads to the periodical change of bound circulation, hence leads
to the azimuthal variation of tip vortex strength. Since the vortex circulation is conserved, we
compare the circulation of the first recorded tip vortex (referred to as leading tip vortex) at
each cross-stream station. The upwind and downwind released tip vortex are distinguished in
the analysis.
Tip vortex circulation is integrated in the region bounded by an iso-vorticity contour. The con-
tour contains the circular (or elliptical) vortex core and the wake region on which the inboard
released vorticity rolls up (known as “vortex tail”). To remove background noise, an appropri-
ate vorticity cutoff limit is determined with a sensitivity analysis presented in Figure 7.4. The
analysis was performed on an isolated vortex in order to eliminate the influence of “vortex
tail” and other surrounding vortical structures. Result shows that the circulation approaches
to a constant only when the cutoff limit is sufficiently close to zero. The discrepancies of
using different cutoff limits are negligible given the results are normalized. Consequently an
arbitrary vorticity cutoff of 0.5 is applied consistently to all vortices.
7.2 Tip Vortex Dynamics 55
−0.1 −0.08 −0.06 −0.04 −0.02 0
0.8
0.85
0.9
0.95
1
1.05
cutoff, ω c /u
∞
Γ/Γcutoff=0
Figure 7.4: Sensitivity analysis of the background cutoff criteria
Figure 7.1(b) shows that the leading tip vortex has been convected downstream of the blade
at the recorded time, which implies the vortex was released at an earlier time instance. After
releasing, the cross-stream flow convection might have shifted the vortex location, so that the
observed tip vortex was actually produced at a different y/R, that is, a different azimuthal
position θ′. The escaping time ∆t can be derived using the distance from the leading vortex
to the blade ∆s, and the average stream-wise velocity ux:
∆t =
∆s
ux
(7.5)
Using ∆t and mean cross-stream velocity uy, the azimuthal angle at which the vortex is
actually released can be derived:
θ′
= cos−1 R cos θ − ∆y
R
Where ∆y = uy∆t
(7.6)
Where θ is the intersection azimuthal angle of the measurement planes and the blade path.
Since the accuracy of the correction is influenced by measurement misalignment and non-
uniform vortex convective velocity in the y-direction, the corrected δθ is included as horizontal
error bars.
Figure 7.5 displays azimuthal variation of the leading vortex strength. Both circulation and
mean vorticity are plotted. Mean vorticity equals to vortex circulation divided by the area of
vortex region (proportional to the number of particles). The circulation is normalized against
the strongest circulation at y/R = 0, whereas the mean vorticity is normalized against the
strongest value at y/R = −0.4. Vortex strength at the most windward position is not
plotted due to light blockage (Figure 7.1(d)). Normalized (absolute) bound circulation of 2D
simulation result is also given as the baseline for comparison. Assuming bound circulation
outboard of blade tip is zero, the absolute bound circulation is proportional to the circulation
of tip vortex. Vertical error bars indicate the uncertainty in estimating averaged results from
instantaneous measurements.
Overall the measured and simulation results show reasonable agreement at the upwind blade
passage. Both the circulation and the mean vorticity reach the peak values near θ = 90◦, and
56 3D Wake Dynamics
0 45 90 135 180 225 270 315 360
0
0.2
0.4
0.6
0.8
1
Azimuthal position θ
°
Γ/Γ
y/R=0
Upwind vortex
Downwind vortex
2D SIM
(a) Circulation
0 45 90 135 180 225 270 315 360
0
0.2
0.4
0.6
0.8
1
Azimuthal position θ
°
ω/ω
y/R=−0.4
Upwind vortex
Downwind vortex
2D SIM
(b) Mean vorticity
Figure 7.5: Azimuthal variation of tip vortex strength
decline towards the two sides of the rotor. However, the vortex circulation is stronger at the
windward part of the rotor (Figure 7.5(a)), whereas the vorticity is stronger at the leeward
side (Figure 7.5(b)). In comparison, the variation of mean vorticity shows better match with
the 2D simulation results.
Discrepancy between the total and the mean vorticity might be explained by the recorded tip
vortices that are at different vortex ages. Since the flow was measured at θ = 0◦, windward
released tip vortices (0◦ < θ < 90◦) were produced earlier than the leeward released vortices
(90◦ < θ < 180◦). In Figure 7.1(d) the windward vortex cores are larger, and the stream-wise
distances between windward leading vortices and turbine blades are greater, both indicating
the windward vortices are “older”. By the moment the flow field is recorded, there exist
a possibility that tip vortex does not reach its final conserved value, instead, the images
capture the process of vortex strengthening induced by the roll-ups. As the windward released
tip vortex is “older”, larger amount of vorticity has been transported to the vortex core,
resulting in higher total circulation. This roll-up process, however, reduces the strength of
mean vorticity due to the roll-in of weaker vortex particle. Besides, the relatively weaker
windward mean vorticity is also contributed by longer influence of viscous diffusion.
Downwind released tip vortices are much weaker due to the induction of the upwind wake.
Similar to the upwind part of the rotor, the strongest tip vortex is released near the turbine axial
plane. Based on the circulation (Figure 7.5(a)), downwind vortices have only 20% the strength
of upwind vortices, and based on the mean vorticity (Figure 7.5(b)), downwind vortices are
40% weaker. Both the circulation and the mean vorticity are higher in the measured results.
7.2.2 Determination of tip vortex core position and peak vorticity
In Section 6.5.1, we argued that the data quality near the shed vortex core is not strongly
compromised by reduced particle density. However, this is not true for tip vortex since stronger
centrifugal causes significant drop of data quality at the vortex core. Figure 7.6 shows the
vorticity plot along two orthogonal cuts through the leading tip vortex of the measurement
plane y/R = 0. Strong vorticity fluctuations near the vortex core are clear indicators of low
7.2 Tip Vortex Dynamics 57
data quality.
(a) The cuts
0.48 0.49 0.5 0.51 0.52
−12
−10
−8
−6
−4
−2
0
z/H
ω
z
c/u
∞
(b) ux along the vertical cut
−0.76 −0.74 −0.72 −0.7 −0.68 −0.66
−15
−10
−5
0
x/R
ω
z
c/u
∞
(c) uy along the horizontal cut
Figure 7.6: Vorticity distribution at the vortex core
(a) The cuts
0.48 0.49 0.5 0.51 0.52
−15
−10
−5
0
5
z/H
ω
z
c/u
∞
z
peak
(b) ux along vertical cut
−0.76 −0.74 −0.72 −0.7 −0.68 −0.66
−15
−10
−5
0
5
x/R
ω
z
c/u
∞
x
peak
(c) uy along horizontal cut
Figure 7.7: Vorticity distribution away from the vortex core
To determine the location of vortex core, two orthogonal cuts are moved away from the
vortex core until the first un-distorted vorticity profile is observed. The corresponding cuts
are referred to as the critical cuts. The vorticity peak along the critical cuts give the x- and
z-coordinates of the vortex center. Connecting the vortex center and the intersection of two
cuts gives the critical radius. If the vortex core is set as the center, and critical radius is set
as the radius, the “peak vorticity” is evaluated as the mean vorticity of the circle.
Assuming particle density is inversely proportional to vortex strength and peak vorticity decays
over time, the lowest particle density (i.e. the lowest data quality) is found at the leading tip
vortex. This means, if the vorticity of the leading vortex is reliable, the vorticity of downstream
tip vortices are also unaffected by data quality, given an identical critical circle is used. The
critical radius of the upwind released tip vortex equals to 13.4 mm, and the critical radius
of the downwind released tip vortex is smaller (1.7 mm) due to lower vortex strength. Since
axial-symmetric tip vortex is implicitly assumed in this method, the uncertainty increases with
the deformation of tip vortex.
7.2.3 Tip vortex motions in the xz-plane
Using the method outlined in the last section, the locations of tip vortex core are determined.
Tip vortex is tracked down until 4R downstream of the rotor before vortical structures become
58 3D Wake Dynamics
undetectable. In the results of Figure 7.8, upwind vortices are indicated by the blue circular
markers and downwind vortices are indicated by the red square markers.
−1 0 1 2 3 4
0
0.4
0.8
z/H
y/R=+1.0
−1 0 1 2 3 4
0
0.4
0.8
z/H
y/R=−0.4
−1 0 1 2 3 4
0
0.4
0.8
z/H
y/R=+0.8
−1 0 1 2 3 4
0
0.4
0.8
z/H
y/R=−0.8
−1 0 1 2 3 4
0
0.4
0.8
z/H
y/R=+0.4
−1 0 1 2 3 4
0
0.4
0.8z/H
y/R=−1.0
−1 0 1 2 3 4
0
0.4
0.8
x/R
z/H
y/R=0
Upwind vortices
Downwind vortices
Figure 7.8: Tip vortex trajectory in the xz-plane
As an important feature of H-rotor wakes, the mechanism of inboard tip vortex motion is
illustrated first. Considering two trailed vortex in Figure 7.9: vortex A is released from the
blade tip and vortex B is released inboard of the tip. Mutual induction between the vortices
A B dislocates them in opposite direction with respect to each other (B downward and A
upward). The height difference immediately results in an inboard motion of the tip vortex A
and an outboard motion of the trailed vortex B. Since inboard trailed vortices are usually much
weaker than the tip vortex, the global vortex convection is defined by the inboard trajectory
of the tip vortex. Moreover, the suction force between two vortices (due to low pressure) also
enhances the inboard movement of the tip vortex.
The same phenomenon has also been reported behind aircraft wings and in the near wake of
an HAWT [13][20]. The main difference with these cases relies upon the strong counteraction
of the wake expansion which dominates the vortex convection. In case of VAWT, momentum
loss in the vertical direction is compensated by the wake expansion in the horizontal plane,
allowing continuous inboard motion downwind of the rotor. According to [14][19], the inboard
tip vortex motion of an H-rotor is also contributed by the U-shape wake curvature, in which
the vortices near the turbine axial plane convect inboard due to the induction of outboard
vortices.
Within the rotor swept volume, the inboard vortex path is blocked by the turbine tower
and the horizontal struts. The effect of blockage is clearly visible at y/R=+0.4,0,-0.4,-0.8,
where the height of in rotor tip vortex stays almost unchanged. Additionally, the outboard
7.2 Tip Vortex Dynamics 59
Wind Vortex B
Vortex A
Top View Front View
Vortex AVortex B
vind-A
vind-A
vind-B
vind-B
Wing
Wind
Wing
Wind
Wing
Wind
Figure 7.9: Schematics of vortex inboard motion
movement of the vortices generated by the struts tends to push the tip vortex outboard (y/R =
+0.4, 0, −0.4 of Figure 7.1(d)). Numerical observed immediate inboard tip vortex motion
[36] was not seen in the measurements. This observation reveals an important difference
between the experiment and the numerical simulation. The presence of tower and struts
of an H-rotor prevents the immediate inboard vortex motion within the rotor swept area,
which lowers the chance of BVI and consequent detrimental loading condition at downwind
blade passage. Outboard tip vortex motions are observed near two sides of the rotor (y/R =
+1.0, +0.8, −1.0).
Behind the rotor area, the tip vortex restores its inboard motion near the turbine axial plane and
keeps moving outboard at y/R = +1.0, +0.8, −1.0. The inboard movements are the quickest
at y/R = 0 and y/R = −0.4, where the tip vortex are the strongest (see Section 7.2.1). At
these two positions, the inboard tip vortex motion results in a vertical diameter reduction of
26% at 3R downstream of the rotor. The outboard motions is faster at the windward side.
3R behind the rotor, wake diameter has increased by 50% and 22% at the windward and the
leeward sides respectively.
The outboard tip vortex motion is most likely attributed to the blockage of turbine blades,
which forces the vortex sheets lying in the blade path to move outboard. The blockage effect
is stronger at the windward side since the motion of advancing blade is opposite to the inflow
direction.
Figure 7.8 also presents the position of downwind released tip vortex. Tip vortices at y/R =
+1.0 and y/R = −1.0 are not detectable due to low vortex strength. In the vertical direction,
the relative height between upwind and downwind vortices depends on the vortex motion
within the rotor volume. If the tip vortex moves outboard, the roll-up and the downstream
convection of downwind tip vorticrs would lie beneath the trajectory of upwind vortex as been
60 3D Wake Dynamics
observed at y/R = +0.4, +0.8. Near the turbine axial plane, vortex roll-up pulls the downwind
tip vortex above the trajectory of the upwind tip vortex.
Once released from blade tip, upwind and downwind vortices start leap frogging until their
finally merging into a single vortical structure. As shown in Figure 7.10, mutual induction
gives a positive stream-wise induction to the upper vortex and a negative induction to the
lower vortex, resulting in faster advancing of the upper vortex and a consequent roll-over of
the vortex pair. The rolling motion locally enhances vortex stretching and turbulent diffusion,
which contributes to the breakdown of the coherent vortical structure. This process resembles
the vortex leap-frogging in the wake of an HAWT [9].
Figure 7.10: Illustration of vortex pair roll-over, y/R = 0
7.2.4 Stream-wise evolution of tip vorticity
In order to study stream-wise vortex decays, it is impractical to use time invariant flow proper-
ties such as vortex circulation. Here peak vorticity is used as a measure of vorticity evolution.
The determination of peak vorticity however poses two challenges. As a point property, the
magnitude of peak vorticity is influenced by the misalignment mentioned in Section 7.2.1.
Correcting the misalignment is usually difficult because the orientation of vortex tube changes
along its convection. Second, the measured vorticity at the vortex core subjects to large
uncertainty due to the reduction of particle density (Section 7.2.2).
Figure 7.11 shows the stream-wise vorticity evolution at vertical measurement planes. The
presented data is not corrected for misalignment. The results of the most windward and
leeward sides are not presented due to the large uncertainty at the vortex core. Upwind
vorticity is shown in blue and downwind vorticity is shown in red. Vertical error bars indicates
the result uncertainties. After releasing, uncertainty reduces as the data quality improves at
the vortex core. The uncertainty increases again with the growth of turbulent level 2R behind
the rotor. This increment is not visible in Figure 7.11 due to low vorticity strength.
Comparing Figure 7.11 and Figure 6.15 clearly shows that the tip vortex in the vertical planes
is much stronger than the shed vortex in the mid-span horizontal plane. The leeward released
vortex is 20-40% stronger than the windward tip vortex, which is in line with the azimthual
variation of mean vorticity as discussed in Section 7.2.1.
As for the moment of releasing, the downwind vorticity is much weaker than the upwind re-
leased vorticity. Comparing vorticity strength at the same stream-wise positions, the situation
varies from station to station. Near y/R = 0, the leading downwind tip vortex is stronger
than the upwind tip vortex convected to the same x/R, whereas at outboard stations the
7.2 Tip Vortex Dynamics 61
−1 0 1 2 3
−20
−15
−10
−5
0
ωz
c/u∞
y/R=+0.8
−1 0 1 2 3
−20
−15
−10
−5
0
ω
z
c/u
∞
y/R=−0.4
−1 0 1 2 3
−20
−15
−10
−5
0
ωz
c/u∞
y/R=+0.4
−1 0 1 2 3
−20
−15
−10
−5
0
ω
z
c/u
∞
y/R=−0.8
−1 0 1 2 3
−20
−15
−10
−5
0
x/R
ωz
c/u∞
y/R=0
Upwind vortices
Downwind vortices
Figure 7.11: Stream-wise variation of tip vorticity
0T 1T 2T 3T 4T 5T 6T
0%
25%
50%
75%
100%
ω
nT
/ω
0
y/R=+0.8
0T 1T 2T 3T 4T 5T 6T
0%
25%
50%
75%
100%
ωnT
/ω0
0T 1T 2T 3T 4T 5T 6T
0%
25%
50%
75%
100%
ω
nT
/ω
0
y/R=+0.4
0T 1T 2T 3T 4T 5T 6T
0%
25%
50%
75%
100%
ωnT
/ω0
0T 1T 2T 3T 4T 5T 6T
0%
25%
50%
75%
100%
Turbine rotational period
ωnT
/ω
0
y/R=0
Upwind vortices
Figure 7.12: Decay of tip vorticity
62 3D Wake Dynamics
downwind tip vortex is even weaker than the upwind one that has already decayed within the
rotor area.
Further downstream the variation of vorticity is strongly influenced by the roll-over of vortex
pair. At y/R = +0.4, 0, −0.4, the vortex interaction leads to a quick descend of the (stronger)
downwind tip vorticity, and a corresponding slowing down of the (weaker) upwind vortex decay.
At y/R = 0.8, −0.8, the situation is reversed. This observation shows the roll-over of vortex
pair tends to remove the vorticity difference by accelerating the vorticity decay of the stronger
vortex and reducing the decay rate of the weaker vortex.
The decay rate of upwind released tip vorticity is shown in Figure 7.12. The horizontal axis
represents vortex age that measured by turbine rotational period T; and the vertical axis
represents the relative vortex strength with respect to the newly released vortex. The first
upwind tip vortex behind the rotor area is highlighted by the red box.
The decay rate within the rotor swept volume is positively related to the strength of tip
vorticity. The strongest vorticity decay is observed at y/R = −0.4, in which the vorticity
reduces 92% at the most downwind of the rotor. Vorticity decay at y/R = 0 is slightly
slower, achieving 82% vorticity decrease within the rotor volume. In-rotor vorticity at other
positions stay around 60-70%. Stronger decay near the turbine axial plane is also contributed
by the longer vortex age (3T) in comparison to the outboard stations (2T or 1T). Behind the
rotor swept volume, vortex decay is slow and decay rate is modified by the interaction with
downwind released tip vortex.
Figure 7.12 compares the measured decay rate with a Lamb-Oseen vortex model. By definition
[18], the vorticity on a circular contour of radius r is determined by :
ω(r, t) =
Γ
rc
2π
exp
−r2
rc
2
(7.7)
Where x is the stream-wise distance, t is the vortex age, and t0 is the vortex core radius and
equals to
√
4νt. The evaluation radius r is the same as the actual radius on which “peak
vorticity” is extracted from the measured results.
Result shows a reasonable match between measured decay rate and that predicted by the
Lamb-Oseen model. Large discrepancies are observed within the rotor area at y/R = 0 and
y/R = +0.4. Comparing with the theoretical model, vorticity decay at y/R = 0 is slower
in front of the turbine tower (up to 2T) and faster behind the tower; the vortex decay at
y/R = +0.4 is constantly faster. Apart from the uncertainty induced by lower quality data
and uncorrected plane misalignments, the underlying assumptions of the Lamb-Ossen vortex
model might explain the difference. Lamb-Ossen model represents a solution to the laminar
Navier-Stokes equations, which assumes 2D axial-symmetrical vorticity distribution without
3D vortex dynamics such as vortex stretching [40]. However, the actual tip vortex might not
be completely laminar; vortex deformation makes the assumption of axial-symmetrical vortex
invalid; and 3D effect such as vortex stretching could locally modify the vorticity strength.
7.3 3D Wake Geometry 63
7.3 3D Wake Geometry
As wake geometry in the vertical xz-plane can be represented by the in-plane tip vortex motion
(Section 7.2.3), this section focuses on the wake geometry in the horizontal xy-plane and the
vertical yz-plane. Assuming continuous vortex convection, wake geometry is obtained by
connecting the spatial locations of the tip vortex core.
7.3.1 Wake geometry in the xy-plane
Figure 7.13 displays the wake geometry of the xy-plane at the blade tip height. U-shape
wake segments, similar to that at the turbine mid-span plane, are clearly visible. The U-
shape geometry is a result of periodical blade motion which trailed vortex along a curved
trajectory. Convex and concave wake segments can be distinguished. The convex segments are
released from the upwind blade passage and are obtained by connecting upwind tip vortices;
the concave segments are released from the downwind blade passage and are obtained by
connecting downwind tip vortices. For reference, the ideal turbine wake with no induction
(zero induction wake geometry) is plotted in dashed lines.
Results show that the geometry of convex wake segments are well-preserved in its downstream
transport, while the geometry of concave wake segments are clearly distorted due to the shift
of vortex position during the roll-over of vortex pairs. Comparing with the “zero-induction”
wake geometry, wake convection in the induction field is much slower. Compared to the zero
induction ideal wake, the real convection is much slower in the experimental induction field.
The pitch distance between neighbouring wake segments varies with a non-monotonic behav-
ior. Phenomena observed in simulation results such as wake stretching and wake curvature
[14] modifications are not observed in the present results.
7.3.2 Wake geometry in the yz-plane
Wake geometry in yz-plane is displayed in Figure 7.14. This plot gives the cross-section view
in the direction of the free-stream flow. Downward pointing arrow indicates the direction
of increasing x/R. Because of the vertical wake contraction near y/R = 0 and of the
asymmetrical wake expansion between the windward and the leeward rotor, a non-symmetrical
wake geometry is observed in the yz-plane. The strongest contraction is observed at the
leeward side of the turbine axial plane (y/R = −0.2), and the greatest wake expansion is seen
at the windward side. The curvature of the geometry increases further away from the rotor.
7.4 Stream-wise Wake Velocity Profiles
To understand the evolution of stream-wise velocity in the vertical measurement planes, ve-
locity profiles are extracted at 5 stream-wise positions x/R=2.0, 3.0, 4.0 5.0 and 5.9. The
results are presented in Figure 7.15.
Assuming the wake region can be measured by the area between the horizontal axis z/H =
0 and the velocity profile, the stream-wise variation of wake area shows good agreement
64 3D Wake Dynamics
−1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5
−1
−0.5
0
0.5
1
x/R
wind
y/R
(a) Convex wake segment
−1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5
−1
−0.5
0
0.5
1
x/R
wind
y/R
(b) Concave wake segment
Figure 7.13: Wake geometry in the xy-plane
wind
y/R
z/H
Downstream
direction
Figure 7.14: Wake geometry in the yz-plane
7.4 Stream-wise Wake Velocity Profiles 65
with tip vortex motions in vertical planes. At y/R = +0.4, 0, −0.4, −0.8, the wake area
reduces with the inboard tip vortex motion. Conversely, outboard tip vortex motions at
y/R = +1.0, +0.8, −1.0 lead to the expansion of low speed wake region. The observed wake
contraction is beneficial to the wind farm operation as downstream turbines perceive large
volume of undisturbed free-stream and are only exposed to wake deficit of the upwind turbine
near the mid-span.
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
z/H
y/R=+1.0
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
z/H
y/R=−0.4
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
z/H
y/R=+0.8
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
z/H
y/R=−0.8
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
z/H
y/R=+0.4
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
z/H
y/R=−1.0
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
u
x
/u
∞
z/H
y/R=0
x/R=2.0
x/R=3.0
x/R=4.0
x/R=5.0
x/R=5.9
Figure 7.15: Wake velocity profile in xy-plane
Similarly to the velocity profile of 2D mid-span plane, local velocity fluctuations are induced
along the trajectory of tip vortex. Excluding the influence of vortex induction, the peak
velocity deficit is plotted in Figure 7.16. Results show the increase of peak velocity deficit
before x/R = 4.0. The highest wake deficit is observed near y/R = 0, and the windward
deficit is greater than the leeward one.
Downstream of x/R = 4.0, the stream-wise velocity starts to recover closer to the turbine
axial plane. The quickest recoveries occur near the windward side of the turbine axial plane
at y/R = +0.4 and y/R = 0. Wake recovery at y/R = +0.8 and y/R = −0.4 is slower and
the recovery starts 5R downstream of the rotor. Velocity recovery is not observed outboard of
the rotor at y/R = +1.0, −0.8. Interestingly the peak deficit of y/R = −1.0 becomes stable
downstream of x/R = 5.0 while the velocity deficit keeps increasing inboard of this station
(y/R = −0.8).
The evolution of peak velocity deficit is influenced by a number of factors, which includes model
asymmetry, tip vortex dynamics, and the asymmetrical wake development of the horizontal
struts.
The larger windward velocity deficit is primarily due to the stronger windward blockage as the
advancing blade causes greater flow deceleration than the receding blade at the leeward side.
66 3D Wake Dynamics
2 3 4 5 6
50
60
70
80
90
x/R
Peakvelocitydeficit[100%]
y/R=+1.0
y/R=+0.8
y/R=+0.4
y/R=0
y/R=−0.4
y/R=−0.8
y/R=−1.0
Figure 7.16: Peak velocity deficit of 3D vertical planes
Figure 7.1(a) shows that the stream-wise velocity is generally higher at the leeward region.
High velocity deficit near y/R = 0 might be caused by strong induction of inboard tip
vortex motion. Since tip vortices also enhance wake recovery through flow mixing and energy
transporting across the wake boundary, the stream-wise vortex induction is overcome at around
4R downstream of the rotor, and the wake recovery begins.
The asymmetrical wake recovery speed is most likely attributed to the asymmetric wake
evolution of the horizontal struts. In Figure 7.1(d), struts wake are represented by the light
blue region around the height of z/R = 0.3. The struts wake is the greatest when the strut
is in perpendicular to the free-stream direction (i.e. y/R = +1.0 and y/R = −1.0). The
convection of the struts wake share similar features to the tip vortex motion in the vertical
direction. At the windward side, the struts wake is deflected outboard to a higher z/R,
leaving the downstream wake region from z/R = 0 to z/R = 0.3 unaffected; in contrast,
the convection of the leeward struts wake follows approximately the same height, letting the
inboard wake flow continuously influenced by the struts wake. Inspections of the velocity
profile of y/R = −0.8 and y/R = −1.0 (Figure 7.15) shows that the greatest velocity deficits
are all observed around z/H = 0.2, which fall within the influencing region of the struts wake.
