(4.8 MB)

(4.8 MB)
Development of a Rig and Testing Procedures for the Experimental Investigation of
Horizontal Axis Kinetic Turbines
by
Catalina Lartiga
B.Sc., Catholic University of Chile, 2001
A Thesis Submitted in Partial Fulfilment of the
Requirements for the Degree of
MASTER OF APPLIED SCIENCES
in the Department of Mechanical Engineering
c Catalina Lartiga, 2012
University of Victoria
All rights reserved. This thesis may not be reproduced in whole or in part, by
photocopying or other means, without the permission of the author.
ii
Development of a Rig and Testing Procedures for the Experimental Investigation of
Horizontal Axis Kinetic Turbines
by
Catalina Lartiga
B.Sc., Catholic University of Chile, 2001
Supervisory Committee
Dr. Curran Crawford., Supervisor
(Department of Mechanical Engineering)
Dr. Peter Oshkai, Departmental Member
(Department of Mechanical Engineering)
iii
Supervisory Committee
Dr. Curran Crawford., Supervisor
(Department of Mechanical Engineering)
Dr. Peter Oshkai, Departmental Member
(Department of Mechanical Engineering)
ABSTRACT
The research detailed in this thesis was focused on developing an experimental
testing system to characterize the non-dimensional performance coefficients of horizontal axis kinetic turbines, including both wind turbines and tidal turbines. The
testing rig was designed for use in a water tunnel with Particle Image Velocimetry (PIV) wake survey equipment to quantify the wake structures. Precision rotor
torque measurement and speed control was included, along with the ability to yaw
the rotor. The scale of the rotors were purposefully small, to enable rapid-prototyping
techniques to be used to produce many different test rotors at low cost to furnish a
large experimental dataset.
The first part of this work introduces the mechanical design of the testing rig
developed for measuring the output power of the scaled rotor models with consideration for the requirements imposed by the PIV wake measurements. The task was to
design a rig to fit into an existing water tunnel facility with a cross sectional area of
45 by 45 cm, with a rotor support structure to minimize the flow disturbance while
allowing for yawed inflow conditions. A rig with a nominal rotor diameter of 15 cm
was designed and built. The size of the rotor was determined by studying the fluid
similarities between wind and tidal turbines, and choosing the tip speed ratio as a
scaling parameter. In order to maximize the local blade Reynolds number, and to
obtain different tip speed ratios, the rig allows a rotational speed in the range of 500
to 1500 RPM with accurate rotor angular position measurements. Rotor torque measurements enable rotor mechanical power to be calculated from simulation results.
Additionally, it is included in this section a description of the instrumentation for
measurement and the data acquisition system.
iv
It was known from the outset that measurements obtained in the experiments
would be subject to error due to blockage effects inherent to bounded testing facilities.
Thus, the second part of this work was dedicated to developing a novel Computational
Fluid Dynamics (CFD) methodology to post-process the experimental data acquired.
This approach utilizes the velocity field data at the rotor plane obtained from the
water tunnel PIV test data, and CFD simulations based on the actuator disk concept
to account for blockage without the requirement for thrust data which would have
been unreliable at the low forces encountered in the tests.
Finally, the third part of this work describes the practical aspects of the laboratory
project, including a description of the operational conditions for turbine testing. A set
of preliminary measurements and results are presented, followed by conclusions and
recommendations for future work. Unfortunately, the water tunnel PIV system was
broken and thus unavailable for more than a year, so only mechanical measurements
were possible with the rig during the course of this thesis work.
v
Contents
Supervisory Committee
ii
Abstract
iii
Table of Contents
v
List of Tables
viii
List of Figures
ix
Nomenclature
xii
Acknowledgments
xvii
Dedication
xviii
1 Introduction
1.1 Horizontal Axis Tidal Turbines . . . . . . . . . . .
1.2 Experimental Kinetic Turbine Rotor Investigations
1.2.1 Previous Test Campaigns . . . . . . . . . .
1.2.2 Blockage effects . . . . . . . . . . . . . . . .
1.3 Motivation and Contributions . . . . . . . . . . . .
1.4 Thesis Outline . . . . . . . . . . . . . . . . . . . . .
2 Rig Design
2.1 Water Tunnel Facility . .
2.2 Scaling Parameters . . .
2.2.1 Rotor Size . . . .
2.2.2 Force Estimation
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2.3
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4 Tunnel Blockage Correction Models
4.1 Thrust Based Analytical Models . . . . . . . . . . . . . . . . . . . . .
4.1.1 Momentum Based Model . . . . . . . . . . . . . . . . . . . . .
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2.4
2.5
Finite Element Method (FEM) Modelling . . . .
2.3.1 Failure Criteria and Maximum Deflection
2.3.2 Modal