Chapter 8
Uncertainty Analysis
Measurement accuracy is influenced by systematic errors and random errors. Systematic
errors are caused by system bias which results in constant deviations from the true value.
Calibration error, for instance, is a typical systematic error in PIV measurements. Random
errors are statistical fluctuations due to inherent imperfection of equipments or measurement
techniques. A typical example of random error of aerodynamic measurement results from
undesired fluctuations of flow velocity [35].
Uncertainties of instantaneous measurement arise when prescribed quantities (e.g. free-stream
velocity) or model operational conditions (e.g. rotational frequency) are not constant during
measurements. The certainty level can be improved by averaging increasing numbers of
instantaneous sample:
¯M = V +
σins
2
√
N
(8.1)
Where ¯M represents the measured averaged result, V is the true value, σins is the standard
deviation of instantaneous measurement and N is the number of samples.
A proper number of averaging samples was determined by convergence analysis at one inter-
rogation window within the rotor swept area and one window in the far wake (Figure 8.1).
The horizontal axis represents the number of samples, and the vertical axis represents the
maximum difference between the averaged results of N + 1 samples and N samples. Results
show 150 samples ensure the convergence (95% confidence level) of both in-rotor and far wake
flow regions. Therefore, 150 instantaneous measurements were taken at each interrogation
window.
The uncertainties of experimental results are grouped into four categories:
• Uncertainty due to variations of free-stream velocity
• Uncertainty due to model imperfections and changes of model operational condition
• Uncertainty in PIV measurements
• Uncertainty in PIV data processing
67
68 Uncertainty Analysis
0 50 100 150 200
0
0.5
1
1.5
2
Number of samples
Differenceofmean/u
∞
[%]
In rotor
Far wake
Figure 8.1: Convergence of the mean flow
8.1 Free-stream Velocity
In low speed incompressible flow measurements, the variation of free-stream velocity is caused
by a number of factors including model blockage, growth of tunnel shear layer, flow turbulence,
and flow temperature variation.
Since flow is free to expand in the open test section, blockage induced velocity variations are
relatively weaker. Considering 50% wake expansion at 4R behind the rotor and 16% reduction
of uniform flow area (due to the development of tunnel shear layer) at the same position, the
influence of shear layer growth is hardly detectable in the measurement range. Analysis of the
turbulent fluctuations shows a variation range from 1% in the free-stream to 25% in the vortex
inner core. Variations of flow temperature might result from system related heat sources (e.g.
tunnel fan) or the change of weather condition over the testing period. In the experiment the
flow temperature was kept within the range from 19.4◦C to 20.8◦C. Assuming the flow obeys
ideal gas law p∞ = ρRT, with p∞ being the static gas pressure in pascal, ρ the gas density
in kg/m3, T the gas temperature in Kelvin, Rconst the specific gas constant which equals
to 287.1 J/(kg·K). At 20◦C, the standard atmosphere pressure is 101325 pa and density is
1.204 kg/m3. As the windtunnel is not completely sealed, the static and the total pressure
are assumed constant, hence the change of tunnel temperature is related to a change of flow
density:
ρ =
p∞
RT
⇒ upper bound ρu =
101325
287.1 · (19.4 + 273.15)
= 1.206 kg/m3
lower bound ρl =
101325
287.1 · (20.8 + 273.15)
= 1.201 kg/m3
(8.2)
Assuming the free-stream flow is potential, the velocity variation can be derived using the
8.2 Model Uncertainty 69
Bernoulli’s equation [7]:
p∞ +
1
2
ρv2
∞ = Const
=p∞ +
1
2
ρlv2
u = p∞ +
1
2
ρuv2
l
⇒ vl =
ρ∞
ρu
v∞ = 9.25 m/s
vu =
ρ∞
ρl
v∞ = 9.27 m/s
(8.3)
Adding the influence of turbulence fluctuations, the free-stream flow varies from 9.24 m/s to
9.28 m/s.
8.2 Model Uncertainty
Model induced uncertainties are related to inherent model imperfections and change of model
operational conditions during the test.
8.2.1 Model imperfections
Inherent model imperfections result from deficiencies in the manufacturing and installation
chain, which yields turbine model deviating from its design specifications. In this experiment,
the straightness of the steel turbine tower was a constant limiting factor. During the ex-
periment it became clear that having a perfectly straight hollow tube of 3 meters is nearly
impossible, not even to mention additional bending and distortion during the transporting
and the machining process. Referring to Figure 5.3, it is easy to imagine that a non-straight
turbine tower could cause strong vibrations at the top part of the turbine. If not properly
damped, this vibration could result in a devastating structure failure. During the start-up and
slow-down phases, the tower vibration increased dramatically around the resonance range.
With the proceeding of the experiment, these repeating cycles lead to an increased tower
bending. The resulting blade motion deviated from its circular path, causing corresponding
shifts of flow phenomena (e.g. vorticity shedding) at the blade proximity.
Besides, the testing model was not entirely axial-symmetric. Due to imperfections during
the manufacturing, painting and installation processes, the dimension and weight of two
blades were different. Although the discrepancies were compensated by adjusting the tightness
of thread rods or adding compensation mass, the inherent rotor asymmetry may not be
completely removed.
Quantifying the mentioned model imperfections was uneasy, but their potential influence was
fully considered in analyses.
70 Uncertainty Analysis
8.2.2 Operational conditions
Apart from imperfections that were inherent in the turbine model, uncertainties could also be
induced by the variation of turbine model during the test.
First, the turbine rotational speed was oscillating. Since the electric motor was only capable
of keeping the velocity within a finite range (due to electric jitter), the actually motor velocity
varied over time. Overall the turbine rotational frequency oscillated between 13.25 Hz and
13.30 Hz with a mean value of 13.27 Hz. Assuming the reference time of phase locking
acquisition was fixed, the uncertainty of tip speed ratio can be determined by:
ub = ωr = 2πfr
⇒ub = 41.63 m/s ∼ 41.78 m/s
⇒λ = 4.5 − 0.005 ∼ 4.5 + 0.012
(8.4)
Thus the tip speed ratio varies by 0.27%.
Second, the measurement accuracy was strongly influenced by blade bending (Figure 8.2). Due
to centrifugal forces, turbine radius increased at the mid-span and blade tips, which coincided
with the positions of the measurement planes. Based on characteristic flow phenomena such
as blade vorticity shedding, corrected radius of 0.51 m was determined and was used to non-
dimensionalizes the 2D (at mid-span plane) and the 3D (near blade tip) results. It is worth
noting that the actual rotor radius varied with time due to azimuthal variation of aerodynamic
forces.
Tower
Struts
Deformed
Blade
Undeformed
Blade
Figure 8.2: Schematic of blade deformation (exaggerated)
Uncertainty of the triggering and timing system (Standford box) was negligible since the
accuracy of the system was in the order of picosecond.
8.3 Measurement Uncertainty 71
8.3 Measurement Uncertainty
The quality of PIV images relies on the accuracy of system alignments and calibrations. A
laser alignment tool was used to align subsystems in stream-wise and cross-stream directions.
Minor misalignment, however, might still exist due to finite beam width or misplacements of
model markers. The PIV measurement results are sensitive to two types of misalignment.
Misalignment between the calibration plate and the free-stream direction results in the projec-
tion of out-of-plane velocity component onto the measurement plane. Misalignment between
the calibration plate and the laser sheet introduces systematic error in stereoscopic vector
calculations. For all SPIV measurements, self-calibration was applied to manually adjust the
measurement plane to the middle of the laser sheet.
In the horizontal measurements, a scaling paper was used for calibration. An inspection
of corrected images in DaVis shows a displacement uncertainty of 0.5 mm. In the vertical
measurements, the calibration was performed by fitting a camera pinhole model using mul-
tiple views of a multi-level calibration plate. The calibration uncertainties of vertical plane
measurements are summarized in Table 8.1 .
Travs. sys. Fit RMS [pixel] Camera scale [pixel/mm] Displacement uncertainty [mm]
TS4 0.21 9.36 0.023
TS5 0.18 9.42 0.019
TS6 0.33 9.36 0.036
TS7 0.20 8.20 0.025
TS8 0.53 10.30 0.052
TS9 0.14 10.10 0.014
Table 8.1: Uncertainty of image calibration
Since the global flow field was stitched from individual interrogation window, the resulting
accuracy was also affected by the uncertainty of traversing system and image stitching. Owing
to the limited mechanical accuracy, the coordinate specified by the traversing system might
differ from the actual value. Possible misalignment of the traversing system and the incoming
flow direction would result in step-wise window shifts and relative rotations between neigh-
boring images. Over a large measurement distance, a small misalignment could add up to a
significant error. Linear window shifts had been corrected manually by matching character-
istic flow features at image boundaries, while image rotation had not been corrected due to
the complicity of angle determination. Since flow measurements were performed at different
times, flow field misalignment were not completely removed after the corrections.
Other factors that might potentially compromise the data quality include non-uniform parti-
cle distributions, laser reflections, camera aberrations, and unpredictable equipment motions
during the measurement. Some of the mentioned errors, such as non-uniform particle distri-
butions, can be detected and corrected during the measurement; errors like image distortions
have been accounted in the calibration process; whereas errors like flow-induced camera mo-
tions could only be visualized in the image stitching phase.
72 Uncertainty Analysis
8.4 Data Processing
The uncertainty induced by data processing is mainly related to the cross-correlation operation.
The selection of PIV processing parameters (e.g. interrogation window size, overlap ratio, etc.)
has a strong impact on image resolution and results credibility. In the pre- and post-processing
phases, additional uncertainties were introduced due to modifications (delete, interpolate, etc.)
of image data and velocity vector.
At the present measurement scales the cross correlation uncertainty had a lower impact than
other sources of uncertainties. Typical values for such an error had been reported less than
0.1 pixel for a range of window sizes down to 32×32 pixels [42]. Transforming to the velocity
scale, this is equivalent to a displacement uncertainties of ±0.010 mm in the horizontal
measurements and ±0.008 mm in the vertical measurements.
Data quality is even lower at strong vorticity regions like the vortex core. Detailed approaches
to reduce the influence of these uncertainties can be found in Chapter 6 and Chapter 7.
Chapter 9
Conclusions and Recommendations
The wake development of an H-type VAWT was investigated using two PIV set-ups: a 2C-PIV
measurements at the mid-span plane, and a SPIV measurements at 7 cross-stream vertical
planes. This study revealed important characteristics of 3D wake development and provided
high quality experimental data for code validation.
In this chapter, key observations of the measurement results are summarized in Section 9.1
and recommendations for future work are proposed in Section 9.2.
9.1 Conclusions
9.1.1 2D wake dynamics
• Circulation peaks along the windward and the leeward wake segments are induced by
wake interactions. In comparison the leeward circulation peaks are stronger. Although
the overall trends are similar, 2D simulation overestimates the wake circulation due to
the higher lift slope of the airfoil.
• Blade-Wake Interaction (BWI) and Wake-Wake Interaction (WWI) trigger the roll-ups
of vortical structure by locally strengthening wake circulation at the position of interac-
tions. Single circulation peak of the experimental result leads to concentrated vortical
structures, whereas simulation predicted multiple peaks result in scattered vortical struc-
ture downstream of the rotor.
• Shed vorticity decay is faster at the leeward side. Due to the absence of viscosity,
simulation underestimates the vorticity decay rate by 10%.
• The total wake circulation and the total rotor circulation are zero.
• The measured horizontal wake expansion is faster at the windward side. The windward
deflection of the tower wake is mainly responsible for this asymmetry. Without modeling
73
74 Conclusions and Recommendations
the tower wake, the simulation predicts a slower and more symmetrical wake expansion.
At 3.5R downstream of the rotor, the measured wake diameter increases by 41%.
• The measured stream-wise velocity profiles deflect to the windward side due to faster
windward wake expansion. In comparison the simulation predicted wake velocity is
higher. Wake recovery has not been observed until 4R downstream of the rotor, neither
in the experimental nor in the simulation results.
9.1.2 3D wake dynamics
• The strongest tip vortex is produced near the turbine axial plane. With increasing |y/R|
the strength of tip vortex reduces. Downwind released tip vortices are much weaker due
to the induction of upwind wakes.
• Tip vortex is stronger than the shed vortex in the mid-span position. Vorticity decay
within the rotor swept volume accounts for 60% - 90% of the overall decay. Behind the
rotor, vorticity decay is influenced by the interaction of downwind-upwind vortex pair.
Rate of vorticity decay is proportional to the magnitude of vorticity.
• Tip vortex motions in the xz-planes vary from station to station. Close to the turbine
axial plane, the tendency of inboard vortex motion is blocked by the turbine tower and
the struts while the inboard motion restores behind the rotor swept volume. The rate
of inboard motion is positively related to the strength of tip vortex; and the fastest
inboard motion is observed at y/R = 0 and y/R = −0.4. Weaker tip vortex strength
and stronger blade blockage result in outboard vortex motions at two sides of the rotor,
which is stronger at the windward side.
• Wake geometry in the xy-plane consists of convex wake segments (trajectory of upwind
released vortices) and concave wake segments (trajectory of downwind released vortices).
The geometry of the convex wake segments are mostly convected downstream, while
the concave wake segments are clearly distorted due to the vortex roll-over. Comparing
with the ideal case of no flow induction, the downwind transport of wake segments is
slower due to negative stream-wise inductions.
• Wake geometry in the yz-plane is non-symmetrical. The strongest wake contraction
occurs at the leeward side of y/R = −0.2, and the strongest wake expansion is observed
at the most windward side of the rotor.
• The stream-wise evolution of wake area is consistent with the tip vortex motion in
the vertical direction. Wake contraction inboard of the rotor results in larger volumes
of energetic inflow, which benefits the efficiency of downwind turbines. Wake deficits
increase until x/R = 4.0 and starts to recover afterwards near the turbine axial plane.
Wake recoveries are the quickest at y/R = +0.4 and y/R = 0, while recoveries at the
most windward and the most leeward positions are not observed until 5.9R downstream
of the rotor. Asymmetrical velocity distribution might be explained by inherent model
asymmetry, inboard tip vortex motion, and asymmetrical development of the struts
wake.
9.2 Recommendations 75
9.2 Recommendations
The present study observes the wake recovery in the vertical direction, while the wake recovery
in the horizontal mid-span plane is not observed. To deepen the understanding of wake
recovery of an H-rotor, future experiments are encouraged to extend the measurement range
further downstream. The horizontal measurement shows asymmetrical wake development
at the turbine mid-span position. The understanding of horizontal wake evolution can be
improved by examining other span-wise planes. Since vortical structure has already been
undetectable at 6R downstream of the rotor, uncorrelated sampling is suggested instead of
phase-locked measurement. Detailed flow analyses on cross wake momentum transport and
vortex induced flow mixing could help to understand how vortex evolution influences wake
recovery. In particular, the roll-over of the upwind-downwind vortex pair deserves an in-depth
study of its role in the process of vortex breakdown.
Since the presence of tower and horizontal struts are crucial to the development of turbine
wake, it is interesting to examine the optimal turbine configurations which not only maximizes
the power output but also yields favorable wake characteristics.
The resolution of flow fields can be improved by measuring at different blade azimuthal
positions. Tests at different tip speed ratios could uncover the variation of wake development
with change of rotational speed. The reconstruction of 3D tip vortex dynamics will benefit
from increasing numbers of vertical measurement planes in the cross-stream direction.
At the numerical side, comparing 2D experimental results with the 3D simulation results
will help to understand 3D induction effect at the mid-span plane. In order to reproduce
the asymmetrical wake development, it is suggested to model the effect of turbine tower and
horizontal struts in simulations. And the experimental results can also be used to validate
higher order simulation code (e.g. the hybrid code).
MSc_Thesis_Wake_Dynamics_Study_of_an_H-type_Vertical_Axis_Wind_Turbine
References
[1] Davis 7.2 - flowmaster product manual, 2007.
[2] Open jet facility - focus of the faculty of aerospace engineering. http://www.lr.
tudelft.nl/en/research/blinde-paginas/open-jet-facility, 2010.
[3] Open jet facility (ojf). http://www.lr.tudelft.nl/en/organisation/
departments-and-chairs/aerodynamics-and-wind-energy/wind-energy/
facilities/open-jet-facility, 2010.
[4] Geforce gtx 570 - specifications. http://www.geforce.com/hardware/
desktop-gpus/geforce-gtx-570, 2012.
[5] Wind power makcan. http://makcan.ca/solutions/energy-solutions/
renewable-energy/wind-power, 2012.
[6] R.E. Altenhofen. Rectification. Manual of Photogrammetry (American Society of Pho-
togrammetry, Washington, DC, 1952), page 457, 1952.
[7] J.D. Anderson. Fundamentals of aerodynamics, volume 2. McGraw-Hill New York, 2001.
[8] M.P. Arroyo and C.A. Greated. Stereoscopic particle image velocimetry. Measurement
Science and Technology, 2(12):1181, 1999.
[9] D. Baldacchino. Horizontal axis wind turbine (hawt) wake stability investigations. Mas-
ter’s thesis, Delft University of Technology, 2012.
[10] M.T. Brahimi, A. Allet, and I. Paraschivoiu. Aerodynamic analysis models for vertical-axis
wind turbines. International Journal of Rotating Machinery, 2(1):15–21, 1995.
[11] P.W. Carlin, A.S. Laxson, and E.B. Muljadi. The history and state of the art of variable-
speed wind turbine technology. Wind Energy, 6(2):129–159, 2003.
[12] J.O. Dabiri. Potential order-of-magnitude enhancement of wind farm power density via
counter-rotating vertical-axis wind turbine arrays. arXiv preprint arXiv:1010.3656, 2010.
77
78 References
[13] W.J. Devenport, M.C. Rife, S.I Liapis, and G.J. Follin. The structure and development
of a wing-tip vortex. Journal of Fluid Mechanics, 312(67):106, 1996.
[14] K.R. Dixon. The near wake structure of a vertical axis wind turbine. Master’s thesis,
Delft University of Technology, 2008.
[15] G.E. Elsinga, F. Scarano, B. Wieneke, and B.W. Van Oudheusden. Tomographic particle
image velocimetry. Experiments in Fluids, 41(6):933–947, 2006.
[16] S. Eriksson, H. Bernhoff, and M. Leijon. Evaluation of different turbine concepts for
wind power. Renewable and Sustainable Energy Reviews, 12(5):1419–1434, 2008.
[17] P. Gipe. Flowind: The world’s most successful vawt (vertical axis wind
turbine). http://www.wind-works.org/cms/index.php?id=43&tx_ttnews%5Btt_
news%5D=2194&cHash=d1b21f3bd1f35d9e4804f1598b27bd86, 2012.
[18] S. Green. Fluid Vortices: Fluid Mechanics and Its Applications, volume 30. Springer,
1995.
[19] C. Hofemann, C.S. Ferreira, K. Dixon, G. van Bussel, G. van Kuik, and F. Scarano. 3d
stereo piv study of tip vortex evolution on a vawt. Proceedings of EWEC, Brussels, 2008.
[20] D. Hu and Z. Du. Near wake of a model horizontal-axis wind turbine. Journal of
Hydrodynamics, Ser. B, 21(2):285–291, 2009.
[21] A.K.M.F. Hussain and W.C. Reynolds. The mechanics of an organized wave in turbulent
shear flow. J. Fluid Mech, 41(2):241–258, 1970.
[22] M. Islam, D.S.K. Ting, and A. Fartaj. Aerodynamic models for darrieus-type straight-
bladed vertical axis wind turbines. Renewable and Sustainable Energy Reviews,
12(4):1087–1109, 2008.
[23] J. Katz and A. Plotkin. Low speed aerodynamics, volume 13. Cambridge University
Press, 2001.
[24] K. Kiger. Introduction of particle image velocimetry. Lecture slides.
[25] M. Kinzel, Q. Mulligan, and J.O. Dabiri. Energy exchange in an array of vertical-axis
wind turbines. Journal of Turbulence, 13(1), 2012.
[26] M. Marini, A. Massardo, and A. Satta. Performance of vertical axis wind turbines with
different shapes. Journal of Wind Engineering and Industrial Aerodynamics, 39(1):83–93,
1992.
[27] I.D. Mays and C.A. Morgan. The 500 kw vawt 850 demonstration project. In Proceedings
1989 European wind energy conference, Glasgow, Scotland, pages 1049–53, 1989.
[28] I. Paraschivoiu. Double-multiple streamtube model for studying vertical-axis wind tur-
bines. Journal of propulsion and power, 4(4):370–377, 1988.
[29] I. Paraschivoiu. Wind turbine design: with emphasis on Darrieus concept. Montreal:
Polytechnic International Press, 2002.
[30] S. Peace. Another approach to wind-vertical-axis turbines may avoid the limitations of
today’s standard propeller-like machines. Mechanical Engineering, 126(6):28–31, 2004.
References 79
[31] A.K. Prasad. Stereoscopic particle image velocimetry. Experiments in fluids, 29(2):103–
116, 2000.
[32] M. Raffel, C.E. Willert, and J. Kompenhans. Particle image velocimetry: a practical
guide. Springer Verlag, 1998.
[33] D. Ragni, B.W. Van Oudheusden, and F. Scarano. 3d pressure imaging of an aircraft pro-
peller blade-tip flow by phase-locked stereoscopic piv. Experiments in fluids, 52(2):463–
477, 2012.
[34] S.J. Savonius. The s-rotor and its applications. Mech. Eng, 53:333–338, 1931.
[35] F. Scarano. Lecture notes - course experimental aerodynamics. University Lecture, 2012.
[36] C.J. Sim˜ao Ferreira. The near wake of the VAWT, 2D and 3D views of the VAWT aerody-
namics. PhD thesis, PhD Thesis, Delft University of Technology, Delft, the Nederlands,
2009.
[37] C.J. Sim˜ao Ferreira, K.R. Dixon, C. Hofemann, G.A.M. Van Kuik, and G.J.W. Van Bussel.
The vawt in skew: stereo-piv and vortex modeling. 2009.
[38] CJ Sim˜ao Ferreira, A. Van Zuijlen, H. Bijl, G. Van Bussel, and G. Van Kuik. Simulating
dynamic stall in a two-dimensional vertical-axis wind turbine: verification and validation
with particle image velocimetry data. Wind Energy, 13(1):1–17, 2009.
[39] D.R. Smith. The wind farms of the altamont pass area. Annual review of energy,
12(1):145–183, 1987.
[40] H. Tryggeson. Analytical Vortex Solutions to the Navier-Stokes Equation. PhD thesis,
PhD Thesis, V¨aj¨o University, V¨aj¨o, Sweden, 2007.
[41] L.J. Vermeer, J.N. Sørensen, and A. Crespo. Wind turbine wake aerodynamics. Progress
in aerospace sciences, 39(6):467–510, 2003.
[42] J. Westerweel. Analysis of piv interrogation with low-pixel resolution. In SPIE’s 1993
International Symposium on Optics, Imaging, and Instrumentation, pages 624–635. In-
ternational Society for Optics and Photonics, 1993.
[43] W. Zang and A.K. Prasad. Performance evaluation of a scheimpflug stereocamera for
particle image velocimetry. Applied optics, 36(33):8738–8744, 1997.
MSc_Thesis_Wake_Dynamics_Study_of_an_H-type_Vertical_Axis_Wind_Turbine
Appendix A
Image stitching Function
The image stitching function consists of three major steps: standard pattern transformation,
overlap detection and area partition, and image stitching. In the first step, the relative
image position is detected and converted to three standard alignment patterns as shown in
Figure A.1. This step eliminates the need of treating different alignment patterns separately.
W2
W1
W2W1 W2
W1
Standard pattern 1:
corner-to-corner
Standard pattern 2:
side-by-side
Standard pattern 3: containing
Figure A.1: Standard window alignment patterns
Image conversion is performed with basic operations such as matrix swap, rotation, matrix
mirroring. Table A.1 gives an overview of the matrix operations corresponding to the window
patterns displayed in Figure A.2. Each operation is flagged and reverse operations at the end
of the stitching module converts the stitched windows to the original pattern.
In the second step, the row and column indices of the overlapped area are determined by
comparing the leading/ending coordinates. Using detected overlap, the combined rectangular
windows are partitioned into sub-windows as shown in Figure A.3. Areas that belongs to
neither windows are filled with NaN. If no overlap exists, NaN will be filled across the empty
region between two windows.
In Figure A.3, dash line represents the boundary of sub-windows, OV and NOV stand for
overlapped and non-overlapped windows, subscript l(eft), r(ight), b(ottom) and t(op) indicate
the relative position with respect to the overlapped sub-window. The smoothing direction is
81
82 Image stitching Function
W2
W1
W1
W2
W2
W1
W2
W2
W2
W2
W1 W1W2 W2 W1 W1 W2
W1
W1
W2
W2
W1
W1
W2
W2 W1 W2W1
pattern 1 pattern 2 pattern 3 pattern 4
pattern 5 pattern 6 pattern 7 pattern 8
pattern 9 pattern 10 pattern 11
pattern 13 pattern 14
pattern 12
Figure A.2: Possible window alignment patterns
W2W1
W2
W1
OV_l
OV_l
OV_t
OV_t
OV
OV
OV_b OV_b
OV_r
OV_r
NOV NOV
NOV
NOVNaN
NaN NaN
NaN
Figure A.3: Standard window alignment patterns
83
Pattern Operation
corner-to-corner window arrangement
1 -
2 swap w1 and w2
3 mirror w1 and w2 around y=0
4 swap w1 and w2, then mirror both around y=0
side-by-side window arrangement
5 -
6 swap w1 and w2
7 mirror w1 and w2 around x=0
8 swap w1 and w2, then mirror both around x=0
9 rotate w1 and w2 90◦ clockwise
10 swap w1 and w2, then rotate 90◦ clockwise
11 rotate w1 and w2 90◦ counter-clockwise
12 swap w1 and w2, then rotate 90◦ counter-clockwise
containing window arrangement
13 -
14 swap w1 and w2
Table A.1: Converting operation to standard window alignment pattern
determined automatically: if the number of overlapped (horizontal) row is greater than the
number of overlapped (vertical) column, smoothing will be performed in the x-direction, and
vice versa. At overlap regions, simple stitching or linear interpolations can be chosen. Simple
stitching uses the data of one window as the data of the overlapped region in the combined
image. Linear interpolation uses the boundary value at the overlap and non-overlap regions;
the results are added to the mean value of two windows. The effect of smoothening could be
improved with higher order interpolation, but this is left for future work.
MSc_Thesis_Wake_Dynamics_Study_of_an_H-type_Vertical_Axis_Wind_Turbine

More Related Content

PDF
grDirkEkelschotFINAL__2_
PDF
ubc_2015_november_angus_edward
PDF
Ali-Dissertation-5June2015
PDF
20120112-Dissertation7-2
PDF
Chang_gsas.harvard.inactive_0084L_11709
PDF
Richard fitzpatrick
PDF
[Sapienza] Development of the Flight Dynamics Model of a Flying Wing Aircraft
PDF
Stabilitynotes1
grDirkEkelschotFINAL__2_
ubc_2015_november_angus_edward
Ali-Dissertation-5June2015
20120112-Dissertation7-2
Chang_gsas.harvard.inactive_0084L_11709
Richard fitzpatrick
[Sapienza] Development of the Flight Dynamics Model of a Flying Wing Aircraft
Stabilitynotes1

What's hot (19)

PDF
BenThesis
PDF
Sarda_uta_2502M_12076
PDF
CDR General Report
PDF
Efficient Model-based 3D Tracking by Using Direct Image Registration
PDF
A Three Dimensional Vortex Particle-Panel Code For Modeling Prope
PDF
The Cellular Automaton Interpretation of Quantum Mechanics
PDF
Jung.Rapport
PDF
feilner0201
PDF
978 1-4615-6311-2 fm
PDF
Anwar_Shahed_MSc_2015
PDF
Durlav Mudbhari - MSME Thesis
PDF
Seismic Tomograhy for Concrete Investigation
PDF
Antenna study and design for ultra wideband communications apps
PDF
Lecture notes-in-structural-engineering-analysis-design
PDF
MastersThesis
PDF
phd-thesis
PDF
Efficiency Optimization of Realtime GPU Raytracing in Modeling of Car2Car Com...
BenThesis
Sarda_uta_2502M_12076
CDR General Report
Efficient Model-based 3D Tracking by Using Direct Image Registration
A Three Dimensional Vortex Particle-Panel Code For Modeling Prope
The Cellular Automaton Interpretation of Quantum Mechanics
Jung.Rapport
feilner0201
978 1-4615-6311-2 fm
Anwar_Shahed_MSc_2015
Durlav Mudbhari - MSME Thesis
Seismic Tomograhy for Concrete Investigation
Antenna study and design for ultra wideband communications apps
Lecture notes-in-structural-engineering-analysis-design
MastersThesis
phd-thesis
Efficiency Optimization of Realtime GPU Raytracing in Modeling of Car2Car Com...
Ad

Viewers also liked (20)

PDF
Vortex lattice modelling of winglets on wind turbine blades
PPTX
marco aleman visual resume
PDF
Parables of the Seekers of Forgiveness
PDF
performance evaluation of mhd renewable energy source for electric power gene...
PPT
Ingeniería jp&ca
DOCX
La ubicación del problema en que y para que intervenir
DOCX
6. Chapters
KEY
BUG July 2011 Microtalks
PPTX
Bladeless wind mill ppt BY KADIYAM SUNEEL
PPTX
Bladeless wind turbine
PDF
Seminar Report on MHD (Magneto Hydro Dynamics)
PPT
Tesla bladeless turbine
PDF
Case Study of MHD Generator for Power Generation and High Speed Propulsion
PPT
Magneto hydro-dynamic-power-generation-mhd
PPTX
Unidad educativa municipal
PDF
Comercio interior del libro en España 2010
PPS
PPT
Fisica
PPT
Proxecto Educativo
Vortex lattice modelling of winglets on wind turbine blades
marco aleman visual resume
Parables of the Seekers of Forgiveness
performance evaluation of mhd renewable energy source for electric power gene...
Ingeniería jp&ca
La ubicación del problema en que y para que intervenir
6. Chapters
BUG July 2011 Microtalks
Bladeless wind mill ppt BY KADIYAM SUNEEL
Bladeless wind turbine
Seminar Report on MHD (Magneto Hydro Dynamics)
Tesla bladeless turbine
Case Study of MHD Generator for Power Generation and High Speed Propulsion
Magneto hydro-dynamic-power-generation-mhd
Unidad educativa municipal
Comercio interior del libro en España 2010
Fisica
Proxecto Educativo
Ad

Similar to MSc_Thesis_Wake_Dynamics_Study_of_an_H-type_Vertical_Axis_Wind_Turbine (20)

PDF
aerodynamic models for darrieus type
PPTX
Numerical Investigation of the Aerodynamic Characteristics for a Darrieus H-t...
PDF
Final course project report
PDF
IRJET- Investigation of Effects of Trailing Edge Geometry on Vertical Axis Wi...
PDF
Final Report
PDF
Performance Analysis of Giromill Vertical Axis Wind Turbine with NACA 63618 A...
PDF
Portable Small-Scale Vertical Axis Wind Turbine with Pitch Angle Control Syst...
PDF
5_ISMTII2015_1281_VAWT_ShiehHsiao_et.al_manuscript_15Juli2015_vorlage
PDF
IRJET- Design and Analysis of Vertical Axis Wind Turbine
PDF
MSc Thesis - Jaguar Land Rover
PDF
Project Report on 'Modulation of Vertical Axis Wind Turbine'
PDF
Christopher Kelley - National Rotor Testbed Design
PDF
Experimental Investigation of Optimal Aerodynamics of a Flying Wing UAV(Link)
PDF
DESIGN AND ANALYSIS OF BLADELESS WIND TURBINE
PDF
2014 Sandia Wind Turbine Blade Workshop- Maniaci
PDF
Power Generation through the Wind Energy Using Convergent Nozzle
PDF
A Study of Wind Turbine Blade Power Enhancement Using Aerodynamic Properties
DOCX
scopus vertical Axis wind power generation
PDF
Design Development and Analytical Process of Small Vertical Axis Wind Turbine
PDF
Lp3420942103
aerodynamic models for darrieus type
Numerical Investigation of the Aerodynamic Characteristics for a Darrieus H-t...
Final course project report
IRJET- Investigation of Effects of Trailing Edge Geometry on Vertical Axis Wi...
Final Report
Performance Analysis of Giromill Vertical Axis Wind Turbine with NACA 63618 A...
Portable Small-Scale Vertical Axis Wind Turbine with Pitch Angle Control Syst...
5_ISMTII2015_1281_VAWT_ShiehHsiao_et.al_manuscript_15Juli2015_vorlage
IRJET- Design and Analysis of Vertical Axis Wind Turbine
MSc Thesis - Jaguar Land Rover
Project Report on 'Modulation of Vertical Axis Wind Turbine'
Christopher Kelley - National Rotor Testbed Design
Experimental Investigation of Optimal Aerodynamics of a Flying Wing UAV(Link)
DESIGN AND ANALYSIS OF BLADELESS WIND TURBINE
2014 Sandia Wind Turbine Blade Workshop- Maniaci
Power Generation through the Wind Energy Using Convergent Nozzle
A Study of Wind Turbine Blade Power Enhancement Using Aerodynamic Properties
scopus vertical Axis wind power generation
Design Development and Analytical Process of Small Vertical Axis Wind Turbine
Lp3420942103

MSc_Thesis_Wake_Dynamics_Study_of_an_H-type_Vertical_Axis_Wind_Turbine

  • 1. Master of Science Thesis Wake Dynamics Study of an H-type Vertical Axis Wind Turbine Chenguang He August 12, 2013 Faculty of Aerospace Engineering · Delft University of Technology
  • 3. Wake Dynamics Study of an H-type Vertical Axis Wind Turbine Master of Science Thesis For obtaining the degree of Master of Science in Aerospace Engineering at Delft University of Technology Chenguang He August 12, 2013 Faculty of Aerospace Engineering · Delft University of Technology
  • 4. Copyright c Chenguang He All rights reserved.
  • 5. Delft University Of Technology Department Of Aerodynamics and Wind Energy The undersigned hereby certify that they have read and recommend to the Faculty of Aerospace Engineering for acceptance a thesis entitled “Wake Dynamics Study of an H-type Vertical Axis Wind Turbine” by Chenguang He in partial fulfillment of the requirements for the degree of Master of Science. Dated: August 12, 2013 Head of department: Prof. dr. G.J.W. van Bussel Supervisor: Dr. ir. C.J. Simao Ferreira Reader: Dr. Daniele Ragni Reader: Dr. Marios Kotsonis
  • 7. Summary Recent developments in wind energy have identified vertical axis wind turbines as a favored candidate for megawatt-scale offshore systems. Compared with the direct horizontal axis competitors they poss higher potentials for scalability and mechanical simplicity. The wake dynamics of an H-type vertical axis wind turbine is investigated using Particle Image Velocimetry (PIV). The experiments are conducted in an open jet wind tunnel with a turbine model of 1 m diameter constituted of 2 straight blades generated from a NACA0018. The turbine model is operated at a tip speed ratio of 4.5 and at a maximum chord Reynolds of 210,000. Two-component planar PIV measurements at the mid-span plane focus on vorticity shedding and horizontal wake expansion. Stereoscopic PIV measurements at 7 cross-stream vertical planes are performed to study tip vortex dynamics and evolution of 3D wake structures. Measurement at the turbine mid-span plane shows that the roll-up of shed vortex is triggered by wake interactions. Vorticity decay is asymmetrical with the faster decay rate at the leeward side. The faster windward wake expansion is attributed to the windward deflection of the tower wake. Wake recovery has not been observed in the horizontal measurement plane up to 4R downstream of the rotor. Experimental results on the vertical planes show that the tip vortex is stronger than the shed vortex in the horizontal plane. The strongest tip vortex is produced near the turbine axial plane (y/R = 0), and the in-rotor vorticity decay accounts for 60% - 90% of the overall decay. Near y/R = 0, tip vortices move inboard behind the rotor, whereas the turbine tower and the horizontal struts obstruct the inboard motion within the rotor swept volume. The rate of inboard motion is proportional to the vorticity strength. Due to weak vortex strength and strong blade blockage, tip vortices move outboard at two sides of the rotor primarily towards the windward side. Roll-over of vortex pairs contributes to the breakdown of vortical structure behind the rotor. Vertical wake recovery begins 4R downstream of the rotor, and the fastest recovery is observed near y/R = 0. v
  • 9. Acknowledgements Hereby, I would express my sincere gratitude to my supervisor Dr. Carlos Sim˜ao Ferreira for your continuous support and encouragement throughout the project. Also I would like to thank my daily supervisors Dr. Daniele Ragni, Giuseppe Tescione and Dr. Artur Palha. Your guidances and supports were vital to the success of this project. Thanks Prof. Fulvio Scarano for your valuable suggestions on my thesis work. I would also like to thank the members of my graduation committee, Prof. Gerard van Bussel and Dr. Marios Kotsonis for your helpful advice and suggestions in general. Thanks to my office roommates, Chidam, Lento, Mark, Rob for the laugh we shared in the past ten months. And thanks to all my Chinese and International friends for being the surrogate family during my five years of stay in Holland, and making me feel at home thousands miles away from China. Finally a sincere thanks to my girlfriend Nuo, and my families. Without your understanding, great patience and endless love I would not be able to accomplish all these. vii
  • 11. Contents List of Figures xii List of Tables xiii Nomenclature xv 1 Project Outline 1 2 Vertical Axis Wind Turbine - A Brief Introduction 3 2.1 VAWT vs. HAWT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3 Fundamental Aspects of VAWT Wake Aerodynamics 7 3.1 Definitions and Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Generation of Vorticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Vorticity and Energy Considerations . . . . . . . . . . . . . . . . . . . . . . 11 4 Particle Image Velocimetry 13 4.1 Fundamentals of 2C-PIV . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.2 Stereoscopic PIV (SPIV) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.2.1 Working principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.2.2 Translational and rotational configurations . . . . . . . . . . . . . . . 16 4.2.3 Image reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5 Experimental Set-up and Image Processing 19 5.1 Wind Tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 5.2 Turbine Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5.3 Operational Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 5.4 PIV Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 5.5 PIV Set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 5.6 System of Reference and Field of View . . . . . . . . . . . . . . . . . . . . . 23 5.7 Image Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 ix
  • 12. x Contents 6 2D Wake Dynamics 27 6.1 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 6.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 6.3 In-rotor Vorticity Shedding . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 6.3.1 Evaluation method . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 6.3.2 On path tracking of wake circulation . . . . . . . . . . . . . . . . . . 32 6.4 Blade-wake and Wake-wake Interaction . . . . . . . . . . . . . . . . . . . . . 34 6.5 Vortex Dynamics Along the Wake Boundary . . . . . . . . . . . . . . . . . . 36 6.5.1 Determination of vortex core position and peak vorticity . . . . . . . 36 6.5.2 Vortex trajectory and vortex pitch distance . . . . . . . . . . . . . . . 38 6.5.3 Evolution of peak vorticity . . . . . . . . . . . . . . . . . . . . . . . 39 6.6 Wake Circulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 6.7 Wake Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 6.8 Induction and Wake Velocity Profile . . . . . . . . . . . . . . . . . . . . . . 43 6.8.1 Stream-wise velocity profiles . . . . . . . . . . . . . . . . . . . . . . 43 6.8.2 Cross-stream velocity profiles . . . . . . . . . . . . . . . . . . . . . . 45 7 3D Wake Dynamics 47 7.1 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 7.2 Tip Vortex Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 7.2.1 Azimuthal variation of tip vortex circulation . . . . . . . . . . . . . . 53 7.2.2 Determination of tip vortex core position and peak vorticity . . . . . 56 7.2.3 Tip vortex motions in the xz-plane . . . . . . . . . . . . . . . . . . . 57 7.2.4 Stream-wise evolution of tip vorticity . . . . . . . . . . . . . . . . . . 60 7.3 3D Wake Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 7.3.1 Wake geometry in the xy-plane . . . . . . . . . . . . . . . . . . . . . 63 7.3.2 Wake geometry in the yz-plane . . . . . . . . . . . . . . . . . . . . . 63 7.4 Stream-wise Wake Velocity Profiles . . . . . . . . . . . . . . . . . . . . . . . 63 8 Uncertainty Analysis 67 8.1 Free-stream Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 8.2 Model Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 8.2.1 Model imperfections . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 8.2.2 Operational conditions . . . . . . . . . . . . . . . . . . . . . . . . . 70 8.3 Measurement Uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 8.4 Data Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 9 Conclusions and Recommendations 73 9.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 9.1.1 2D wake dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 9.1.2 3D wake dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 9.2 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 References 77 A Image stitching Function 81
  • 13. List of Figures 2.1 Examples of VAWT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3.1 Schematic of 2D VAWT division . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 CP -TSR diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.3 Free body diagram of inflow vector . . . . . . . . . . . . . . . . . . . . . . . 9 3.4 2D characteristics, without induction . . . . . . . . . . . . . . . . . . . . . . 10 3.5 2D characteristics, with induction . . . . . . . . . . . . . . . . . . . . . . . 11 3.6 Schematic of tip vortex release along blade trajectory . . . . . . . . . . . . . 12 3.7 Schematics of wake vortex sheets . . . . . . . . . . . . . . . . . . . . . . . . 12 4.1 Schematics of PIV set-up [35] . . . . . . . . . . . . . . . . . . . . . . . . . . 14 4.2 Multi-pass vs. single-pass . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.3 Schematics of stereo camera arrangement . . . . . . . . . . . . . . . . . . . 16 4.4 Configurations PIV systems [31] . . . . . . . . . . . . . . . . . . . . . . . . 17 4.5 Effect of Scheimpflug adapter [1] . . . . . . . . . . . . . . . . . . . . . . . . 17 4.6 Multi-level Calibration Plate [32] . . . . . . . . . . . . . . . . . . . . . . . . 18 5.1 Schematics of OJF [3] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 5.2 Lift characteristics of the airfoil . . . . . . . . . . . . . . . . . . . . . . . . . 20 5.3 Configuration of horizontal measurements . . . . . . . . . . . . . . . . . . . 22 5.4 Configuration of vertical measurements . . . . . . . . . . . . . . . . . . . . . 22 5.5 Schematics of measurement windows of horizontal plane . . . . . . . . . . . 23 5.6 Schematics of measurement windows of vertical planes . . . . . . . . . . . . 24 5.7 Example of raw images and processed image . . . . . . . . . . . . . . . . . . 25 6.1 Contour of wake velocity and wake vorticity, 2D phase-locked experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 6.2 Contour of wake velocity and wake vorticity, 2D phase-locked simulation results 30 6.3 Change of bound circulation vs. vorticity shedding . . . . . . . . . . . . . . . 31 6.4 Schematics of integration window . . . . . . . . . . . . . . . . . . . . . . . . 31 6.5 Sensitivity analysis of box length . . . . . . . . . . . . . . . . . . . . . . . . 32 xi
  • 14. xii List of Figures 6.6 On path circulation tracking . . . . . . . . . . . . . . . . . . . . . . . . . . 32 6.7 Maximum circulation position . . . . . . . . . . . . . . . . . . . . . . . . . . 33 6.8 Illustration of Blade-Wake Interaction . . . . . . . . . . . . . . . . . . . . . 35 6.9 Vorticity strengthening due to wake-wake interaction . . . . . . . . . . . . . 35 6.10 Velocity distribution at vortex core . . . . . . . . . . . . . . . . . . . . . . . 36 6.11 Vorticity distribution at vortex core . . . . . . . . . . . . . . . . . . . . . . . 37 6.12 Schematics of vortex core center . . . . . . . . . . . . . . . . . . . . . . . . 38 6.13 Vortex pitch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 6.14 RMS of absolute velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 6.15 Peak vorticity distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 6.16 Wake circulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 6.17 Schematics of the wake geometry . . . . . . . . . . . . . . . . . . . . . . . . 42 6.18 Wake geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 6.19 Phase-locked stream-wise velocity profile . . . . . . . . . . . . . . . . . . . . 44 6.20 Peak velocity deficit of horizontal mid-span plane . . . . . . . . . . . . . . . 44 6.21 Schematic of wake stream-wise velocity distribution . . . . . . . . . . . . . . 45 6.22 Schematics 3D induction due to tip vortex . . . . . . . . . . . . . . . . . . . 45 6.23 Simulated wake development until 16R downwind of the turbine . . . . . . . 46 6.24 Cross-stream velocity profile . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 7.1 Contour of wake velocity and wake vorticity, 3D phase-locked experimental results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 7.2 Illustration of the influence of misalignment angle on uy . . . . . . . . . . . 52 7.3 Illustration of bound circulation of a skewed measurement plane . . . . . . . 53 7.4 Sensitivity analysis of the background cutoff criteria . . . . . . . . . . . . . . 55 7.5 Azimuthal variation of tip vortex strength . . . . . . . . . . . . . . . . . . . 56 7.6 Vorticity distribution at the vortex core . . . . . . . . . . . . . . . . . . . . . 57 7.7 Vorticity distribution away from the vortex core . . . . . . . . . . . . . . . . 57 7.8 Tip vortex trajectory in the xz-plane . . . . . . . . . . . . . . . . . . . . . . 58 7.9 Schematics of vortex inboard motion . . . . . . . . . . . . . . . . . . . . . . 59 7.10 Illustration of vortex pair roll-over, y/R = 0 . . . . . . . . . . . . . . . . . . 60 7.11 Stream-wise variation of tip vorticity . . . . . . . . . . . . . . . . . . . . . . 61 7.12 Decay of tip vorticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 7.13 Wake geometry in the xy-plane . . . . . . . . . . . . . . . . . . . . . . . . . 64 7.14 Wake geometry in the yz-plane . . . . . . . . . . . . . . . . . . . . . . . . . 64 7.15 Wake velocity profile in xy-plane . . . . . . . . . . . . . . . . . . . . . . . . 65 7.16 Peak velocity deficit of 3D vertical planes . . . . . . . . . . . . . . . . . . . 66 8.1 Convergence of the mean flow . . . . . . . . . . . . . . . . . . . . . . . . . 68 8.2 Schematic of blade deformation (exaggerated) . . . . . . . . . . . . . . . . . 70 A.1 Standard window alignment patterns . . . . . . . . . . . . . . . . . . . . . . 81 A.2 Possible window alignment patterns . . . . . . . . . . . . . . . . . . . . . . 82 A.3 Standard window alignment patterns . . . . . . . . . . . . . . . . . . . . . . 82
  • 15. List of Tables 8.1 Uncertainty of image calibration . . . . . . . . . . . . . . . . . . . . . . . . 71 A.1 Converting operation to standard window alignment pattern . . . . . . . . . 83 xiii
  • 17. Nomenclature Latin Symbols B Number of blade [-] CPmax maximum power coefficient [-] c Blade chord [m] H Blade span [m] N Number of samples [-] p∞ Static pressure [pa] R Rotor radius [m] t0 Vortex core radius [m] Rec Chord based Reynolds number [-] Rconst specific gas constant [J/(kg·K)] t Vortex age [s] T Temperature [K] u Velocity vector [m/s] ub Blade velocity [m/s] ures Local inflow velocity [m/s] uv Vorticity sheet convective velocity [m/s] u∞ Free-stream velocity [m/s] w Width of vorticity sheet [m] xv
  • 18. xvi Nomenclature Greek Symbols α Angle of attack [rad] Γ Blade circulation [m2/s] ˙γ Pitching rate [rad/s] θ Blade azimuthal angle [deg] λ Tip speed ratio [-] ρ Density [kg/m3] σ Blade solidity [-] ψ Misalignment angle [rad] ω Vorticity vector [1/s]
  • 19. Acronyms 2D Two dimensional 3D Three dimensional 2C-PIV Two Components PIV AoA Angle of Attack BWI Blade-Wake Interaction CFD Computational Fluid Dynamics DUWIND Wind Energy Research Group HAWT Horizontal Axis Wind Turbine OJF Open Jet Facility PTU Processing Time Unit PIV Particle Image Velocimetry SPIV Stereoscopic PIV TSR Tip Speed Ratio TU Delft Delft University of Technology VAWT Vertical Axis Wind Turbine WWI Wake-Wake Interaction xvii
  • 21. Chapter 1 Project Outline The re-merging interests on Vertical Axis Wind Turbine (VAWT) for urban or off-shore appli- cations require an improved understanding of rotor aerodynamics for performance optimization and wind farm design. The present project investigated the wake development of an H-type VAWT using Particle Image Velocimetry (PIV). Phase-locked flow properties were measured at a fixed tip speed ratio of 4.5. Two types of PIV measurements were conducted: a two- component planar PIV measurement at the horizontal mid-span plane, and a three-component stereoscopic PIV measurement at vertical measurement planes (aligned with free-stream). The study aims to: • Identifying main characteristics of three dimensional (3D) wake development of an H- type VAWT, both in detailed vortex scale and in global wake scale. • Validating the two dimensional (2D) unsteady inviscid panel code using measurement results at turbine mid-span plane. Based on the obtained measurement data, detailed flow analyses were performed with the focus on following aspects. At horizontal mid-span plane: • Circulation of wake vorticity sheets. • Blade-wake interaction and wake-wake interaction, investigating the triggering mecha- nism of vortical structures roll-up. • Shed vortex dynamics along wake shear layer, focusing on vortex convective trajectory and vorticity evolution. • Wake geometry at mid-span position, with specific attention to asymmetrical wake expansion. • Induction field and stream-wise evolution of wake velocity profiles. At vertical measurement planes: 1
  • 22. 2 Project Outline • Azimuthal variation of tip vortex strength. • Tip vortex motion in vertical planes, focusing on the cross-stream variation of vortex motions and vortex pair roll-over behind the rotor swept volume. • Stream-wise vorticity decay, with a comparison with simple theoretical vortex model. • 3D wake geometry. • Evolution of stream-wise velocity profile in vertical planes.
  • 23. Chapter 2 Vertical Axis Wind Turbine - A Brief Introduction Based on the alignment of rotational axis, two types of wind turbines are distinguished: Horizontal Axis Wind Turbine (HAWT) with rotational axis lying parallel to the ground, and Vertical Axis Wind Turbine (VAWT) with rotational axis standing vertically. Besides their different appearances, the underlying working principle is same. Wind turbine extracts kinetic energy from the wind, converting it into mechanical energy in the form of rotational motion; through built-in electricity generator, the mechanical energy is converted into electric energy which is delivered to electric networks. VAWTs are divided into two streams: drag-driven type and lift-driven type. The drag-driven type is propelled by the drag difference between the upstream and the downstream part of rotor blade. A famous example of drag-driven VAWT is the Savonius rotor (Figure 2.1(a)) named after Finish engineer Sigurd Savonius who invented it in 1925 [34]. Structural simplicity and relatively high reliability make drag-driven VAWTs particularly suitable for applications such as wind-anemometers and Flettner Ventilators. The former ones are commonly seen on the building rooftop whereas the latter ones are typically used as the cooling system of road vehicles. Despite their simplicity, the Savonius rotors, as with other variants of drag-driven VAWTs, have generally low operational efficiency (CPmax =0.17) when compared with their horizontal axis competitors (CPmax =0.59). Another Typology of VAWT is driven by lift. One famous example is the so-called Darrieus turbine (Figure 2.1(b)) patented by American Engineer Georges Darrieus in 1931 [29]. In theory Darrieus turbines are the most efficient VAWT, achieving an optimal power coefficient of CP =0.42 [26]. Since turbine blades are curved into an egg-beater shape (to reduce the stress induced by centrifugal force), Darrieus turbines are also known as the egg-beater rotors. In 1970s and 1980s, this configuration was extensively studied in Canada and the United States. In particular, the research work at Sandia National Laboratories proved the feasibility of large scale Darrieus turbines [30]. In 1984, the completion of Eole C (Figure 2.1(b)), the largest VAWT ever built [11], marked the culmination of a decade research efforts. In the 3
  • 24. 4 Vertical Axis Wind Turbine - A Brief Introduction end of 1980s, the shrinkage of North America market cut down research funding, resulting in a research stop for almost 15 years. In the following decades commercial development took over, companies like FloWind launched massive implementations of Darrieus turbines. In its full development during 1987, the power output of all FloWind VAWTs could supply the electricity use of nearly 20,000 California families. However, the glorious commercial success was not sustained as series of fatigue-related failures finally dragged down FloWind at the end of 2004 [17][30][39]. To overcome the structural deficiency of Darrieus turbines, a number of design concepts were explored since 1980s. Among them, the H-type VAWT or H-rotor (Figure 2.1(c)) stand out for its simplicity and efficiency. The use of straight blade reduces the difficulty of manufacturing curved blade; and the use of inherent blade stall characteristic removes the need of speed- break mechanism [30]. H-rotor researches during 1980s produced famous prototypes like VAWT-850, which is the largest H-rotor in Europe [27]. In 1990s, years of research efforts were transformed into commercial developments. Companies like Solwind of New Zealand, Ropatec of Italy, Neuh¨aususer of Germany designed and produced a range of H-rotors [16]. (a) Savonius type VAWT [5] (b) Darrieus turbines (Eole C) [30] (c) H-rotor [30] Figure 2.1: Examples of VAWT
  • 25. 2.1 VAWT vs. HAWT 5 2.1 VAWT vs. HAWT As an omni-directional machine, VAWT eliminates the need of pitching system hence reduces mechanical complexity [22]. VAWTs are generally quieter than HAWTs, making them suit- able for densely populated areas [19]. The ground-based equipment (e.g. transmission and electrical generation, etc.) makes VAWTs lighter, and easier for maintenance [12]. In offshore applications, low center of gravity allows an enhanced floating stability and a reduced gravi- tational load. The possibility of under-water electric generator further decreases the size and cost of the floating support structure. VAWTs have great potentials in wind farm operations. As the power output of a wind turbine is proportional to blade swept area, growing demand of power output has pushed the size of HAWTs to limit. Larger wind turbine size results in higher centrifugal force and bending stresses. Longer turbine blade requires larger turbine spacing hence lower wind farm density [30]. On the other hand, the size of VAWT can be extended vertically without a significant increase of occupied area. Recent researches showed that the wake recovery of a VAWT is faster, allowing for clustered array and increases wind farm power output [12][25]. However VAWT has its problems. Besides the well-known self-starting problem, the occurrence of dynamics stall at low rotational speed also shortens the turbine life. The inherent rotor asymmetry and unsteady operation of VAWTs lead to complicated blade loading and flow phenomena, which challenge blade designs and flow analyses [10].
  • 27. Chapter 3 Fundamental Aspects of VAWT Wake Aerodynamics The wake of a VAWT is inherently unsteady. The unsteadiness originates from periodical change of local Angle of Attack (AoA) at the blade level and from blade-wake interactions at the rotor level. Flow phenomena due to this unsteadiness include time varying vorticity shedding, unsteady wake evolution, blade vortex interaction, etc. Wake dynamics of VAWTs is further complicated by the strong asymmetry between the advancing and receding sides of the rotor [36]. Decades of research discontinuity leads to a limited understanding of these complicated phenomena. In the past few years, wake aerodynamics of an H-rotor was extensively studied in the Wind Energy Research Group (DUWIND) of Delft University of Technology (TU Delft). An inviscid unsteady panel code has been developed to simulate time dependent wake evolution [14]. Recently, the development of hybrid code has started, coupling Computational Fluid Dynamics (CFD) solver at turbine blades and vortex method at turbine wakes. Both methods are grid-free, making them insensitive to numerical dissipation hence well suitable for vortical flow simulation. In parallel to the numerical works, a range of experimental studies (e.g. smoke visualization, hot-wire and PIV measurement, etc.) were performed to validate numerical codes [36][37][38]. This chapter addresses fundamental aspects of the H-rotor wake dynamics, focusing on the generation and spatial distribution of vorticity within the rotor swept volume. The evolution of the vortical structures downstream of the rotor will be discussed in Chapter 6 and Chapter 7 in combined with the discussion of experimental results. 3.1 Definitions and Notations The wake of a VAWT can be divided into a region within the rotor swept volume and a region behind the rotor. Traditional momentum-based streamtube models treated a turbine rotor as 7
  • 28. 8 Fundamental Aspects of VAWT Wake Aerodynamics two half cups to adapty classical momentum theories [28]. Although this division accurately predicts integral forces, its capability in capturing the details of vortex dynamics is limited. The inefficiency lies in its incomplete treatment of the regions between upwind and downwind half of the rotor. These two regions, commonly referred to as the windward and the leeward, are essential to vorticity shedding and energy extraction of a VAWT. A better way of rotor division is proposed in [36]: • Upwind 45◦ < θ < 135◦ • Leeward 135◦ < θ < 225◦ • Downwind 225◦ < θ < 315◦ • Windward 315◦ < θ < 360◦ ∪ 0◦ < θ < 45◦ With θ being the azimuthal angle and θ = 90◦ being the most upwind. Figure 3.1 display a schematics of this division. The Cartesian reference system is origined at the turbine center, x-axis directs positively downwind of the turbine, y-axis points windward and z-axis points upwards. Counter-clockwise rotation is defined positive seen from above. In the following context, x-direction is referred to as the stream-wise direction and y-direction is referred to as the cross-stream directions. The turbine axial plane is the plane y/R = 0. In the horizontal direction, inboard refers to the direction of decreasing |y/R|, and outboard refers to the direction of increasing |y/R|. In the vertical direction, inboard refers to the direction of decreasing |z/H|, and outboard refers the direction of increasing |z/H|. x y R θ = 0˚ θ = 45˚ θ = 270˚θ = 90˚ θ = 180˚ θ = 135˚ θ = 225˚ θ = 315˚ u∞ ω Upwind Windward Leeward Downwind Figure 3.1: Schematic of 2D VAWT division Like other rotational machines, two parameters are important for VAWTs. Blade Solidity σ describes the percentage of the rotor area covered by solid blades: σ = Bc R (3.1) Where B is the number of blade, c blade chord and R rotor radius. Large blade solidity creates strong rotor blockage hence large flow induction. The Tip Speed Ratio (TSR) λ determines
  • 29. 3.2 Generation of Vorticity 9 turbine rotational frequency and is crucial to the power output: λ = ωR u∞ (3.2) Where ω is the rotor angular velocity in radius per second and u∞ is the free-stream velocity. According to a typical CP -TSR diagram (Figure 3.2) the peak power is found at the medium range of TSR. Low TSR tends to trigger dynamic stall, which postpones the occurrence of normal stall but intensifies unsteady blade loading, whereas high TSR results in low AoA, both compromising turbine efficiency. 1 2 3 4 5 6 7 8 0 0.1 0.2 0.3 0.4 TSR C P Re=150,000 Re=300,000 Figure 3.2: CP -TSR diagram 3.2 Generation of Vorticity The wake of VAWTs consist of shed and trailed vorticities. Due to unsteady blade motions, the release and distribution of vorticity are time dependent. x y R u∞ λu∞ ueff ω θ u∞ Figure 3.3: Free body diagram of inflow vector Based on the schematics of Figure 3.3, the geometrical AoA α can be derived as a function
  • 30. 10 Fundamental Aspects of VAWT Wake Aerodynamics of blade azimuthal angle θ: α = tan−1 − cos θ λ − sin θ (3.3) Time variations of AoA and inflow velocity lead to a periodically varying bound circulation, which, according to the Kelvin’s theorem [23] generates shed vorticity proportional to the negative change rate of bound circulation Γ: ωshed (t, z) = − ∂Γ (t, z) ∂t (3.4) The bound circulation can be derived using the unsteady formulation of the KuttaJoukowski theorem [23]: Γ = Γinflow + Γpitching = cπ uresα + c 2 1 2 − a ˙γ (3.5) Where ures the local inflow velocity, a the distance from rotation center to the leading edge of airfoil, and ˙γ the pitching rate. The first right-hand-side term measures the circulation due to inflow velocity, and the second term specifies the additional circulation of blade pitching motions. The magnitude of trailed vorticity is determined by the spatial gradient of bound circulation in the z-direction: ωtrailed (t, z) = − ∂Γ (t, z) ∂z (3.6) Shed vorticity aligns with the blade trailing edge, and trailed vorticity is orientated perpen- dicular to the blade trailing edge. Two types of vorticity have a phase difference of 90◦. 0 45 90 135 180 225 270 315 360 −30 −20 −10 0 10 20 30 θ° α° λ = 3 λ = 4 λ = 5 (a) Geometrical AoA 0 45 90 135 180 225 270 315 360 −1 −0.5 0 0.5 1 θ° Γ/Γ θ=90 ° ,λ=3 λ = 3 λ = 4 λ = 5 (b) Normalized bound circulation 0 45 90 135 180 225 270 315 360 −1 −0.5 0 0.5 1 θ° ω/ω θ=0 ° ,λ=5 λ = 3 λ = 4 λ = 5 (c) Normalized shed vorticity Figure 3.4: 2D characteristics, without induction Figure 3.4 displays the azimuthal variation of the geometrical AoA, bound circulation and vorticity shedding at three TSRs. The greatest AoAs are found at the leeward side around θ = 130◦ and θ = 230◦ (varying with TSR). Increasing TSR causes a drop of AoA, which reduces the likelihood of dynamics stall. Result shows that bound circulation is independent of TSR. The strongest circulations are observed at the most upwind and downwind sides of the rotor; whereas the greatest changes rate of bound circulation (i.e. the strongest vorticity
  • 31. 3.3 Vorticity and Energy Considerations 11 shedding) occurs at the most windward and leeward sides. Shed vorticity plot (Figure 3.4(c)) shows that vorticity shedding increases with TSR since the change rate of bound circulation becomes higher. The analysis so far has not considered the effect of flow induction. In reality, vorticity distribu- tion is non-symmetrical at two sides of the rotor. This is primary due to the asymmetrical flow induction as the windward advancing blade has different inflow conditions from the leeward receding blade. In the stream-wise direction, wake induction of the upwind blade passage re- duces the inflow velocity hence vorticity shedding downwind of the rotor, therefore the global wake dynamics is mainly determined by the wake generated at the upwind half of the rotor. Figure 3.5 displays the effective AoA and vorticity shedding from 2D simulation. 0 45 90 135 180 225 270 315 360 −5 0 5 10 15 20 θ° α ° (a) Effective AoA 0 45 90 135 180 225 270 315 360 −1 −0.5 0 0.5 1 θ° ω/ωmax (b) Normalized shed vorticity Figure 3.5: 2D characteristics, with induction Trailed vortex is generated along the finite span of a 3D VAWT. The strongest trailed vortex, known as the tip vortex, is released at the blade tip where the spatial gradient of the circulation is the highest. Neglecting ground effects and gravitational forces, the distribution of tip vortex is symmetrical with respect to the turbine axial plane y/R = 0. Figure 3.6 shows a schematic of tip vortex releasing along blade trajectory. Curved arrow represents the direction of vortex roll-up; plus and minus signs indicate pressure and suction sides of the blade. Tip vorticity changes its orientation at the most windward and leeward sides of the rotor, as a result of the sign change of bound circulation (Figure 3.4(b)). The production of trailed vorticity is weaker at the downwind part of the rotor due to reduced bound circulation. As shedding vorticity is determined by the time variation of bound circulation, the strongest vorticity shedding concentrates at the turbine mid-span where bound circulation is usually the highest. 3.3 Vorticity and Energy Considerations Assuming the energy extraction of a wind turbine can be measured by the Bernoulli constant ∇H, it can be shown that ∇H is determined by the local flow velocity u and the vorticity field ω [23]: ∇H = ρ (u × ω) (3.7)
  • 32. 12 Fundamental Aspects of VAWT Wake Aerodynamics + - -+ 0˚ 180˚ 90˚ 270˚ u∞ Figure 3.6: Schematic of tip vortex release along blade trajectory where vorticity is related to the curl of blade force by: Dω Dt = 1 ρ ∇ × f = 1 ρ ∂fx ∂z j − ∂fx ∂y k (3.8) For 2D VAWT spatial derivatives and force terms in z-direction are omitted, implying vorticity shedding and energy exchange occur at azimuthal positions where ∂fy ∂x − ∂fx ∂y is non-zero. To extract power in 3D, both shed and trailed vorticity are essential. Figure 3.7 shows a simplified schematic of a VAWT wake consisting of an array of vortex sheets. Shed vortices form the red sheets perpendicular to the inflow direction, and trailed vortices form the blue sheets parallel to the incoming flow. Two types of vortex sheet form a square wake tube which deforms along its convection. u∞ (a) Shedding vorticity sheets u∞ (b) Trailing vorticity sheets Figure 3.7: Schematics of wake vortex sheets
  • 33. Chapter 4 Particle Image Velocimetry Particle Image Velocimetry (PIV) is a non-intrusive flow diagnostic technique allowing flow field measurements. Comparing with intrusive flow measurement techniques like hot wire anemometer or pressure tube, PIV eliminates the need of instrumental intrusions by using non-intrusive laser light and tracer particles. Using Two Components PIV (2C-PIV) technique two velocity components within a planar interrogation window are obtained, and by using Stereoscopic PIV (SPIV) a third velocity component normal to the measurement plane can be resolved. Recently, the development of Tomographic PIV [15] extends the measurement range to a 3D volume. Fundamentals of 2C-PIV measurements are discussed in Section 4.1. A brief introduction to SPIV technique is presented in Section 4.2. If not stated otherwise, the content of 2C-PIV is based on the lecture notes of the course Flow Measurement Techniques of TU Delft [35], PIV lecture slides of A. James Clark School of Engineering, University of Maryland [24] and the book Particle Image Velocimetry - A Practical Guide [32]. The content of SPIV is based on the paper of Arroyo and Greated [8] and the review paper of Prasad [31]. 4.1 Fundamentals of 2C-PIV A typical 2C-PIV set-up consists of following components: a laser generator producing light sheet for particle illumination, a camera capturing the particle scattered light, and a PIV software for image acquisition and data processing. Figure 4.1 shows a basic PIV set-up. Key components are discussed in the following context. Tracer particles PIV measures flow velocity by cross correlating tracer particle positions of two consecutive image frames. Tracer particles must be small enough to faithfully trace the fluid motion; in the meanwhile, the size of the tracer particle should be large enough to scatter adequate 13
  • 34. 14 Particle Image Velocimetry Figure 4.1: Schematics of PIV set-up [35] light. The contradictory requirements make it non-trivial to select a proper particle size. Small particles are excellent flow tracer (due to low mass inertia) but are not good scatter (due to limited size); whereas the situation is opposite for large particles. For micro-metric particles used in PIV measurements, light scattering occurs at Mie regime where particle diameter is comparable or larger than the laser wavelength. In this regime, the strongest scattering occurs at 0◦ and 180◦ with respect to the incoming light, while the weakest scattering concentrates in the direction normal to the camera viewing direction. Since the contrast of PIV image is strongly determined by the scattering intensity, it is preferred to use the largest possible tracer particles without interfering flow properties. The diameter of typical tracer particles is about 1-3 µm in air flow measurement. Integration window Average particle displacement of interrogation window is derived using cross correlation. For statistically significant results, it is important to have a sufficient number of tracer particles; in the meanwhile over-seeding should also be avoided to prevent multi-phase flow. Typically, a desired particle concentration lie within the range from 109 to 1012 particles/m3 and each integration window should contain at least 10 particles. If large velocity variation presents in the measurement domain, the selection of a proper window size becomes difficult. A small window tends to cause particle loss, whereas large window size inevitably averages out flow details. To overcome this difficulty, the so-called multi-pass technique is developed. Starting with large window, this approach pre-shifts smaller interrogation windows (of the next pass) by using the distance estimated at the current pass. This process continues until the smallest window size is reached. Figure 4.2 demonstrates an example of applying single pass and multi-pass operations to a same measurement area. It is
  • 35. 4.2 Stereoscopic PIV (SPIV) 15 clear that multi-pass operation is capable of resolving flow field with large velocity contrast between the vortex region and the background free-stream region, which is impossible by using single-pass operation. Single-pass window size 24×24 Multi-pass min. window size 24×24 Figure 4.2: Multi-pass vs. single-pass Overlap between neighboring interrogation windows is often preferred to increase the use of measurement data. Since particles near the edge of windows are less likely to be captured in both frames, the processed image tends to be less accurate around window edges. By overlapping, these data are replaced by the data of neighboring window which does not lies at the edge. 20-30% overlap is common in practice. PIV acquisition and processing software The complicity of PIV measurement requires a real-time control of mutual dependent sub- systems. Modern PIV softwares (e.g. LaVision, PIVtec, TSI, etc) integrate control of various sub-systems (e.g. laser, cameras, etc.) into a central control unit which supports online processing in parallel to measurements. 4.2 Stereoscopic PIV (SPIV) 4.2.1 Working principle Stereoscopic PIV determines the velocity component normal to the measurement plane by using two synchronized cameras viewing from different angles. In a single camera set-up (Figure 4.4(a)), out-of-plane velocity is projected onto the object plane causing perspective errors. Using two off-axis cameras, the perspective error is converted into information about out-of-plane velocity components. Figure 4.3 shows the 2D schematic of a stereoscopic camera arrangement. Velocity compo-
  • 36. 16 Particle Image Velocimetry u ux ux1 ux2 uz CAM1 CAM2 α1 α2 X z Y Object plane Figure 4.3: Schematics of stereo camera arrangement nents in x-, y- and z- directions can be derived as: ux = ux1 tan α2 + ux2 tan α1 tan α1 + tan α2 uy = uy1 tan β2 + uy2 tan β1 tan β1 + tan β2 uz = ux1 − ux2 tan α1 + tan α2 = uy1 − uy2 tan β1 + tan β2 (4.1) Where α and β represent camera viewing angle with respect to yz- and xz-plane. To avoid singularity as α and β approaches zero, Equation 4.1 can be modified to: ux = ux1 + ux2 2 + uz 2 (tan α1 − tan α2) uy = uy1 + uy2 2 + uz 2 (tan β1 − tan β2) (4.2) 4.2.2 Translational and rotational configurations Based on camera arrangements, two SPIV configurations are distinguished. A translational configuration consists of two parallel standing cameras with lens axes normal to the light sheet (Figure 4.4(b)). This configuration allows for uniform magnification and good image focus, but its resolution is restricted by viewing angle θ (or camera off-axis angle). It can be shown that the accuracy of out-of-plane displacement is inversely proportional to viewing angle [43]: σ∆z σ∆x = 1 tan α (4.3) Where σ∆z and σ∆x represent the errors of out-of-plane and in-plane velocity components. With increasing viewing angle, the viewing axis deviates from lens design specification, causing substantial performance decay. The restriction on viewing angle is removed with a rotational configuration (Figure 4.4(c)). Since lens axes align with the viewing directions, the viewing angle can be increased without
  • 37. 4.2 Stereoscopic PIV (SPIV) 17 104 (a) Planar PIV (b) SPIV - Translational system (c) SPIV - Rotational system Figure 4.4: Configurations PIV systems [31] (a) Before using Scheimpug adapter (b) After using Scheimpug adapter Figure 4.5: Effect of Scheimpflug adapter [1]
  • 38. 18 Particle Image Velocimetry compromising lens performance, thereby allowing higher accuracy of out-of-plane velocity components. Rotating cameras bring the drawback of non-uniform image magnification. To retrieve uniform magnification cameras have to be mounted according to the Scheimpflug condition [6], which requires a co-linear alignment of object plane, lens plane and image plane. Without proper alignment the resulting image has only a narrow band of focused region as shown in Figure 4.5(a). A practical solution is to add a Scheimpug adapter between lens and CCD chip. By manually adjusting the orientation of Scheimpug adapter, a broader focus range can be achieved as shown in Figure 4.5(b) [1]. Although increasing off-axis angle improves measurement accuracy, an excessively large angle should be avoided to prevent strongly distorted image. In practice, the optimal measurement quality is obtained as camera opening angle approaches 90◦. 4.2.3 Image reconstruction To obtain displacement vectors in the object plane, the data of image plane is projected back using mapping function. This process is known as image reconstruction. If the complete geometry of PIV system is known, geometrical reconstruction can be used to link the image plane data x to the object plane data X. Since this approach requires a complete knowledge of imaging parameters, its practical use is limited. A more useful method, known as calibration-based reconstruction, reconstructs the mapping function through a calibration process. A typical mapping function reads: x = f (X) (4.4) Where f is usually a polynomial function with undetermined coefficients. Since the number of calibration points often exceeds the number of unknown coefficients, the polynomial coef- ficients are commonly determined using least square approximations. Calibration is performed using a calibration target, typically a rectangular metal plate with prescribed grid marker (cross, dots, etc.). For the calibration of a 2C-PIV set-up, a single image of the calibration plate is sufficient; for the calibration of a SPIV set-up, a second image is required at a known distance offset the laser sheet. Most commonly, a multi-level calibration plate (Figure 4.6) is used for the calibration of SPIV configuration. Figure 4.6: Multi-level Calibration Plate [32]
  • 39. Chapter 5 Experimental Set-up and Image Processing 5.1 Wind Tunnel The PIV experiments have been performed in the Open Jet Facility (OJF) of TU Delft. The OJF is a closed-circuit, open-jet wind tunnel with an octagonal cross-section of 2.85 × 2.85 m2 and a contraction ratio of 3:1. The tunnel jet is free to expand in a 13.7 × 6.6 × 8.2 m3 test section. Driven by a 500 kW electric motor, the OJF delivers free stream velocity range from 3 m/s to 34 m/s with a flow uniformity of ±0.5% and a turbulence level of 0.24% [2]. A 350 kW heat exchanger maintains a constant temperature of 20◦C in the test section. A schematic of the wind tunnel is shown in Figure 5.1. Figure 5.1: Schematics of OJF [3] 19
  • 40. 20 Experimental Set-up and Image Processing 5.2 Turbine Model The testing model is a two bladed H-type VAWT (H-rotor) with a rotor radius of 0.5 m. The rotor blades are generated by straight extrusion of a NACA0018 airfoil to 1 m span and 6 cm chord. Both sides of the blade are tripped with span-wise zig zag tapes, approximately 10% chord from the blade leading edge. Each blade is supported by two aerodynamically profiled struts (0.5 m) mounted at 0.2R inboard of blade tips, giving an aspect ratio of 1.8 and a blade solidity of 0.11. The entire turbine model, including blades, struts and supporting shaft is painted in black to reduce laser reflections. The wind turbine is supported by a 3 m steel shaft connected to a Faulhaber R brushless DC Motor at the bottom. With the maximum output power of 202 W, this motor drives the turbine at low wind speeds and maintains constant rotational speed. A Faulhaber gearbox with 5:1 gear ratio is coupled to the electrical engine to obtain sufficient torque at the operating regimes. An optical trigger is mounted on the shaft to synchronize the PIV system for the phased-lock acquisition. 5.3 Operational Conditions The turbine was operated at a fixed TSR of λ =4.5. The operational TSR was determined by a CP -TSR diagram similar to the one of Figure 3.2. Simulation shows λ = 4.5 yields the optimal power output (CP = 0.4) for the testing turbine. At a rotational speed of 800 RPM, the chord-based Reynolds Rec number is computed: Rec = ρωRc µ = 175, 000 Considering free-stream velocity and flow inductions, the actual chord-based Reynolds number varied between 130, 000 to 210, 000. 0 5 10 15 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Angle of attack α ° CL NACA0018, Re=∞ NACA0018, Re=130,000 NACA0018, Re=210,000 NACA0003, Re=∞ αmax =12.5o (a) Lift polar 0 5 10 15 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Angle of attack α° dCL /dα NACA0018, Re=∞ NACA0018, Re=130,000 NACA0018, Re=210,000 NACA0003, Re=∞ αmax =12.5o (b) Slope of lift polar Figure 5.2: Lift characteristics of the airfoil
  • 41. 5.4 PIV Equipment 21 Both lift coefficient and lift slope are important for VAWTs. The former one specifies the magnitude of bound circulation hence the strength of tip vortex, whereas the latter one determines unsteady vorticity shedding hence the power efficiency of the turbine. Since one of objectives is to validate vorticity shedding at the mid-span plane of the 2D simulation, it is more important to use an airfoil with comparable lift slope as the viscous NACA0018 airfoil used in the experiment. The lift polar and lift slope of a NACA0018 airfoil are given in Figure 5.2. Since the lift slope reduces in viscous flow, a thinner airfoil (NACA0003, dCL dα = 0.1) was used in the inviscid simulation to ensure the same performance of VAWT. Noted although the lift characteristics of inviscid NACA0003 airfoil are closer to the viscous NACA0018 airfoil, its higher lift slope is still an important cause of discrepancies in latter comparisons. Neglecting flow inductions, the maximum angle of attack of 12.5◦ is highlighted by the vertical dashed line in Figure 5.2. 5.4 PIV Equipment The tracer particle was produced by a SAFEX R twin fog generator placed downstream of the rotor. This generator produces Diethyl glycol-based seeding particles of 1 µm median diameter with a relaxation time of less than 1 µs [33]. Uniform mixing in the test section was ensured by the wind tunnel closed loop. A Quantel Evergreen R double pulsed Nd:YAG laser system was used as the light source. With the emitting power of 200 mJ per pulse, this system provides green light of wavelength 532 nm creating laser sheet of approximately 2 mm width and 40×30 cm2 illuminating area. The pulsed laser energy, repetition rate and time delay between pulses were controlled by a Processing Time Unit (PTU) and a sychnozation box called the Standford box. Two LaVision R Imager pro LX 16M cameras were used for image acquisition. The cameras have a resolution of 4870×3246 pixels2 with the pixel size of 7.4×7.4 µm2. Each camera was equipped with a Nikon R lens with focal length varying with desired Field of View (FOV) and image resolution (see Section 5.5 for details). Day light filter was added to reduce ambient light. Camera acquisition was synchronized to the laser shooting using the DaVis acquisition software. 5.5 PIV Set-up The measurements were conducted with PIV system in two set-ups: a 2C-PIV measurements at the horizontal plane and a SPIV measurements at the vertical planes. The first set-up investigated horizontal measurement plane at the rotor mid-span position (Figure 5.3). Given vertical symmetry of the rotor and that no relevant out of plane velocity component has been detected across the mid-span plane, a planar PIV setup has been used by combining two cameras into a single field of view. These two cameras were mounted on an horizontal beam, side by side at 1.3 m beneath the horizontal laser sheet. Each camera was equipped with an f = 105 mm Nikon lens, with a measuring aperture of f/4 and magnification factor of M = 0.09. The Field of View (FOV) of single camera was 266 × 399 mm2, and the combined FOV was 266 × 755 mm2 with an overlap of 44 mm in the y-direction.
  • 42. 22 Experimental Set-up and Image Processing In the second set-up, measurements were taken in the vertical planes of 7 cross-stream posi- tions (Figure 5.4). The SPIV set-up had two rotational cameras at two ends of a horizontal beam; a laser generator in middle of the beam produced vertical laser sheet to illuminate the measurement region. The cameras, mounted about d = 2.0 m from the measurement plane, were equipped with f = 180 mm Nikon lenses (f/4) with a relative viewing angle of δ = 96◦ and a magnification factor of M = 0.07. The resulting FOV was 365 × 430 mm2. Figure 5.3: Configuration of horizontal measurements Figure 5.4: Configuration of vertical measurements
  • 43. 5.6 System of Reference and Field of View 23 5.6 System of Reference and Field of View To synchronize the motion of cameras and laser, a two degrees-of-freedom traversing system was used, providing a stream-wise range of 1.4 m and a cross-stream range of 1.0 m. The horizontal measurements covers the rotor swept area and the wake region up to 4R downstream of the rotor. The positions of measurement window were optimized to minimize blade and tower shadows. To cover the target measurement domain, the traversing system was placed at two stream-wise positions. The first traversing system position covered the measurement range of x/R = [−1.88, 1.38], y/R = [−1.34, 1.35] and the second position covers the range of x/R = [1.13, 4.43], y/R = [−1.77, 1.77]. Figure 5.5 shows a schematic of the measurement domain. Each interrogation window is labeled with a unique ID, with the first digit indicating the number of traversing system position and the second alphabet indicating the window sequence. In the stream-wise direction windows were overlap by 7.1% to 19.9% of window width, in the cross-stream direction window overlap was constant and equaled to 21.6%. Between the first and second traversing system positions, two overlapped windows (1N, 2H) were measured for alignment. Convergence of the averaged phase-locked velocity was ensured with 150 images taken at θ = 90◦. 0 3 4 0 wind Figure 5.5: Schematics of measurement windows of horizontal plane The vertical measurements covered the stream-wise range from x/R = −1.10 to x/R = 6.00 at 7 cross-stream positions, y/R = -1.0, -0.8, -0.4, 0, +0.4, +0.8, +1.0. Measurement windows were placed at three height of z/H = 0.18, 0.50, 0.75, capturing flow behaviors in the vertical range from z/H = −0.07 to z/H = 1.01. Figure 5.6 shows the side view and the top view of the measurement domain. The stream-wise window overlap ranged from 19.0-43.6% of the window size. Between neighboring traversing system positions, overlapped windows were measured to determine their relative positions. To reduce blade shadows, phase- locked measurements were performed at θ = 0◦, with 150 images taken at each interrogation window.
  • 44. 24 Experimental Set-up and Image Processing 0 2 3 4 5 6 7 0 TS4TS4TS4 4H TS4 4I TS4 4L TS4 TS6TS6TS6TS6TS6TS6TS6 TS7TS7TS7TS7TS7TS7TS7 TS5TS5TS5TS5TS5TS5TS5 TS9TS9TS9 wind x/R z/H (a) Side view 0 2 3 4 5 6 7 0 y/R=0 wind x/R y/R (b) Top view Figure 5.6: Schematics of measurement windows of vertical planes 5.7 Image Processing LaVision R Davis software was used for image processing. Data processing includes 3 major steps: pre-processing, processing and post-processing. In the pre-processing phase, background noise was removed by subtracting the minimum average; a 3 × 3 Gaussian filter was used to ensure Gaussian profile shape and to reduce the effect of peak locking; spatial disparities of image intensity were excluded by removing the sliding background. The images were processed with a multi-pass correlation with the minimal window size of 32 × 32 pixels2 and an overlap ratio of 50%. The cross-correlation was sped up with built-in GPU mode of DaVis, using NVIDIA GeForce R GTX 570 GPU (480 cores, 1405.4 GFlops in double precision and 152.0 GB/s memory bandwidth) [4]. In the post-processing phase outliers of cross-correlation results were removed by applying a median filter. Final results were exported as DAT-files, which includes the following scale quantities: • Velocity field: ux, uy, uz, |u| • Standard deviation: σux , σuy , σuz , σ|u| • Reynold stress: τxy, τxz, τyz, τxx, τyy, τzz
  • 45. 5.7 Image Processing 25 Figure 5.7 gives an example of a raw image and the corresponding pre-processed and processed images. (a) Raw image (b) Pre-processed image (c) Processed image Figure 5.7: Example of raw images and processed image Since the DaVis exported data is based on local coordinates, it is essential to stitch individual images using global coordinates. Details of the stitching function can be found in Appendix A. At overlap regions, the interrogation window with better image quality was used. Averaging or image interpolation was not applied.
  • 47. Chapter 6 2D Wake Dynamics The study of 2D wake dynamics at the turbine mid-span plane focuses on 6 aspects: • Vorticity shedding within the rotor swept area (Section 6.3) • Blade-wake and wake-wake interaction (Section 6.4) • Vortex dynamics along the wake boundary (Section 6.5) • Wake circulation behind the rotor swept area (Section 6.6) • Wake geometry (Section 6.7) • Wake induction and velocity profiles (Section 6.8) Experimental and simulation results are displayed in Section 6.1 and Section 6.2. Detailed analyses based on these results are presented from Section 6.3 to Section 6.8. 6.1 Experimental Results Measurement results of the mid-span plane are presented in Figure 6.1. Figure 6.1(a) and Figure 6.1(b) show the contour plots of stream-wise velocity ux and cross-stream velocity uy, respectively. Figure 6.1(c) shows the out-of-plane vorticity contour ωz. The results were averaged over a phased-locked sampling of 150 images when blades were at the most upwind and downwind positions. Spatial coordinates are non-dimensionalized with the turbine radius R; velocity components are non-dimensionalized with the free-stream velocity u∞ and vorticity is non-dimensionalized with u∞ c . The wind came from the left and the turbine rotated in the counter-clockwise direction. Turbine blades, its trajectory, supporting struts and turbine tower are indicated in black, while the shadow blocked areas are blanked. Experimental results show asymmetrical wake expansion with faster expansion at the windward side. Velocity deficit induced by energy extraction is visible in the stream-wise velocity plot. The highest velocity gradients are observed in the most upwind and downwind blade positions, 27
  • 48. 28 2D Wake Dynamics (a) Non-dimensionalized stream-wise velocity (b) Non-dimensionalized cross-stream velocity (c) Non-dimensionalized out-of-plane vorticity Figure 6.1: Contour of wake velocity and wake vorticity, 2D phase-locked experimental results
  • 49. 6.2 Simulation Results 29 when blade circulation is respectively maximum in positive (counter clockwise) and negative (clockwise) signs. Due to periodic blades motion, shed vorticity sheets follow curved trajectories. The down- stream convection of the curved vorticity sheets form a U-shape wake geometry (Figure 6.1(c)). Defining vorticity sheet released over one turbine period as a complete wake cycle, each wake cycle consists of a convex upwind segment and a downwind concave segment. Wake geometry at the mid-span xy-plane is characterized by downstream transport of convex wake segments within the rotor swept area and downstream transport of concave wake segments behind the rotor. Windward and leeward counter-rotating vortical structure resemble a K´arm´an vortex street behind a cylinder. Near wake vortex roll-ups and interactions with neighboring vortices cause vortex deformation along its convection. Further downstream, vorticity strength reduces under diffusion and the concentrated vortex spreads to a broader area. 6.2 Simulation Results Results presented in this section are produced by the 2D version of the in-house developed unsteady inviscid free wake panel code. In the simulation, two airfoil are discretized using constant sources and doublet elements, with their strengths are determined by the Kutta condition imposed at trailing edges. The wake is modeled as a lattice of straight vortex filament and is free to evolve under mutual inductions. Direct computation of wake induction is accelerated by parallelization on GPU. Vortex elements are modeled as Rankine-type vortex, representing free vortex at the outer radius (potential flow) and rigid body rotation at the inner radius. Viscous diffusion is not accounted in the current version of the simulation code. An Adam-Bashforth second order time scheme is used for time marching. To investigate fully developed wake flow, the simulation ran until the convergence of integral force parameter (e.g. CT ), which corresponded to 15 rotations with a wake extension of 25R downstream of the turbine. The phase-locked results shown in Figure 6.2 were obtained by averaging instantaneous flow fields of 1◦ azimuthal step over 10 turbine rotations. 6.3 In-rotor Vorticity Shedding Vorticity shedding is a result of unsteady aerodynamics at the blade level, and is crucial to wake development and energy extraction of an H-rotor. Examining the vorticity sheet emanating from the blade (Figure 6.1(c)), counter-rotating vorticity sheets are clearly visible as a result of non-sharp trailing edge. 6.3.1 Evaluation method According to the Kelvin’s theorem [23], the magnitude of shed vorticity equals to the negative change rate of blade bound circulation Γ. Deriving vorticity using this relation requires a time sequence of measurements over a blade enclosed domain. Unfortunately light blockages
  • 50. 30 2D Wake Dynamics (a) Normalized stream-wise velocity (b) Normalized cross-stream velocity (c) Normalized out-of-plane vorticity Figure 6.2: Contour of wake velocity and wake vorticity, 2D phase-locked simulation results
  • 51. 6.3 In-rotor Vorticity Shedding 31 of rotor blades and other supporting structures often result in discontinuous measurement contour. An alternative way of determining the magnitude of the shed vorticity is by considering a finite domain near the blade trailing edge. As shown in Figure 6.3, the vorticity ω that are released in infinitesimal time interval δt is related to the change in bound circulation δΓ by: δΓ = ω · (wδs′ ) Where δs′ = δsb − δsv = (ub − uv)δt (6.1) Where w is the local width of vorticity sheet, ub is the velocity of blade motion and uv is the convective velocity of the vorticity sheet. δsb δsv Γ t t+δt Γ+δΓ u Figure 6.3: Change of bound circulation vs. vorticity shedding l d wt Figure 6.4: Schematics of integration window Although the underlying principle is straightforward, the aforementioned method is difficult in practice. First, the finite window length implicitly introduces uncertainties by summing up the vorticity released at earlier time instances. To reduce this uncertainty, it is preferred to minimize the window length l, and to shorten the distance between the window and the blade trailing edge d. However, it is difficult to have the domain very close to the blade trailing edge as blade edge laser reflections often leads to a larger masked area than the actual size of the blade. Also an excessively small domain size cannot guarantee improved accuracy. Strong velocity gradient confined within the thin layer of vorticity sheet makes precise capturing difficult using standard multi-pass correlation. Assuming the wake sheet just emanated from the blade is 1 mm wide (comparable to the thickness of blade trailing edge), and considering the camera scale is approximately 10 pixels/mm, the resulting resolution in the direction of wake width is only 10 vectors. This is apparently insufficient to resolve dynamic flow behavior within the wake sheet. Second, a precise estimation of vorticity convective distance δsv is often difficult due to the non-uniform convective velocity of vorticity sheets. A sensitivity analysis near blade trailing edge shows that the computed circulation varies significantly with the change of domain size, therefore it is not feasible to use this approach to the wake sheets just released from the blade.
  • 52. 32 2D Wake Dynamics 6.3.2 On path tracking of wake circulation Although the experimental resolution does not allow to resolve the vorticity release close to the blade trailing edge, the method outlined in the last section is applicable to the wake segment further away from the blade. Viscous diffusion and wake sheet expansion reduce sharp velocity gradients, making the application less sensitive to the size of integration window. 0 0.02 0.04 0.06 0.08 −0.8 −0.75 −0.7 −0.65 −0.6 −0.55 Box length ωc/u∞ Figure 6.5: Sensitivity analysis of box length The on path circulation is computed using integration windows along the wake sheet. Each window is orientated such that the window length l (short edge) aligns with tangential direction of the vorticity sheet. Window lengths are non-uniform and are determined based on a similar sensitive analysis as shown Figure 6.5. Results show that an overly small window length results in large fluctuations due to the the uncertainty on image processing. The smallest length that produces steady circulation is chosen as the window length. Window widths w (long edge) vary along the wake curve. In order to eliminate the influence of background vorticity, window width is chosen to be the local width of vorticity sheet t (Figure 6.4). 0 0.5 1 1.5 2 2.5 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 s/R Γ/Lu∞ EXP SIM, NACA0018 SIM, NACA0003 (a) Wake of upwind blade 0.511.522.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 s/R Γ/Lu∞ EXP SIM, NACA0018 SIM, NACA0003 (b) Wake of downwind blade Figure 6.6: On path circulation tracking Figure 6.6 displays the results of on path wake circulation. Horizontal axis represents the path coordinate along the wake, with the origin defined at the blade trailing edge (Figure 6.7);
  • 53. 6.3 In-rotor Vorticity Shedding 33 vertical axis measures the circulation per unit length, which is non-dimensionalized by the free- stream velocity u∞. The y-axis of Figure 6.6(a) and the x-axis of Figure 6.6(b) are reversed for easy comparison. Comparing two simulation results shows that the wake circulation trailed from a NACA0018 airfoil is stronger due to the larger lift slope, as expected in Section 5.3. Figure 6.6(a) compares the measured windward wake circulation with the result of 2D simu- lation. Simulation predicted circulations are generally higher owing to the higher lift slopes. Agreement between the measurement and the simulation is reasonable from s/R = 0 to s/R = 1.5. Assuming limited wake convection, this part of wake corresponds to the vorticity shed from θ = 0◦ to θ = 90◦, where the decreasing change rate of bound circulation results in a steady decline of wake strength towards the upwind side of the rotor. Both simulation and experimental results observe two circulation peaks with the measured peaks lying more upwind. The measured upwind peak (at around s/R = 1.4) is partially blocked by the tower shadow. The positions of peak circulation are highlighted by black circles in Figure 6.7. Wake circulation reduces dramatically downstream of the peaks due the induction of upwind wakes. Fluctuations of the measured result might result from a number of factors including variations of data quality, sensitivity of integration window sizes and residual background noises. s/R s/R (a) Experiments s/R s/R (b) Simulation, NACA0018 s/R s/R (c) Simulation, NACA0003 Figure 6.7: Maximum circulation position The wake strength at the leeward side of the rotor is presented in Figure 6.6(b). The experi- mental circulation shows an increase from the large s/R (upwind part), climbing to its peak values (leeward part) in the middle range of s/R and drops drastically from the peak onward (downwind part). Although the simulation predicts a similar trend, the discrepancies in detail are different. First, the simulation predicted upwind circulation is much higher. Second, three local peaks are are observed in the simulation results, whereas only one peak is observed in the measured results. In contrast to the windward side, the measured leeward peak shifts down- wind with respect to the simulation results. In average the leeward observed peak circulation is 20% higher than the peak circulation at the windward wake. The variation of wake circulation is determined by three factors: • Strength of newly released wake • Vorticity convection along the curved wake segment • Vorticity strengthening due to wake interactions
  • 54. 34 2D Wake Dynamics The convection velocity of the vorticity sheets is determined by viscous blade dragging and local velocity field. In general vorticity convection along the path is relatively slower than the downstream wake transport. Since wake interactions only causes local modifications of wake circulation, the global difference of upwind circulation is most likely attributed to the circulation difference just released from the blade. It seems that the numerical simulation predicts the windward wake circulation reasonably well, whereas it tends to overestimate at the leeward side. Comparing with a nominal shed vorticity distribution (Figure 3.5(b)), the increase of circulation presented in Figure 6.6 is more abrupt. Since most circulation peaks correspond to the positions of wake crossing, the strengthening of local vorticity field is most likely caused by wake interactions which also shift the position of the peak circulation. Detailed effects of wake interaction are discussed in the next section. 6.4 Blade-wake and Wake-wake Interaction Blade-Wake Interaction (BWI) arise when a downwind turbine blade crosses the wake segments generated by the other blades or generated by the blade itself during previous revolutions. Wake-Wake Interaction (WWI) occur when different wake segments cross each other. For VAWTs, BWI and WWI have two major implications: • On blades: BWI changes the local velocity field, which alters pressure distribution and blade loading of downwind blades. • On wakes: BWI and WWI cause local change of wake vorticity, which triggers the roll-up of vortical structure. Using moving interrogation windows the phenomenon of BWI and WWI were captured. Fig- ure 6.8(a) displays the flow field at three time instances separated by 25◦ azimuthal angles (corresponding to 5.2 ms). Blade crossing occurs at approximately θ = 185◦ and the box in the bottom image highlights the wake segment influenced by the interaction. Different wake segment can be distinguished by locations and intensities. Corresponding 2D simulation results are presented in Figure 6.8(b). Comparing the location of the boxes shows that the measured influenced region is more downwind and more inboard of the rotor. To understand how BWI and WWI triggers the roll-up of vortical flow structure, the on path circulation is computed. Figure 6.9 presents the results in 3D: the vorticity contour lies on the 2D plane; the lower curve indicates the trajectory on which the circulation is evaluated; and the height between the upper and lower curve represents the circulation strength. The evaluation method is similar to the one introduced in Section 6.3.1. Results show that circulation increase at the position of BWI. At the crossing point the vorticity is transferred from the newly released vorticity sheet to the weaker wake segment, creating a region of higher vorticity gradients. In case of BWI, the examined wake segment of Figure 6.9 corresponds to the weak one. After crossing, the strengthened local vorticity field leads to a counter-clockwise flow rotation, which rolls up the wake segment into large vortical structures (i.e. shed vortices). The mechanism of WWI is similar although the intensity of wake interaction is lower due to more diffused vorticity content.
  • 55. 6.4 Blade-wake and Wake-wake Interaction 35 (a) Experimental result (b) Numerical result Figure 6.8: Illustration of Blade-Wake Interaction Γ/(L u∞ )=0.63 Γ/(L u∞ )=0.25 (a) Experimental result Γ/(L u∞ )=0.84 Γ/(L u∞ )=0.42 Γ/(L u∞ )=0.61 Γ/(L u∞ )=0.23 (b) Numerical result Figure 6.9: Vorticity strengthening due to wake-wake interaction
  • 56. 36 2D Wake Dynamics The measured circulation is generally lower than the simulation prediction, coherently with the observations in Section 6.3. Simulation predicts multiple circulation peaks induced by BWI or WWI, while the WWI induced circulation peak is almost undetectable in the measurement results. This difference might be explained by the effect of viscous diffusion which reduces wake strength and intensity of wake interaction. Moreover, the effect of diffusion tends to remove strong vorticity gradients (results from wake interaction), leading to flattened circulation peaks. The number of circulation peaks has substantial impacts on the vortex roll-up downwind of the rotor. Single circulation peak triggers single vortex roll-up, which produces concentrated shed vortex in the experimental result (Figure 6.1(c)); in contrast, multiple peaks trigger vortex roll-up at multiple spatial locations, which gives rise to a more scattered vortical structure in the simulation result (Figure 6.2(c)). 6.5 Vortex Dynamics Along the Wake Boundary Shed vortices are generated by BWIs and WWIs discussed in the last section. The down- stream convections of the vortical structure have strong influences on the wake development at horizontal planes. Vortex trajectory defines wake geometry, and induction of shed vorticity is crucial to wake velocity field. 6.5.1 Determination of vortex core position and peak vorticity (a) The cuts 1.1 1.15 1.2 1.25 1.3 1.35 1.4 −0.1 0 0.1 0.2 0.3 0.4 x/R u y /u ∞ (b) uy along horizontal cut 1 1.1 1.2 1.3 1.4 −0.6 −0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 y/R ux /u∞ (c) ux along vertical cut Figure 6.10: Velocity distribution at vortex core Important vortex properties include vortex core position, vortex core radius, vorticity distri- bution, and vortex circulation strength. For studying time varying vortex properties, flow measurements at different phase angles are required. With available phase-locked results, we exploit the periodical wake characteristic to bypass the difficulty of not having phase varying data. Assuming wake flow repeats itself every integer numbers of turbine rotational period T, studying consecutive released vortices can be considered equivalent to the tracking of single vortex over a sequence of time instances separated by T. Although this approach works well with isolated vortex, it becomes less capable when connected vortices are encountered (see for instance Figure 6.1(c) and Figure 6.2(c)). Interference of neighboring vortices makes the anal- ysis sensitive to the definition of vortex domain. Consequently, the following analysis would
  • 57. 6.5 Vortex Dynamics Along the Wake Boundary 37 not focus on domain dependent properties such as vortex core radius and circulation strength, instead, domain independent properties such as peak vorticity and vortex core position are discussed. Studying peak vorticity evolution allows a quantitative measurement of the change rate of shed vorticity. An accurate determination of peak vorticity is, however, impeded by low particle densities at the vortex core (due to centrifugal forces). To evaluate the effect of reduced particles, velocity distributions is plot along a vertical cut and a horizontal cut passing through the vortex core. The orthogonal cuts and corresponding velocity profiles are displayed in Figure 6.10. Both profiles show continuous velocity distribution in the region between velocity peaks, implying data quality of the vortex core is not significantly affected by the reduction of particle density (probably due to relatively low vorticity). Similar results are observed at other vortices. 1.1 1.15 1.2 1.25 1.3 1.35 1.4 −1.5 −1 −0.5 0 0.5 1 xpeak x/R ωz c/u∞ (a) ωz along horizontal cut 1 1.1 1.2 1.3 1.4 −1.5 −1 −0.5 0 0.5 ypeak y/R ω z c/u ∞ ypeak (b) ωz along vertical cut Figure 6.11: Vorticity distribution at vortex core Since vorticity is the strongest at vortex core, the vortex core location is assumed identical to the location of the peak vorticity. Two methods are used to determine the location of the peak vorticity. The first method makes use of the vorticity plot along the cuts of Figure 6.10(a). Although the vorticity field is more oscillating, comparable oscillation amplitude between the vortex core and the surrounding flow region suggests that the observed fluctuations are not a result of low data quality but are induced by flow unsteadiness. Since it is difficult to match the observed asymmetrical vorticity field with an axial-symmetrical vortex model, the vorticity profile is fitted with a polynomial function (dashed line). The stream-wise and cross-stream positions of the maximum vorticity correspond to the locations of peak vorticity in the x- and y-direction. The second method determines the vortex core position (¯x, ¯y) by using weighted average over an iso-vorticity contour: ¯x = xi,jωi,jdA ωi,jdA , ¯y = yi,jωi,jdA ωi,jdA (6.2) Where ωi,j is the vorticity of vortex particle, xi,j and yi,j are spatial coordinates of the vortex particle and dA is the pixel size. In order to examine the sensitivity of the cutoff limit, different cutoff limits are tested. Results show that the difference between two methods are negligible (maximum 1.6%). For simplicity, the first method was used.
  • 58. 38 2D Wake Dynamics Peak vorticity is determined by averaging the (absolute) maximum vorticity along two orthog- onal cuts which pass through the vortex core. 6.5.2 Vortex trajectory and vortex pitch distance Figure 6.12 displays a schematic of shed vortex positions downstream of the rotor. Two groups of vortices are distinguished: the 1st, 3th and 5th vortices are released from one blade and the 2nd, 4th and 6th vortices are generated by the other blade. The × signs and ⋆ signs indicate the position of vortex core in the windward and leeward sides respectively. Non-dimensionalized vorticity field with an absolute cutoff limit of 0.3 is added to the background for reference. Vortices of the same ID number show one-to-one correspondences between the simulation and measured results. As discussed in Section 6.4, the simulated vorticity field is less concentrated due to multiple vortex roll-ups. −1 0 1 2 3 4 −1.5 −1 −0.5 0 0.5 1 1.5 wind x/R y/R ωz c/u∞ −1.2 −0.8 −0.4 0 0.4 0.8 1.2 2 3 4 5 6 2 43 1 5 6 (a) Experimental results −1 0 1 2 3 4 −1.5 −1 −0.5 0 0.5 1 1.5 wind x/R y/R ωz c/u∞ −1.2 −0.8 −0.4 0 0.4 0.8 1.2 21 3 4 5 21 3 4 65 (b) Simulation results Figure 6.12: Schematics of vortex core center Vortex convective velocity is measured by the variation of vortex pitch, which is defined as the distance that a vortex is transported during one blade rotation. Assuming vortices released from two blades are identical, the average distances of neighboring vortices are used to compute vortex pitch in half rotation. The vortex pitches are plotted at the midpoints of neighboring vortices (Figure 6.13). The measured vortex pitches are comparable at two sides of the rotor, whereas the simulation predicted vortex pitches are larger at the windward side. Higher wake velocity (see Section 6.8.1) yields the simulation predicted pitch distance generally larger than the measured one. The plot of cross-stream vortex pitch (Figure 6.13(b)) shows that the outboard vortex motion is faster at the windward side. With increasing downstream distance, the pitch distance reduces with the slowing down of wake expansion. Results show reasonable agreement between the measurement and the simulation at the leeward side, while the discrepancy is large at the windward side. Stronger windward expansion explains the larger pitch distance in the experimental results.
  • 59. 6.5 Vortex Dynamics Along the Wake Boundary 39 1 1.5 2 2.5 3 3.5 4 0.4 0.5 0.6 0.7 0.8 x/R ux /u∞ windward, EXP leeward, EXP windward, SIM leeward, SIM (a) Stream-wise pitch 1 1.5 2 2.5 3 3.5 4 −0.2 −0.1 0 0.1 0.2 x/R u y /u ∞ windward, EXP leeward, EXP windward, SIM leeward, SIM (b) Cross-wise pitch Figure 6.13: Vortex pitch 6.5.3 Evolution of peak vorticity The vorticity variation is determined by the combined effect of vortex roll-up and viscous. In the near wake, the roll-up of inboard released vortex particles locally strengthens the vortex circulation; but the roll-up does not necessarily increase the vorticity of individual vortex par- ticle. For instance, if weaker vortex particle is rolled into the vortex core, the total circulation will increase but the mean vorticity will decrease. In the meanwhile, strong velocity gradients are removed by viscosity, resulting in a reduced vorticity peak and an expanded vortex core. Vorticity is further reduced by the turbulent diffusion through flow mixing and kinetic energy cascade. The growing magnitude of turbulent diffusion is demonstrated in the standard devi- ation plot of Figure 6.14. As shown, the influence of turbulence is low in the near wake but grows rapidly with increasing x/R. Comparing two sides of the rotor, the turbulence induced uncertainty is stronger at the windward side. Although turbulence diffusion scheme is not explicitly included in the simulation, the propagation of small numerical error resembles the growing effect of turbulence diffusion. Figure 6.14: RMS of absolute velocity Figure 6.15 illustrates the variation of peak vorticity in the stream-wise direction. Negative
  • 60. 40 2D Wake Dynamics windward vorticity is shown in red and the positive leeward vorticity is shown in blue. The error bars represent the uncertainty in estimating the phase-averaged results using instantaneous measurements (based on Figure 6.14). The windward and leeward measured shed vorticity have comparable strength just released from the rotor, but their downstream evolution becomes different. Vorticity of windward side increases from x/R = 1.5 to x/R = 2.3, suggesting viscous diffusion is locally overcome by vortex roll-up. Further downstream, the roll-up strength decreases and vorticity decays under diffusion. Overall, peak vorticity reduces to 30% of its original strength (at x/R = 1.3) at 3.6R behind the rotor. The decay of leeward vorticity is almost linear, resulting in a total vorticity decrease of 70% at 3.5R behind the rotor. Interestingly, decay rate downstream of x/R = 2.3 is approximately the same between the windward and the leeward sides. 0.5 1 1.5 2 2.5 3 3.5 4 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 x/R Peakvorticityωz c/u∞ windward, EXP leeward, EXP windward, SIM leeward, SIM Figure 6.15: Peak vorticity distribution The differences between experimental and simulation results are large. At the windward side the simulation predicted peak vorticity is in average 40% lower than the measured result; whereas at the leeward side the simulation overestimates the vorticity by 15%. This discrep- ancy might be explained by different wake expansion pattern that will be discussed in detail in Section 6.7. In the experiment, the windward deflected wake squeezes the shear layer along the wake boundary, resulting in an increased velocity gradient hence a locally enhanced vorticity field; conversely, the stretched leeward shear layer causes a decrease of vorticity. Examining Figure 6.1(a) it is clear that the windward shear layer is thinner than the leeward one. Since the simulation predicts an opposite wake expansion pattern, the squeezing and stretching effects are reversed. As shown in Figure 6.15, the rate of vorticity decay are almost identical at the two sides of the rotor. The numerical simulation underestimates the decay rate by 10%, which might be traced back to the absence of diffusion scheme. 6.6 Wake Circulation Due to the difficulty of specifying vortex domains, circulations of a bound vortex contour is not computed; instead, the circulation of equally spaced sub-domains moving downstream is
  • 61. 6.7 Wake Geometry 41 evaluated. Circulation at windward (y/R > 0) and leeward (y/R < 0) regions are derived separately. Figure 6.16(a) displays the wake circulation as a function of the stream-wise position x/R. Results show strong fluctuations near vortex cores, which reduces with increasing downstream distance. Detailed differences between the experimental and the simulation results (e.g. the shift of stream-wise peak circulation, etc.) are consistent with the discussion of vortex dy- namics in the last section. To reduce vortex induced fluctuations, accumulated circulation is plotted. In Figure 6.16(b), the value at a certain x/R corresponds to the total circulation summed over all sub-domains upstream of this position. Linear circulation increase are observed at both sides of the rotor, which implies the total circulation is conserved. Results from the 2D simulation show a similar evolution trend but it overestimates the circulation by 10%. Summing up the windward and leeward wake circulation, the total circulation is represented by the black curves in Figure 6.16(b). As seen, the total wake circulation is conserved and equals to zero. Since the circulation of the complete rotor system (rotor+wake) is zero, this observation implies the circulation of the rotor is zero. 1 1.5 2 2.5 3 3.5 4 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 x/R Γ z /Lu ∞ windward, EXP leeward, EXP windward, SIM leeward, SIM (a) Circulation 1 1.5 2 2.5 3 3.5 4 −1.5 −1 −0.5 0 0.5 1 1.5 x/R Γz /Lu∞ windward, EXP leeward, EXP windward+leeward, EXP windward, SIM leeward, SIM windward+leeward, SIM (b) Accumulated circulation Figure 6.16: Wake circulation 6.7 Wake Geometry Wake geometry defines global wake shape and provides important reference scale for wind farm designs. Conventionally wake geometry is defined by using streamline that corresponds to certain velocity cutoff or by using vortex trajectory [41]. Determining streamlines requires time-averaged results which are not available to the current study, thus the following context analyzes the horizontal wake geometry based on the convective trajectory of shed vortices. Figure 6.17 displays the wake geometry obtained by least square fitting of vortex core positions. For reference the streamline that corresponds to 99% free-stream velocity of time-averaged simulation results is added to the plot. Both experimental and simulation results show the
  • 62. 42 2D Wake Dynamics −1 0 1 2 3 4 −1.5 −1 −0.5 0 0.5 1 1.5 x/R y/R wind Exp SIM SIM, 99% u ∞ streamline Figure 6.17: Schematics of the wake geometry horizontal wake expansion as a result of energy extraction. In comparison the experiment observes a faster expansion at the windward side while the simulation predicts a more sym- metrical expansion. In average the measured wake expansion angle is 8◦ at the windward side and 5◦ at the leeward side. The corresponding simulation predicted expansion angles are 4◦ and 5◦ respectively. Comparing with the wake geometry defined by the streamline, the geometry obtained using vortex trajectory lies slightly inboard since vortex induction increases the stream-wise velocity outboard of the vortex core. The asymmetrical wake expansion is also demonstrated in the wake centerline plot of Fig- ure 6.18(a). The measured wake centerline lies around y/R = 0.1 and moves towards the windward side with an angle of circa 0.7◦. In contrast the simulation predicted wake center- line, which lies close to y/R = 0, shifts windward with an angle of 0.3◦. This observation is consistent with the asymmetric wake expansion discussed above. The presence of the turbine tower is probably the main cause of measured asymmetrical wake expansion. In Figure 6.1(a), tower wake is represented by the yellow expanding region behind the turbine tower. With flow passing the rotating tower, a leeward pointing lift force is generated; the reaction of this force deflects the tower wake to the windward side of the rotor, which steers the expansion of turbine wake to the same side. To analyze global wake expansion, the cross-stream wake diameter Dw is computed. As shown in Figure 6.18(b), the measured wake diameter increases 41% at 3.5R downstream of the turbine, whereas the wake diameter predicted by the simulation increases 35% at the same downstream distance. Since wake expansion is a direct consequence of energy extraction, the faster measured wake expansion is most probably attributed to the larger velocity deficit that will be discussed in the next section.
  • 63. 6.8 Induction and Wake Velocity Profile 43 1.5 2 2.5 3 3.5 −0.4 −0.2 0 0.2 0.4 x/R Wakecenterlinepositiony/R EXP SIM (a) Wake centerline position 1 1.5 2 2.5 3 3.5 1 1.2 1.4 x/R WakediameterDw /2R EXP SIM (b) Wake diameter Figure 6.18: Wake geometry 6.8 Induction and Wake Velocity Profile Knowledge of wake inductions and wake velocity profiles is crucial to the understanding of wake recovery of a wind turbine. According to Kinze [25], VAWTs exhibit favorable velocity recovery characteristics in comparison to similar sized HAWTs. In the following section, we testify this statement by investigating stream-wise wake velocity profiles in the mid-span plane of the turbine model. The cross-stream velocity profile is also discussed to facilitate the understanding of asymmetrical wake expansion. Comparing with time-averaged results the phase-locked wake velocity profiles are more im- portant for VAWTs. First, cyclic blade loading and extreme loading conditions of downwind rotors are determined by the instantaneous wake velocity of upwind rotors. Second, the kinetic energy perceived by the downwind rotor is time varying. Decomposition the time dependent flow into mean, periodic and randomly fluctuating components [21], it can be shown that the kinetic energy of the time dependent flow is usually higher than the kinetic energy of the mean flow. 6.8.1 Stream-wise velocity profiles Figure 6.19(a) shows the stream-wise wake velocity profiles at 6 positions x/R =1.5, 2.0, 2.5, 3.0, 3.5, and 4.0. The results of phase-locked 2D simulation are plotted in Figure 6.19(b). The measured stream-wise velocity profiles are non-symmetric with respect to y/R = 0. Faster windward expansion shifts the velocity profiles to the windward side. Between y/R = −0.7 and y/R = 0.9, velocity deficits are high and velocity gradients dux dy are low; outboard of this region ux increases rapidly. The shapes of the phase-locked velocity profile are similar to all stream-wise positions. Along the shed vortex trajectory, vortex induced fluctuations are visible at the windward region from y/R = 0.5 to y/R = 1.2 and leeward region from y/R = −0.8 to y/R = −1.0. In the stream-wise direction, the influence of vortex induction diminishes and the velocity profiles become smoother with increasing x/R. The simulation result shows a more symmetrical profile. The maximum velocity deficit is found at y/R = −0.2 and remains at this position with increasing downstream distance. The peak velocity deficit, a non-dimensional number defined by 1 − uxmin /u∞, is presented in Figure 6.20. The figure shows no indication of wake recovery until 4R downstream of the
  • 64. 44 2D Wake Dynamics 0 0.2 0.4 0.6 0.8 1 −1.5 −1 −0.5 0 0.5 1 1.5 u x /u ∞ y/R x/R=1.5 x/R=2.0 x/R=2.5 x/R=3.0 x/R=3.5 x/R=4.0 (a) Experimental results 0 0.2 0.4 0.6 0.8 1 −1.5 −1 −0.5 0 0.5 1 1.5 u x /u ∞ y/R x/R=1.5 x/R=2.0 x/R=2.5 x/R=3.0 x/R=3.5 x/R=4.0 (b) Simulation results Figure 6.19: Phase-locked stream-wise velocity profile turbine. The peak deficits predicted by the 2D simulation are in average 20% lower than the experimental observed values. 1.5 2 2.5 3 3.5 4 50 60 70 80 90 100 x/R Peakvelocitydeficit[100%] EXP SIM Figure 6.20: Peak velocity deficit of horizontal mid-span plane To understand aforementioned observations, the variation of wake velocity behind a generalized wind turbine is plotted in Figure 6.21. Immediately behind the rotor, wake velocity decreases as a result of energy extraction. Wake velocity reaches its minimum of (1 − 2a)u∞ at xcrit, with a being the flow induction factor. Further downstream, flow re-energirization takes place and the wake velocity starts to recover. The observed growing wake deficit suggests that wake recovery has not yet started until x/R = 4.0. The discrepancy of the measured and the simulation results might be traced to two possible sources: • Wake of the turbine tower • Absence of tip vortex induction in 2D simulation As already mentioned in Section 6.7, the presence of the rotating turbine tower is an important cause of wake asymmetry, thus it also contributes to the asymmetrical velocity distribution in Figure 6.19(a). Additionally, the downwind transport of the tower wake also reduces the wake velocity along its path.
  • 65. 6.8 Induction and Wake Velocity Profile 45 x ux xcrit Turbine plane (1-2a)u∞ Figure 6.21: Schematic of wake stream-wise velocity distribution In the 2D simulations, the wake velocity at the mid-span horizontal plane is solely determined by the induction of in-plane shed vorticity. In reality the wake velocity is also influenced by the induction of tip vortex in the vertical direction. Tip vortex induction within the rotor swept area has been discussed in [36], demonstrating it a main cause of stronger velocity deficit in 3D. Behind the rotor, the situation is similar. As will be discussed in Section 7.3.1, tip vortices are distributed along convex and concave vortex tubes as shown in Figure 6.22; the induction of these tubes produces negative components of stream-wise induction, leading to larger velocity deficit at the turbine mid-span plane. Concave tip vortex tube Convex tip vortex tube H-rotor Induction ω Figure 6.22: Schematics 3D induction due to tip vortex Although wake recovery is not observed at the turbine mid-span plane, the other span-wise positions might experience a different flow recovery rate. Wake recovery in the vertical di- rection might also be different due to the inherent rotor asymmetry (Section 7.4). 2D wake simulation until 16R downwind of the rotor (Figure 6.23) shows that wake expansion stops at approximately x/R = 6, which implies wake recovery starts after this distance. 6.8.2 Cross-stream velocity profiles Figure 6.24 shows the phase-locked velocity profiles of cross-stream velocity uy. Comparing with the stream-wise velocity profiles, velocity fluctuations are stronger; the strongest fluctu- ations are found at the most upstream station of x/R = 1.5 and the fluctuations magnitude decrease with increasing x/R. Velocity fluctuations 4R behind the rotor are almost negligible.
  • 66. 46 2D Wake Dynamics Figure 6.23: Simulated wake development until 16R downwind of the turbine It is visible that the positive uy dominates the windward region with its influence further extended to the leeward region; small regions of negative uy is only observed to the most leeward side of the rotor. The cross-stream position of zero uy shifts windward due to non- symmetrical wake expansion. With increasing x/R, the magnitude of cross-stream induction reduces. The velocity distribution is more asymmetrical in the simulation result. Zero cross-stream velocity is observed near the turbine axial plane at y/R = 0.1. Comparing the velocity profiles at the most downstream position of x/R = 4.0 shows that the simulation predicted uy is lower at the windward side and is higher at the leeward side, which is consistent with the cross-stream vortex pitch discussed in Section 6.5.2. −0.15 −0.1 −0.05 0 0.05 0.1 0.15 −1.5 −1 −0.5 0 0.5 1 1.5 uy /u∞ y/R x/R=1.5 x/R=2.0 x/R=2.5 x/R=3.0 x/R=3.5 x/R=4.0 (a) Experimental results −0.15 −0.1 −0.05 0 0.05 0.1 0.15 −1.5 −1 −0.5 0 0.5 1 1.5 uy /u∞ y/R x/R=1.5 x/R=2.0 x/R=2.5 x/R=3.0 x/R=3.5 x/R=4.0 (b) Simulation results Figure 6.24: Cross-stream velocity profile
  • 67. Chapter 7 3D Wake Dynamics The release and downstream convection of tip vortices are crucial to the 3D wake development of an H-type VAWT. Tip vortex motions in the xz-plane define wake geometry in the vertical direction, whereas the variations of tip vorticity, among other factors, determine induction fields in 3D. Blade-vortex interactions at the downwind blade passage cause unsteady blade loading and are important sources of noise generation. In this chapter, we examine 3D wake dynamics with the focus on tip vortex dynamics and non-symmetric wake distribution. The following aspects are addressed: • Azimuthal variation of tip vortex strength (section 7.2.1) • Tip vortex motion in the vertical xz-plane (section 7.2.3) • Stream-wise tip vorticity decay (section 7.2.4) • 3D wake geometry (section 7.3) • Stream-wise wake velocity profile in the xz-plane (section 7.4) The experimental results and preliminary observations are presented in Section 7.1. 7.1 Experimental Results Figure 7.1 shows the 3D phase-locked measurement results at 7 cross-stream positions of y/R=+1.0, +0.8, +0.4, 0, -0.4, -0.8, -1.0. To minimize light blockage, velocity fields were acquired with the blades at the most windward/leeward positions. Figure 7.1(a), Figure 7.1(b) and Figure 7.1(c) display the contour plots of stream-wise velocity ux , cross-stream velocity uy and span-wise velocity uz respectively, all defined according to Figure 3.1. The vorticity con- tour ωy is presented in Figure 7.1(d). Spatial coordinates x, y and z are non-dimensionalized using rotor radius R or blade span H; velocity and vorticity are non-dimensionalized similar to the 2D results. Blades, struts and tower are indicated in black, and shadow-blocked areas are blanked. 47
  • 68. 48 3D Wake Dynamics Wind Wind Wind Wind Wind Wind Wind (a) Non-dimensionalized stream-wise velocity
  • 69. 7.1 Experimental Results 49 Wind Wind Wind Wind Wind Wind Wind (b) Non-dimensionalized cross-stream velocity
  • 70. 50 3D Wake Dynamics Wind Wind Wind Wind Wind Wind Wind (c) Non-dimensionalized vertical velocity
  • 71. 7.1 Experimental Results 51 Wind Wind Wind Wind Wind Wind Wind (d) Non-dimensionalized cross-stream vorticity Figure 7.1: Contour of wake velocity and wake vorticity, 3D phase-locked experimental results
  • 72. 52 3D Wake Dynamics Tip vortices are represented by the deep blue regions in Figure 7.1(d). Almost circular tip vortices are observed close to the turbine axial plane; moving outboard tip vortex is stretched due to increasing misalignment between the axis of the vortex core and the normal of the measurement plane. The vorticity plot clearly shows inboard tip vortex motions near y/R = 0 and outboard tip vortex motions at two sides of the rotor. At y/R=+0.4, 0, -0.4, -0.8, the release and roll-up of the downwind tip vortice are visible. Both upwind and the downwind tip vortices have negative vorticity, rotating clock-wisely seen from the leeward side. Tip vortex deforms along its downstream convection. The previously mentioned misalignment also influences the observed cross-stream velocity (Figure 7.1(b)). Considering a windward vortex tube at the upwind part (Figure 7.2), due to the misalignment angle ψ, the induced velocity on the top side of the tube has a negative y-component, and the induced velocity at the bottom side has a positive y-component. At the windward side (y/R = +1.0, +0.8, +0.4), these two velocity components result in a blue region on the top and an orange region at the bottom. At the leeward side, the situation is reversed. Since the velocity component in the y-direction increases with misalignment angle, the deepest blue and the deepest orange vortex regions are observed at the most windward and leeward sides of the rotor. The sign of vertical velocity uz alternates due to vortex induction. x y x y yx z u+y u-y y z u+y u+y u-y u-y x xz y u+y u-y xz y Windward Leeward ψ ψ Figure 7.2: Illustration of the influence of misalignment angle on uy The cross-stream velocity plot (Figure 7.1(b)) also shows the wake of vertical turbine blades and horizontal struts. The blade wake is represented by the red vertical wake segments behind the blade, and the struts wake corresponds to the horizontal wake region released around the struts height (z/H = 0.3).
  • 73. 7.2 Tip Vortex Dynamics 53 7.2 Tip Vortex Dynamics Before detailed discussion, some common terminologies are introduced to ease the discussion. Vortex tube is defined as a stream tube consisting of streamlines bound in the vortex region. The orientation of the vortex tube, or vortex tube axis, aligns with the convective velocity of vortex tube and axial velocity is referred to as the velocity component along the vortex axis. The cross-section plane normal to the vortex axis is referred to as vortex plane. 7.2.1 Azimuthal variation of tip vortex circulation In SPIV measurements, the misalignment between the axis of vortex tube and the normal of the measurement plane leads to the derived flow properties (e.g. out-of-plane vorticity) being just the component projected in the normal direction of the measurement plane. φV φH φH φv Vind-H Vind-V XZ Y A B DE C H Lcosθ Isometric view Front view X Z Y L H Measurement plane Normal plane of the vortex tube Vortex tube Γ ψ Figure 7.3: Illustration of bound circulation of a skewed measurement plane Fortunately, the misalignment does not affect the estimation of bound circulation. Consider a straight vortex line of constant circulation Γ in the left plot of Figure 7.3. The measurement plane, an H height L long solid line rectangular, is misaligned with the dashed vortex plane (normal to the vortex tube) by an angle ψ around the y-axis. Misalignment around the x-axis is zero. In the front view of the vortex tube (right plot of Figure 7.3), the rotated measurement plane is projected onto the normal plane of the vortex tube. The circulation of the measurement plane can be derived using following two formulas: uθ = Γ 2πr Γ = ∂Ω udl (7.1) The first formula computes the vortex induced velocity uθ at a distance |r| away from the vortex core center. uθ is the tangential velocity perpendicular to the radius vector r. The
  • 74. 54 3D Wake Dynamics second formula calculates the bound circulation using line integral of the velocity vector along the contour boundary ∂Ω. On the vertical boundaries of the rotated measurement plane, the circulation is calculated as: AB = L 2 cos ψ, AC = L 2 2 cos2 ψ + y2, cos φV = AB AC ΓV = 2 H 2 − H 2 VindV (y) cos φV dy = 2Γ 2π H 2 − H 2 L 2 cos ψ L 2 2 cos2 ψ + y2 dy = Γ π tan−1 y 2L cos ψ | H 2 − H 2 = 2Γ π tan−1 H L cos ψ (7.2) Similarly, the circulation of the horizontal boundaries can be derived as: AD = H 2 , AE = H 2 2 + y2, cos φH = AD AE ΓH = 2 L 2 − L 2 VindH (x) cos φHdx = 2Γ 2π L 2 − L 2 H 2 cos ψ H 2 2 + x2 dx = Γ π tan−1 x 2H | L 2 − L 2 cos ψ = 2Γ π tan−1 L cos ψ H (7.3) Using the trigonometric property tan−1 x + tan−1 1 x = π 2 , we obtain the total circulation: Γtot = ΓV + ΓH = 2Γ π tan−1 H L cos ψ + 2Γ π tan−1 L cos ψ H = Γ (7.4) Equation 7.4 demonstrates that the measured circulation is independent of the misalignment angle ψ. The proof on the misalignment around x-axis is similar. Using this property, vortex strength can be evaluated. In 3D, the strength of tip vortex is determined by the span-wise circulation gradient at blade tips. The time varying AoA leads to the periodical change of bound circulation, hence leads to the azimuthal variation of tip vortex strength. Since the vortex circulation is conserved, we compare the circulation of the first recorded tip vortex (referred to as leading tip vortex) at each cross-stream station. The upwind and downwind released tip vortex are distinguished in the analysis. Tip vortex circulation is integrated in the region bounded by an iso-vorticity contour. The con- tour contains the circular (or elliptical) vortex core and the wake region on which the inboard released vorticity rolls up (known as “vortex tail”). To remove background noise, an appropri- ate vorticity cutoff limit is determined with a sensitivity analysis presented in Figure 7.4. The analysis was performed on an isolated vortex in order to eliminate the influence of “vortex tail” and other surrounding vortical structures. Result shows that the circulation approaches to a constant only when the cutoff limit is sufficiently close to zero. The discrepancies of using different cutoff limits are negligible given the results are normalized. Consequently an arbitrary vorticity cutoff of 0.5 is applied consistently to all vortices.
  • 75. 7.2 Tip Vortex Dynamics 55 −0.1 −0.08 −0.06 −0.04 −0.02 0 0.8 0.85 0.9 0.95 1 1.05 cutoff, ω c /u ∞ Γ/Γcutoff=0 Figure 7.4: Sensitivity analysis of the background cutoff criteria Figure 7.1(b) shows that the leading tip vortex has been convected downstream of the blade at the recorded time, which implies the vortex was released at an earlier time instance. After releasing, the cross-stream flow convection might have shifted the vortex location, so that the observed tip vortex was actually produced at a different y/R, that is, a different azimuthal position θ′. The escaping time ∆t can be derived using the distance from the leading vortex to the blade ∆s, and the average stream-wise velocity ux: ∆t = ∆s ux (7.5) Using ∆t and mean cross-stream velocity uy, the azimuthal angle at which the vortex is actually released can be derived: θ′ = cos−1 R cos θ − ∆y R Where ∆y = uy∆t (7.6) Where θ is the intersection azimuthal angle of the measurement planes and the blade path. Since the accuracy of the correction is influenced by measurement misalignment and non- uniform vortex convective velocity in the y-direction, the corrected δθ is included as horizontal error bars. Figure 7.5 displays azimuthal variation of the leading vortex strength. Both circulation and mean vorticity are plotted. Mean vorticity equals to vortex circulation divided by the area of vortex region (proportional to the number of particles). The circulation is normalized against the strongest circulation at y/R = 0, whereas the mean vorticity is normalized against the strongest value at y/R = −0.4. Vortex strength at the most windward position is not plotted due to light blockage (Figure 7.1(d)). Normalized (absolute) bound circulation of 2D simulation result is also given as the baseline for comparison. Assuming bound circulation outboard of blade tip is zero, the absolute bound circulation is proportional to the circulation of tip vortex. Vertical error bars indicate the uncertainty in estimating averaged results from instantaneous measurements. Overall the measured and simulation results show reasonable agreement at the upwind blade passage. Both the circulation and the mean vorticity reach the peak values near θ = 90◦, and
  • 76. 56 3D Wake Dynamics 0 45 90 135 180 225 270 315 360 0 0.2 0.4 0.6 0.8 1 Azimuthal position θ ° Γ/Γ y/R=0 Upwind vortex Downwind vortex 2D SIM (a) Circulation 0 45 90 135 180 225 270 315 360 0 0.2 0.4 0.6 0.8 1 Azimuthal position θ ° ω/ω y/R=−0.4 Upwind vortex Downwind vortex 2D SIM (b) Mean vorticity Figure 7.5: Azimuthal variation of tip vortex strength decline towards the two sides of the rotor. However, the vortex circulation is stronger at the windward part of the rotor (Figure 7.5(a)), whereas the vorticity is stronger at the leeward side (Figure 7.5(b)). In comparison, the variation of mean vorticity shows better match with the 2D simulation results. Discrepancy between the total and the mean vorticity might be explained by the recorded tip vortices that are at different vortex ages. Since the flow was measured at θ = 0◦, windward released tip vortices (0◦ < θ < 90◦) were produced earlier than the leeward released vortices (90◦ < θ < 180◦). In Figure 7.1(d) the windward vortex cores are larger, and the stream-wise distances between windward leading vortices and turbine blades are greater, both indicating the windward vortices are “older”. By the moment the flow field is recorded, there exist a possibility that tip vortex does not reach its final conserved value, instead, the images capture the process of vortex strengthening induced by the roll-ups. As the windward released tip vortex is “older”, larger amount of vorticity has been transported to the vortex core, resulting in higher total circulation. This roll-up process, however, reduces the strength of mean vorticity due to the roll-in of weaker vortex particle. Besides, the relatively weaker windward mean vorticity is also contributed by longer influence of viscous diffusion. Downwind released tip vortices are much weaker due to the induction of the upwind wake. Similar to the upwind part of the rotor, the strongest tip vortex is released near the turbine axial plane. Based on the circulation (Figure 7.5(a)), downwind vortices have only 20% the strength of upwind vortices, and based on the mean vorticity (Figure 7.5(b)), downwind vortices are 40% weaker. Both the circulation and the mean vorticity are higher in the measured results. 7.2.2 Determination of tip vortex core position and peak vorticity In Section 6.5.1, we argued that the data quality near the shed vortex core is not strongly compromised by reduced particle density. However, this is not true for tip vortex since stronger centrifugal causes significant drop of data quality at the vortex core. Figure 7.6 shows the vorticity plot along two orthogonal cuts through the leading tip vortex of the measurement plane y/R = 0. Strong vorticity fluctuations near the vortex core are clear indicators of low
  • 77. 7.2 Tip Vortex Dynamics 57 data quality. (a) The cuts 0.48 0.49 0.5 0.51 0.52 −12 −10 −8 −6 −4 −2 0 z/H ω z c/u ∞ (b) ux along the vertical cut −0.76 −0.74 −0.72 −0.7 −0.68 −0.66 −15 −10 −5 0 x/R ω z c/u ∞ (c) uy along the horizontal cut Figure 7.6: Vorticity distribution at the vortex core (a) The cuts 0.48 0.49 0.5 0.51 0.52 −15 −10 −5 0 5 z/H ω z c/u ∞ z peak (b) ux along vertical cut −0.76 −0.74 −0.72 −0.7 −0.68 −0.66 −15 −10 −5 0 5 x/R ω z c/u ∞ x peak (c) uy along horizontal cut Figure 7.7: Vorticity distribution away from the vortex core To determine the location of vortex core, two orthogonal cuts are moved away from the vortex core until the first un-distorted vorticity profile is observed. The corresponding cuts are referred to as the critical cuts. The vorticity peak along the critical cuts give the x- and z-coordinates of the vortex center. Connecting the vortex center and the intersection of two cuts gives the critical radius. If the vortex core is set as the center, and critical radius is set as the radius, the “peak vorticity” is evaluated as the mean vorticity of the circle. Assuming particle density is inversely proportional to vortex strength and peak vorticity decays over time, the lowest particle density (i.e. the lowest data quality) is found at the leading tip vortex. This means, if the vorticity of the leading vortex is reliable, the vorticity of downstream tip vortices are also unaffected by data quality, given an identical critical circle is used. The critical radius of the upwind released tip vortex equals to 13.4 mm, and the critical radius of the downwind released tip vortex is smaller (1.7 mm) due to lower vortex strength. Since axial-symmetric tip vortex is implicitly assumed in this method, the uncertainty increases with the deformation of tip vortex. 7.2.3 Tip vortex motions in the xz-plane Using the method outlined in the last section, the locations of tip vortex core are determined. Tip vortex is tracked down until 4R downstream of the rotor before vortical structures become
  • 78. 58 3D Wake Dynamics undetectable. In the results of Figure 7.8, upwind vortices are indicated by the blue circular markers and downwind vortices are indicated by the red square markers. −1 0 1 2 3 4 0 0.4 0.8 z/H y/R=+1.0 −1 0 1 2 3 4 0 0.4 0.8 z/H y/R=−0.4 −1 0 1 2 3 4 0 0.4 0.8 z/H y/R=+0.8 −1 0 1 2 3 4 0 0.4 0.8 z/H y/R=−0.8 −1 0 1 2 3 4 0 0.4 0.8 z/H y/R=+0.4 −1 0 1 2 3 4 0 0.4 0.8z/H y/R=−1.0 −1 0 1 2 3 4 0 0.4 0.8 x/R z/H y/R=0 Upwind vortices Downwind vortices Figure 7.8: Tip vortex trajectory in the xz-plane As an important feature of H-rotor wakes, the mechanism of inboard tip vortex motion is illustrated first. Considering two trailed vortex in Figure 7.9: vortex A is released from the blade tip and vortex B is released inboard of the tip. Mutual induction between the vortices A B dislocates them in opposite direction with respect to each other (B downward and A upward). The height difference immediately results in an inboard motion of the tip vortex A and an outboard motion of the trailed vortex B. Since inboard trailed vortices are usually much weaker than the tip vortex, the global vortex convection is defined by the inboard trajectory of the tip vortex. Moreover, the suction force between two vortices (due to low pressure) also enhances the inboard movement of the tip vortex. The same phenomenon has also been reported behind aircraft wings and in the near wake of an HAWT [13][20]. The main difference with these cases relies upon the strong counteraction of the wake expansion which dominates the vortex convection. In case of VAWT, momentum loss in the vertical direction is compensated by the wake expansion in the horizontal plane, allowing continuous inboard motion downwind of the rotor. According to [14][19], the inboard tip vortex motion of an H-rotor is also contributed by the U-shape wake curvature, in which the vortices near the turbine axial plane convect inboard due to the induction of outboard vortices. Within the rotor swept volume, the inboard vortex path is blocked by the turbine tower and the horizontal struts. The effect of blockage is clearly visible at y/R=+0.4,0,-0.4,-0.8, where the height of in rotor tip vortex stays almost unchanged. Additionally, the outboard
  • 79. 7.2 Tip Vortex Dynamics 59 Wind Vortex B Vortex A Top View Front View Vortex AVortex B vind-A vind-A vind-B vind-B Wing Wind Wing Wind Wing Wind Figure 7.9: Schematics of vortex inboard motion movement of the vortices generated by the struts tends to push the tip vortex outboard (y/R = +0.4, 0, −0.4 of Figure 7.1(d)). Numerical observed immediate inboard tip vortex motion [36] was not seen in the measurements. This observation reveals an important difference between the experiment and the numerical simulation. The presence of tower and struts of an H-rotor prevents the immediate inboard vortex motion within the rotor swept area, which lowers the chance of BVI and consequent detrimental loading condition at downwind blade passage. Outboard tip vortex motions are observed near two sides of the rotor (y/R = +1.0, +0.8, −1.0). Behind the rotor area, the tip vortex restores its inboard motion near the turbine axial plane and keeps moving outboard at y/R = +1.0, +0.8, −1.0. The inboard movements are the quickest at y/R = 0 and y/R = −0.4, where the tip vortex are the strongest (see Section 7.2.1). At these two positions, the inboard tip vortex motion results in a vertical diameter reduction of 26% at 3R downstream of the rotor. The outboard motions is faster at the windward side. 3R behind the rotor, wake diameter has increased by 50% and 22% at the windward and the leeward sides respectively. The outboard tip vortex motion is most likely attributed to the blockage of turbine blades, which forces the vortex sheets lying in the blade path to move outboard. The blockage effect is stronger at the windward side since the motion of advancing blade is opposite to the inflow direction. Figure 7.8 also presents the position of downwind released tip vortex. Tip vortices at y/R = +1.0 and y/R = −1.0 are not detectable due to low vortex strength. In the vertical direction, the relative height between upwind and downwind vortices depends on the vortex motion within the rotor volume. If the tip vortex moves outboard, the roll-up and the downstream convection of downwind tip vorticrs would lie beneath the trajectory of upwind vortex as been
  • 80. 60 3D Wake Dynamics observed at y/R = +0.4, +0.8. Near the turbine axial plane, vortex roll-up pulls the downwind tip vortex above the trajectory of the upwind tip vortex. Once released from blade tip, upwind and downwind vortices start leap frogging until their finally merging into a single vortical structure. As shown in Figure 7.10, mutual induction gives a positive stream-wise induction to the upper vortex and a negative induction to the lower vortex, resulting in faster advancing of the upper vortex and a consequent roll-over of the vortex pair. The rolling motion locally enhances vortex stretching and turbulent diffusion, which contributes to the breakdown of the coherent vortical structure. This process resembles the vortex leap-frogging in the wake of an HAWT [9]. Figure 7.10: Illustration of vortex pair roll-over, y/R = 0 7.2.4 Stream-wise evolution of tip vorticity In order to study stream-wise vortex decays, it is impractical to use time invariant flow proper- ties such as vortex circulation. Here peak vorticity is used as a measure of vorticity evolution. The determination of peak vorticity however poses two challenges. As a point property, the magnitude of peak vorticity is influenced by the misalignment mentioned in Section 7.2.1. Correcting the misalignment is usually difficult because the orientation of vortex tube changes along its convection. Second, the measured vorticity at the vortex core subjects to large uncertainty due to the reduction of particle density (Section 7.2.2). Figure 7.11 shows the stream-wise vorticity evolution at vertical measurement planes. The presented data is not corrected for misalignment. The results of the most windward and leeward sides are not presented due to the large uncertainty at the vortex core. Upwind vorticity is shown in blue and downwind vorticity is shown in red. Vertical error bars indicates the result uncertainties. After releasing, uncertainty reduces as the data quality improves at the vortex core. The uncertainty increases again with the growth of turbulent level 2R behind the rotor. This increment is not visible in Figure 7.11 due to low vorticity strength. Comparing Figure 7.11 and Figure 6.15 clearly shows that the tip vortex in the vertical planes is much stronger than the shed vortex in the mid-span horizontal plane. The leeward released vortex is 20-40% stronger than the windward tip vortex, which is in line with the azimthual variation of mean vorticity as discussed in Section 7.2.1. As for the moment of releasing, the downwind vorticity is much weaker than the upwind re- leased vorticity. Comparing vorticity strength at the same stream-wise positions, the situation varies from station to station. Near y/R = 0, the leading downwind tip vortex is stronger than the upwind tip vortex convected to the same x/R, whereas at outboard stations the
  • 81. 7.2 Tip Vortex Dynamics 61 −1 0 1 2 3 −20 −15 −10 −5 0 ωz c/u∞ y/R=+0.8 −1 0 1 2 3 −20 −15 −10 −5 0 ω z c/u ∞ y/R=−0.4 −1 0 1 2 3 −20 −15 −10 −5 0 ωz c/u∞ y/R=+0.4 −1 0 1 2 3 −20 −15 −10 −5 0 ω z c/u ∞ y/R=−0.8 −1 0 1 2 3 −20 −15 −10 −5 0 x/R ωz c/u∞ y/R=0 Upwind vortices Downwind vortices Figure 7.11: Stream-wise variation of tip vorticity 0T 1T 2T 3T 4T 5T 6T 0% 25% 50% 75% 100% ω nT /ω 0 y/R=+0.8 0T 1T 2T 3T 4T 5T 6T 0% 25% 50% 75% 100% ωnT /ω0 0T 1T 2T 3T 4T 5T 6T 0% 25% 50% 75% 100% ω nT /ω 0 y/R=+0.4 0T 1T 2T 3T 4T 5T 6T 0% 25% 50% 75% 100% ωnT /ω0 0T 1T 2T 3T 4T 5T 6T 0% 25% 50% 75% 100% Turbine rotational period ωnT /ω 0 y/R=0 Upwind vortices Figure 7.12: Decay of tip vorticity
  • 82. 62 3D Wake Dynamics downwind tip vortex is even weaker than the upwind one that has already decayed within the rotor area. Further downstream the variation of vorticity is strongly influenced by the roll-over of vortex pair. At y/R = +0.4, 0, −0.4, the vortex interaction leads to a quick descend of the (stronger) downwind tip vorticity, and a corresponding slowing down of the (weaker) upwind vortex decay. At y/R = 0.8, −0.8, the situation is reversed. This observation shows the roll-over of vortex pair tends to remove the vorticity difference by accelerating the vorticity decay of the stronger vortex and reducing the decay rate of the weaker vortex. The decay rate of upwind released tip vorticity is shown in Figure 7.12. The horizontal axis represents vortex age that measured by turbine rotational period T; and the vertical axis represents the relative vortex strength with respect to the newly released vortex. The first upwind tip vortex behind the rotor area is highlighted by the red box. The decay rate within the rotor swept volume is positively related to the strength of tip vorticity. The strongest vorticity decay is observed at y/R = −0.4, in which the vorticity reduces 92% at the most downwind of the rotor. Vorticity decay at y/R = 0 is slightly slower, achieving 82% vorticity decrease within the rotor volume. In-rotor vorticity at other positions stay around 60-70%. Stronger decay near the turbine axial plane is also contributed by the longer vortex age (3T) in comparison to the outboard stations (2T or 1T). Behind the rotor swept volume, vortex decay is slow and decay rate is modified by the interaction with downwind released tip vortex. Figure 7.12 compares the measured decay rate with a Lamb-Oseen vortex model. By definition [18], the vorticity on a circular contour of radius r is determined by : ω(r, t) = Γ rc 2π exp −r2 rc 2 (7.7) Where x is the stream-wise distance, t is the vortex age, and t0 is the vortex core radius and equals to √ 4νt. The evaluation radius r is the same as the actual radius on which “peak vorticity” is extracted from the measured results. Result shows a reasonable match between measured decay rate and that predicted by the Lamb-Oseen model. Large discrepancies are observed within the rotor area at y/R = 0 and y/R = +0.4. Comparing with the theoretical model, vorticity decay at y/R = 0 is slower in front of the turbine tower (up to 2T) and faster behind the tower; the vortex decay at y/R = +0.4 is constantly faster. Apart from the uncertainty induced by lower quality data and uncorrected plane misalignments, the underlying assumptions of the Lamb-Ossen vortex model might explain the difference. Lamb-Ossen model represents a solution to the laminar Navier-Stokes equations, which assumes 2D axial-symmetrical vorticity distribution without 3D vortex dynamics such as vortex stretching [40]. However, the actual tip vortex might not be completely laminar; vortex deformation makes the assumption of axial-symmetrical vortex invalid; and 3D effect such as vortex stretching could locally modify the vorticity strength.
  • 83. 7.3 3D Wake Geometry 63 7.3 3D Wake Geometry As wake geometry in the vertical xz-plane can be represented by the in-plane tip vortex motion (Section 7.2.3), this section focuses on the wake geometry in the horizontal xy-plane and the vertical yz-plane. Assuming continuous vortex convection, wake geometry is obtained by connecting the spatial locations of the tip vortex core. 7.3.1 Wake geometry in the xy-plane Figure 7.13 displays the wake geometry of the xy-plane at the blade tip height. U-shape wake segments, similar to that at the turbine mid-span plane, are clearly visible. The U- shape geometry is a result of periodical blade motion which trailed vortex along a curved trajectory. Convex and concave wake segments can be distinguished. The convex segments are released from the upwind blade passage and are obtained by connecting upwind tip vortices; the concave segments are released from the downwind blade passage and are obtained by connecting downwind tip vortices. For reference, the ideal turbine wake with no induction (zero induction wake geometry) is plotted in dashed lines. Results show that the geometry of convex wake segments are well-preserved in its downstream transport, while the geometry of concave wake segments are clearly distorted due to the shift of vortex position during the roll-over of vortex pairs. Comparing with the “zero-induction” wake geometry, wake convection in the induction field is much slower. Compared to the zero induction ideal wake, the real convection is much slower in the experimental induction field. The pitch distance between neighbouring wake segments varies with a non-monotonic behav- ior. Phenomena observed in simulation results such as wake stretching and wake curvature [14] modifications are not observed in the present results. 7.3.2 Wake geometry in the yz-plane Wake geometry in yz-plane is displayed in Figure 7.14. This plot gives the cross-section view in the direction of the free-stream flow. Downward pointing arrow indicates the direction of increasing x/R. Because of the vertical wake contraction near y/R = 0 and of the asymmetrical wake expansion between the windward and the leeward rotor, a non-symmetrical wake geometry is observed in the yz-plane. The strongest contraction is observed at the leeward side of the turbine axial plane (y/R = −0.2), and the greatest wake expansion is seen at the windward side. The curvature of the geometry increases further away from the rotor. 7.4 Stream-wise Wake Velocity Profiles To understand the evolution of stream-wise velocity in the vertical measurement planes, ve- locity profiles are extracted at 5 stream-wise positions x/R=2.0, 3.0, 4.0 5.0 and 5.9. The results are presented in Figure 7.15. Assuming the wake region can be measured by the area between the horizontal axis z/H = 0 and the velocity profile, the stream-wise variation of wake area shows good agreement
  • 84. 64 3D Wake Dynamics −1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 −1 −0.5 0 0.5 1 x/R wind y/R (a) Convex wake segment −1 −0.5 0 0.5 1 1.5 2 2.5 3 3.5 −1 −0.5 0 0.5 1 x/R wind y/R (b) Concave wake segment Figure 7.13: Wake geometry in the xy-plane wind y/R z/H Downstream direction Figure 7.14: Wake geometry in the yz-plane
  • 85. 7.4 Stream-wise Wake Velocity Profiles 65 with tip vortex motions in vertical planes. At y/R = +0.4, 0, −0.4, −0.8, the wake area reduces with the inboard tip vortex motion. Conversely, outboard tip vortex motions at y/R = +1.0, +0.8, −1.0 lead to the expansion of low speed wake region. The observed wake contraction is beneficial to the wind farm operation as downstream turbines perceive large volume of undisturbed free-stream and are only exposed to wake deficit of the upwind turbine near the mid-span. 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 z/H y/R=+1.0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 z/H y/R=−0.4 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 z/H y/R=+0.8 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 z/H y/R=−0.8 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 z/H y/R=+0.4 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 z/H y/R=−1.0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 u x /u ∞ z/H y/R=0 x/R=2.0 x/R=3.0 x/R=4.0 x/R=5.0 x/R=5.9 Figure 7.15: Wake velocity profile in xy-plane Similarly to the velocity profile of 2D mid-span plane, local velocity fluctuations are induced along the trajectory of tip vortex. Excluding the influence of vortex induction, the peak velocity deficit is plotted in Figure 7.16. Results show the increase of peak velocity deficit before x/R = 4.0. The highest wake deficit is observed near y/R = 0, and the windward deficit is greater than the leeward one. Downstream of x/R = 4.0, the stream-wise velocity starts to recover closer to the turbine axial plane. The quickest recoveries occur near the windward side of the turbine axial plane at y/R = +0.4 and y/R = 0. Wake recovery at y/R = +0.8 and y/R = −0.4 is slower and the recovery starts 5R downstream of the rotor. Velocity recovery is not observed outboard of the rotor at y/R = +1.0, −0.8. Interestingly the peak deficit of y/R = −1.0 becomes stable downstream of x/R = 5.0 while the velocity deficit keeps increasing inboard of this station (y/R = −0.8). The evolution of peak velocity deficit is influenced by a number of factors, which includes model asymmetry, tip vortex dynamics, and the asymmetrical wake development of the horizontal struts. The larger windward velocity deficit is primarily due to the stronger windward blockage as the advancing blade causes greater flow deceleration than the receding blade at the leeward side.
  • 86. 66 3D Wake Dynamics 2 3 4 5 6 50 60 70 80 90 x/R Peakvelocitydeficit[100%] y/R=+1.0 y/R=+0.8 y/R=+0.4 y/R=0 y/R=−0.4 y/R=−0.8 y/R=−1.0 Figure 7.16: Peak velocity deficit of 3D vertical planes Figure 7.1(a) shows that the stream-wise velocity is generally higher at the leeward region. High velocity deficit near y/R = 0 might be caused by strong induction of inboard tip vortex motion. Since tip vortices also enhance wake recovery through flow mixing and energy transporting across the wake boundary, the stream-wise vortex induction is overcome at around 4R downstream of the rotor, and the wake recovery begins. The asymmetrical wake recovery speed is most likely attributed to the asymmetric wake evolution of the horizontal struts. In Figure 7.1(d), struts wake are represented by the light blue region around the height of z/R = 0.3. The struts wake is the greatest when the strut is in perpendicular to the free-stream direction (i.e. y/R = +1.0 and y/R = −1.0). The convection of the struts wake share similar features to the tip vortex motion in the vertical direction. At the windward side, the struts wake is deflected outboard to a higher z/R, leaving the downstream wake region from z/R = 0 to z/R = 0.3 unaffected; in contrast, the convection of the leeward struts wake follows approximately the same height, letting the inboard wake flow continuously influenced by the struts wake. Inspections of the velocity profile of y/R = −0.8 and y/R = −1.0 (Figure 7.15) shows that the greatest velocity deficits are all observed around z/H = 0.2, which fall within the influencing region of the struts wake.
  • 87. Chapter 8 Uncertainty Analysis Measurement accuracy is influenced by systematic errors and random errors. Systematic errors are caused by system bias which results in constant deviations from the true value. Calibration error, for instance, is a typical systematic error in PIV measurements. Random errors are statistical fluctuations due to inherent imperfection of equipments or measurement techniques. A typical example of random error of aerodynamic measurement results from undesired fluctuations of flow velocity [35]. Uncertainties of instantaneous measurement arise when prescribed quantities (e.g. free-stream velocity) or model operational conditions (e.g. rotational frequency) are not constant during measurements. The certainty level can be improved by averaging increasing numbers of instantaneous sample: ¯M = V + σins 2 √ N (8.1) Where ¯M represents the measured averaged result, V is the true value, σins is the standard deviation of instantaneous measurement and N is the number of samples. A proper number of averaging samples was determined by convergence analysis at one inter- rogation window within the rotor swept area and one window in the far wake (Figure 8.1). The horizontal axis represents the number of samples, and the vertical axis represents the maximum difference between the averaged results of N + 1 samples and N samples. Results show 150 samples ensure the convergence (95% confidence level) of both in-rotor and far wake flow regions. Therefore, 150 instantaneous measurements were taken at each interrogation window. The uncertainties of experimental results are grouped into four categories: • Uncertainty due to variations of free-stream velocity • Uncertainty due to model imperfections and changes of model operational condition • Uncertainty in PIV measurements • Uncertainty in PIV data processing 67
  • 88. 68 Uncertainty Analysis 0 50 100 150 200 0 0.5 1 1.5 2 Number of samples Differenceofmean/u ∞ [%] In rotor Far wake Figure 8.1: Convergence of the mean flow 8.1 Free-stream Velocity In low speed incompressible flow measurements, the variation of free-stream velocity is caused by a number of factors including model blockage, growth of tunnel shear layer, flow turbulence, and flow temperature variation. Since flow is free to expand in the open test section, blockage induced velocity variations are relatively weaker. Considering 50% wake expansion at 4R behind the rotor and 16% reduction of uniform flow area (due to the development of tunnel shear layer) at the same position, the influence of shear layer growth is hardly detectable in the measurement range. Analysis of the turbulent fluctuations shows a variation range from 1% in the free-stream to 25% in the vortex inner core. Variations of flow temperature might result from system related heat sources (e.g. tunnel fan) or the change of weather condition over the testing period. In the experiment the flow temperature was kept within the range from 19.4◦C to 20.8◦C. Assuming the flow obeys ideal gas law p∞ = ρRT, with p∞ being the static gas pressure in pascal, ρ the gas density in kg/m3, T the gas temperature in Kelvin, Rconst the specific gas constant which equals to 287.1 J/(kg·K). At 20◦C, the standard atmosphere pressure is 101325 pa and density is 1.204 kg/m3. As the windtunnel is not completely sealed, the static and the total pressure are assumed constant, hence the change of tunnel temperature is related to a change of flow density: ρ = p∞ RT ⇒ upper bound ρu = 101325 287.1 · (19.4 + 273.15) = 1.206 kg/m3 lower bound ρl = 101325 287.1 · (20.8 + 273.15) = 1.201 kg/m3 (8.2) Assuming the free-stream flow is potential, the velocity variation can be derived using the
  • 89. 8.2 Model Uncertainty 69 Bernoulli’s equation [7]: p∞ + 1 2 ρv2 ∞ = Const =p∞ + 1 2 ρlv2 u = p∞ + 1 2 ρuv2 l ⇒ vl = ρ∞ ρu v∞ = 9.25 m/s vu = ρ∞ ρl v∞ = 9.27 m/s (8.3) Adding the influence of turbulence fluctuations, the free-stream flow varies from 9.24 m/s to 9.28 m/s. 8.2 Model Uncertainty Model induced uncertainties are related to inherent model imperfections and change of model operational conditions during the test. 8.2.1 Model imperfections Inherent model imperfections result from deficiencies in the manufacturing and installation chain, which yields turbine model deviating from its design specifications. In this experiment, the straightness of the steel turbine tower was a constant limiting factor. During the ex- periment it became clear that having a perfectly straight hollow tube of 3 meters is nearly impossible, not even to mention additional bending and distortion during the transporting and the machining process. Referring to Figure 5.3, it is easy to imagine that a non-straight turbine tower could cause strong vibrations at the top part of the turbine. If not properly damped, this vibration could result in a devastating structure failure. During the start-up and slow-down phases, the tower vibration increased dramatically around the resonance range. With the proceeding of the experiment, these repeating cycles lead to an increased tower bending. The resulting blade motion deviated from its circular path, causing corresponding shifts of flow phenomena (e.g. vorticity shedding) at the blade proximity. Besides, the testing model was not entirely axial-symmetric. Due to imperfections during the manufacturing, painting and installation processes, the dimension and weight of two blades were different. Although the discrepancies were compensated by adjusting the tightness of thread rods or adding compensation mass, the inherent rotor asymmetry may not be completely removed. Quantifying the mentioned model imperfections was uneasy, but their potential influence was fully considered in analyses.
  • 90. 70 Uncertainty Analysis 8.2.2 Operational conditions Apart from imperfections that were inherent in the turbine model, uncertainties could also be induced by the variation of turbine model during the test. First, the turbine rotational speed was oscillating. Since the electric motor was only capable of keeping the velocity within a finite range (due to electric jitter), the actually motor velocity varied over time. Overall the turbine rotational frequency oscillated between 13.25 Hz and 13.30 Hz with a mean value of 13.27 Hz. Assuming the reference time of phase locking acquisition was fixed, the uncertainty of tip speed ratio can be determined by: ub = ωr = 2πfr ⇒ub = 41.63 m/s ∼ 41.78 m/s ⇒λ = 4.5 − 0.005 ∼ 4.5 + 0.012 (8.4) Thus the tip speed ratio varies by 0.27%. Second, the measurement accuracy was strongly influenced by blade bending (Figure 8.2). Due to centrifugal forces, turbine radius increased at the mid-span and blade tips, which coincided with the positions of the measurement planes. Based on characteristic flow phenomena such as blade vorticity shedding, corrected radius of 0.51 m was determined and was used to non- dimensionalizes the 2D (at mid-span plane) and the 3D (near blade tip) results. It is worth noting that the actual rotor radius varied with time due to azimuthal variation of aerodynamic forces. Tower Struts Deformed Blade Undeformed Blade Figure 8.2: Schematic of blade deformation (exaggerated) Uncertainty of the triggering and timing system (Standford box) was negligible since the accuracy of the system was in the order of picosecond.
  • 91. 8.3 Measurement Uncertainty 71 8.3 Measurement Uncertainty The quality of PIV images relies on the accuracy of system alignments and calibrations. A laser alignment tool was used to align subsystems in stream-wise and cross-stream directions. Minor misalignment, however, might still exist due to finite beam width or misplacements of model markers. The PIV measurement results are sensitive to two types of misalignment. Misalignment between the calibration plate and the free-stream direction results in the projec- tion of out-of-plane velocity component onto the measurement plane. Misalignment between the calibration plate and the laser sheet introduces systematic error in stereoscopic vector calculations. For all SPIV measurements, self-calibration was applied to manually adjust the measurement plane to the middle of the laser sheet. In the horizontal measurements, a scaling paper was used for calibration. An inspection of corrected images in DaVis shows a displacement uncertainty of 0.5 mm. In the vertical measurements, the calibration was performed by fitting a camera pinhole model using mul- tiple views of a multi-level calibration plate. The calibration uncertainties of vertical plane measurements are summarized in Table 8.1 . Travs. sys. Fit RMS [pixel] Camera scale [pixel/mm] Displacement uncertainty [mm] TS4 0.21 9.36 0.023 TS5 0.18 9.42 0.019 TS6 0.33 9.36 0.036 TS7 0.20 8.20 0.025 TS8 0.53 10.30 0.052 TS9 0.14 10.10 0.014 Table 8.1: Uncertainty of image calibration Since the global flow field was stitched from individual interrogation window, the resulting accuracy was also affected by the uncertainty of traversing system and image stitching. Owing to the limited mechanical accuracy, the coordinate specified by the traversing system might differ from the actual value. Possible misalignment of the traversing system and the incoming flow direction would result in step-wise window shifts and relative rotations between neigh- boring images. Over a large measurement distance, a small misalignment could add up to a significant error. Linear window shifts had been corrected manually by matching character- istic flow features at image boundaries, while image rotation had not been corrected due to the complicity of angle determination. Since flow measurements were performed at different times, flow field misalignment were not completely removed after the corrections. Other factors that might potentially compromise the data quality include non-uniform parti- cle distributions, laser reflections, camera aberrations, and unpredictable equipment motions during the measurement. Some of the mentioned errors, such as non-uniform particle distri- butions, can be detected and corrected during the measurement; errors like image distortions have been accounted in the calibration process; whereas errors like flow-induced camera mo- tions could only be visualized in the image stitching phase.
  • 92. 72 Uncertainty Analysis 8.4 Data Processing The uncertainty induced by data processing is mainly related to the cross-correlation operation. The selection of PIV processing parameters (e.g. interrogation window size, overlap ratio, etc.) has a strong impact on image resolution and results credibility. In the pre- and post-processing phases, additional uncertainties were introduced due to modifications (delete, interpolate, etc.) of image data and velocity vector. At the present measurement scales the cross correlation uncertainty had a lower impact than other sources of uncertainties. Typical values for such an error had been reported less than 0.1 pixel for a range of window sizes down to 32×32 pixels [42]. Transforming to the velocity scale, this is equivalent to a displacement uncertainties of ±0.010 mm in the horizontal measurements and ±0.008 mm in the vertical measurements. Data quality is even lower at strong vorticity regions like the vortex core. Detailed approaches to reduce the influence of these uncertainties can be found in Chapter 6 and Chapter 7.
  • 93. Chapter 9 Conclusions and Recommendations The wake development of an H-type VAWT was investigated using two PIV set-ups: a 2C-PIV measurements at the mid-span plane, and a SPIV measurements at 7 cross-stream vertical planes. This study revealed important characteristics of 3D wake development and provided high quality experimental data for code validation. In this chapter, key observations of the measurement results are summarized in Section 9.1 and recommendations for future work are proposed in Section 9.2. 9.1 Conclusions 9.1.1 2D wake dynamics • Circulation peaks along the windward and the leeward wake segments are induced by wake interactions. In comparison the leeward circulation peaks are stronger. Although the overall trends are similar, 2D simulation overestimates the wake circulation due to the higher lift slope of the airfoil. • Blade-Wake Interaction (BWI) and Wake-Wake Interaction (WWI) trigger the roll-ups of vortical structure by locally strengthening wake circulation at the position of interac- tions. Single circulation peak of the experimental result leads to concentrated vortical structures, whereas simulation predicted multiple peaks result in scattered vortical struc- ture downstream of the rotor. • Shed vorticity decay is faster at the leeward side. Due to the absence of viscosity, simulation underestimates the vorticity decay rate by 10%. • The total wake circulation and the total rotor circulation are zero. • The measured horizontal wake expansion is faster at the windward side. The windward deflection of the tower wake is mainly responsible for this asymmetry. Without modeling 73
  • 94. 74 Conclusions and Recommendations the tower wake, the simulation predicts a slower and more symmetrical wake expansion. At 3.5R downstream of the rotor, the measured wake diameter increases by 41%. • The measured stream-wise velocity profiles deflect to the windward side due to faster windward wake expansion. In comparison the simulation predicted wake velocity is higher. Wake recovery has not been observed until 4R downstream of the rotor, neither in the experimental nor in the simulation results. 9.1.2 3D wake dynamics • The strongest tip vortex is produced near the turbine axial plane. With increasing |y/R| the strength of tip vortex reduces. Downwind released tip vortices are much weaker due to the induction of upwind wakes. • Tip vortex is stronger than the shed vortex in the mid-span position. Vorticity decay within the rotor swept volume accounts for 60% - 90% of the overall decay. Behind the rotor, vorticity decay is influenced by the interaction of downwind-upwind vortex pair. Rate of vorticity decay is proportional to the magnitude of vorticity. • Tip vortex motions in the xz-planes vary from station to station. Close to the turbine axial plane, the tendency of inboard vortex motion is blocked by the turbine tower and the struts while the inboard motion restores behind the rotor swept volume. The rate of inboard motion is positively related to the strength of tip vortex; and the fastest inboard motion is observed at y/R = 0 and y/R = −0.4. Weaker tip vortex strength and stronger blade blockage result in outboard vortex motions at two sides of the rotor, which is stronger at the windward side. • Wake geometry in the xy-plane consists of convex wake segments (trajectory of upwind released vortices) and concave wake segments (trajectory of downwind released vortices). The geometry of the convex wake segments are mostly convected downstream, while the concave wake segments are clearly distorted due to the vortex roll-over. Comparing with the ideal case of no flow induction, the downwind transport of wake segments is slower due to negative stream-wise inductions. • Wake geometry in the yz-plane is non-symmetrical. The strongest wake contraction occurs at the leeward side of y/R = −0.2, and the strongest wake expansion is observed at the most windward side of the rotor. • The stream-wise evolution of wake area is consistent with the tip vortex motion in the vertical direction. Wake contraction inboard of the rotor results in larger volumes of energetic inflow, which benefits the efficiency of downwind turbines. Wake deficits increase until x/R = 4.0 and starts to recover afterwards near the turbine axial plane. Wake recoveries are the quickest at y/R = +0.4 and y/R = 0, while recoveries at the most windward and the most leeward positions are not observed until 5.9R downstream of the rotor. Asymmetrical velocity distribution might be explained by inherent model asymmetry, inboard tip vortex motion, and asymmetrical development of the struts wake.
  • 95. 9.2 Recommendations 75 9.2 Recommendations The present study observes the wake recovery in the vertical direction, while the wake recovery in the horizontal mid-span plane is not observed. To deepen the understanding of wake recovery of an H-rotor, future experiments are encouraged to extend the measurement range further downstream. The horizontal measurement shows asymmetrical wake development at the turbine mid-span position. The understanding of horizontal wake evolution can be improved by examining other span-wise planes. Since vortical structure has already been undetectable at 6R downstream of the rotor, uncorrelated sampling is suggested instead of phase-locked measurement. Detailed flow analyses on cross wake momentum transport and vortex induced flow mixing could help to understand how vortex evolution influences wake recovery. In particular, the roll-over of the upwind-downwind vortex pair deserves an in-depth study of its role in the process of vortex breakdown. Since the presence of tower and horizontal struts are crucial to the development of turbine wake, it is interesting to examine the optimal turbine configurations which not only maximizes the power output but also yields favorable wake characteristics. The resolution of flow fields can be improved by measuring at different blade azimuthal positions. Tests at different tip speed ratios could uncover the variation of wake development with change of rotational speed. The reconstruction of 3D tip vortex dynamics will benefit from increasing numbers of vertical measurement planes in the cross-stream direction. At the numerical side, comparing 2D experimental results with the 3D simulation results will help to understand 3D induction effect at the mid-span plane. In order to reproduce the asymmetrical wake development, it is suggested to model the effect of turbine tower and horizontal struts in simulations. And the experimental results can also be used to validate higher order simulation code (e.g. the hybrid code).
  • 97. References [1] Davis 7.2 - flowmaster product manual, 2007. [2] Open jet facility - focus of the faculty of aerospace engineering. http://www.lr. tudelft.nl/en/research/blinde-paginas/open-jet-facility, 2010. [3] Open jet facility (ojf). http://www.lr.tudelft.nl/en/organisation/ departments-and-chairs/aerodynamics-and-wind-energy/wind-energy/ facilities/open-jet-facility, 2010. [4] Geforce gtx 570 - specifications. http://www.geforce.com/hardware/ desktop-gpus/geforce-gtx-570, 2012. [5] Wind power makcan. http://makcan.ca/solutions/energy-solutions/ renewable-energy/wind-power, 2012. [6] R.E. Altenhofen. Rectification. Manual of Photogrammetry (American Society of Pho- togrammetry, Washington, DC, 1952), page 457, 1952. [7] J.D. Anderson. Fundamentals of aerodynamics, volume 2. McGraw-Hill New York, 2001. [8] M.P. Arroyo and C.A. Greated. Stereoscopic particle image velocimetry. Measurement Science and Technology, 2(12):1181, 1999. [9] D. Baldacchino. Horizontal axis wind turbine (hawt) wake stability investigations. Mas- ter’s thesis, Delft University of Technology, 2012. [10] M.T. Brahimi, A. Allet, and I. Paraschivoiu. Aerodynamic analysis models for vertical-axis wind turbines. International Journal of Rotating Machinery, 2(1):15–21, 1995. [11] P.W. Carlin, A.S. Laxson, and E.B. Muljadi. The history and state of the art of variable- speed wind turbine technology. Wind Energy, 6(2):129–159, 2003. [12] J.O. Dabiri. Potential order-of-magnitude enhancement of wind farm power density via counter-rotating vertical-axis wind turbine arrays. arXiv preprint arXiv:1010.3656, 2010. 77
  • 98. 78 References [13] W.J. Devenport, M.C. Rife, S.I Liapis, and G.J. Follin. The structure and development of a wing-tip vortex. Journal of Fluid Mechanics, 312(67):106, 1996. [14] K.R. Dixon. The near wake structure of a vertical axis wind turbine. Master’s thesis, Delft University of Technology, 2008. [15] G.E. Elsinga, F. Scarano, B. Wieneke, and B.W. Van Oudheusden. Tomographic particle image velocimetry. Experiments in Fluids, 41(6):933–947, 2006. [16] S. Eriksson, H. Bernhoff, and M. Leijon. Evaluation of different turbine concepts for wind power. Renewable and Sustainable Energy Reviews, 12(5):1419–1434, 2008. [17] P. Gipe. Flowind: The world’s most successful vawt (vertical axis wind turbine). http://www.wind-works.org/cms/index.php?id=43&tx_ttnews%5Btt_ news%5D=2194&cHash=d1b21f3bd1f35d9e4804f1598b27bd86, 2012. [18] S. Green. Fluid Vortices: Fluid Mechanics and Its Applications, volume 30. Springer, 1995. [19] C. Hofemann, C.S. Ferreira, K. Dixon, G. van Bussel, G. van Kuik, and F. Scarano. 3d stereo piv study of tip vortex evolution on a vawt. Proceedings of EWEC, Brussels, 2008. [20] D. Hu and Z. Du. Near wake of a model horizontal-axis wind turbine. Journal of Hydrodynamics, Ser. B, 21(2):285–291, 2009. [21] A.K.M.F. Hussain and W.C. Reynolds. The mechanics of an organized wave in turbulent shear flow. J. Fluid Mech, 41(2):241–258, 1970. [22] M. Islam, D.S.K. Ting, and A. Fartaj. Aerodynamic models for darrieus-type straight- bladed vertical axis wind turbines. Renewable and Sustainable Energy Reviews, 12(4):1087–1109, 2008. [23] J. Katz and A. Plotkin. Low speed aerodynamics, volume 13. Cambridge University Press, 2001. [24] K. Kiger. Introduction of particle image velocimetry. Lecture slides. [25] M. Kinzel, Q. Mulligan, and J.O. Dabiri. Energy exchange in an array of vertical-axis wind turbines. Journal of Turbulence, 13(1), 2012. [26] M. Marini, A. Massardo, and A. Satta. Performance of vertical axis wind turbines with different shapes. Journal of Wind Engineering and Industrial Aerodynamics, 39(1):83–93, 1992. [27] I.D. Mays and C.A. Morgan. The 500 kw vawt 850 demonstration project. In Proceedings 1989 European wind energy conference, Glasgow, Scotland, pages 1049–53, 1989. [28] I. Paraschivoiu. Double-multiple streamtube model for studying vertical-axis wind tur- bines. Journal of propulsion and power, 4(4):370–377, 1988. [29] I. Paraschivoiu. Wind turbine design: with emphasis on Darrieus concept. Montreal: Polytechnic International Press, 2002. [30] S. Peace. Another approach to wind-vertical-axis turbines may avoid the limitations of today’s standard propeller-like machines. Mechanical Engineering, 126(6):28–31, 2004.
  • 99. References 79 [31] A.K. Prasad. Stereoscopic particle image velocimetry. Experiments in fluids, 29(2):103– 116, 2000. [32] M. Raffel, C.E. Willert, and J. Kompenhans. Particle image velocimetry: a practical guide. Springer Verlag, 1998. [33] D. Ragni, B.W. Van Oudheusden, and F. Scarano. 3d pressure imaging of an aircraft pro- peller blade-tip flow by phase-locked stereoscopic piv. Experiments in fluids, 52(2):463– 477, 2012. [34] S.J. Savonius. The s-rotor and its applications. Mech. Eng, 53:333–338, 1931. [35] F. Scarano. Lecture notes - course experimental aerodynamics. University Lecture, 2012. [36] C.J. Sim˜ao Ferreira. The near wake of the VAWT, 2D and 3D views of the VAWT aerody- namics. PhD thesis, PhD Thesis, Delft University of Technology, Delft, the Nederlands, 2009. [37] C.J. Sim˜ao Ferreira, K.R. Dixon, C. Hofemann, G.A.M. Van Kuik, and G.J.W. Van Bussel. The vawt in skew: stereo-piv and vortex modeling. 2009. [38] CJ Sim˜ao Ferreira, A. Van Zuijlen, H. Bijl, G. Van Bussel, and G. Van Kuik. Simulating dynamic stall in a two-dimensional vertical-axis wind turbine: verification and validation with particle image velocimetry data. Wind Energy, 13(1):1–17, 2009. [39] D.R. Smith. The wind farms of the altamont pass area. Annual review of energy, 12(1):145–183, 1987. [40] H. Tryggeson. Analytical Vortex Solutions to the Navier-Stokes Equation. PhD thesis, PhD Thesis, V¨aj¨o University, V¨aj¨o, Sweden, 2007. [41] L.J. Vermeer, J.N. Sørensen, and A. Crespo. Wind turbine wake aerodynamics. Progress in aerospace sciences, 39(6):467–510, 2003. [42] J. Westerweel. Analysis of piv interrogation with low-pixel resolution. In SPIE’s 1993 International Symposium on Optics, Imaging, and Instrumentation, pages 624–635. In- ternational Society for Optics and Photonics, 1993. [43] W. Zang and A.K. Prasad. Performance evaluation of a scheimpflug stereocamera for particle image velocimetry. Applied optics, 36(33):8738–8744, 1997.
  • 101. Appendix A Image stitching Function The image stitching function consists of three major steps: standard pattern transformation, overlap detection and area partition, and image stitching. In the first step, the relative image position is detected and converted to three standard alignment patterns as shown in Figure A.1. This step eliminates the need of treating different alignment patterns separately. W2 W1 W2W1 W2 W1 Standard pattern 1: corner-to-corner Standard pattern 2: side-by-side Standard pattern 3: containing Figure A.1: Standard window alignment patterns Image conversion is performed with basic operations such as matrix swap, rotation, matrix mirroring. Table A.1 gives an overview of the matrix operations corresponding to the window patterns displayed in Figure A.2. Each operation is flagged and reverse operations at the end of the stitching module converts the stitched windows to the original pattern. In the second step, the row and column indices of the overlapped area are determined by comparing the leading/ending coordinates. Using detected overlap, the combined rectangular windows are partitioned into sub-windows as shown in Figure A.3. Areas that belongs to neither windows are filled with NaN. If no overlap exists, NaN will be filled across the empty region between two windows. In Figure A.3, dash line represents the boundary of sub-windows, OV and NOV stand for overlapped and non-overlapped windows, subscript l(eft), r(ight), b(ottom) and t(op) indicate the relative position with respect to the overlapped sub-window. The smoothing direction is 81
  • 102. 82 Image stitching Function W2 W1 W1 W2 W2 W1 W2 W2 W2 W2 W1 W1W2 W2 W1 W1 W2 W1 W1 W2 W2 W1 W1 W2 W2 W1 W2W1 pattern 1 pattern 2 pattern 3 pattern 4 pattern 5 pattern 6 pattern 7 pattern 8 pattern 9 pattern 10 pattern 11 pattern 13 pattern 14 pattern 12 Figure A.2: Possible window alignment patterns W2W1 W2 W1 OV_l OV_l OV_t OV_t OV OV OV_b OV_b OV_r OV_r NOV NOV NOV NOVNaN NaN NaN NaN Figure A.3: Standard window alignment patterns
  • 103. 83 Pattern Operation corner-to-corner window arrangement 1 - 2 swap w1 and w2 3 mirror w1 and w2 around y=0 4 swap w1 and w2, then mirror both around y=0 side-by-side window arrangement 5 - 6 swap w1 and w2 7 mirror w1 and w2 around x=0 8 swap w1 and w2, then mirror both around x=0 9 rotate w1 and w2 90◦ clockwise 10 swap w1 and w2, then rotate 90◦ clockwise 11 rotate w1 and w2 90◦ counter-clockwise 12 swap w1 and w2, then rotate 90◦ counter-clockwise containing window arrangement 13 - 14 swap w1 and w2 Table A.1: Converting operation to standard window alignment pattern determined automatically: if the number of overlapped (horizontal) row is greater than the number of overlapped (vertical) column, smoothing will be performed in the x-direction, and vice versa. At overlap regions, simple stitching or linear interpolations can be chosen. Simple stitching uses the data of one window as the data of the overlapped region in the combined image. Linear interpolation uses the boundary value at the overlap and non-overlap regions; the results are added to the mean value of two windows. The effect of smoothening could be improved with higher order interpolation, but this is left for future work.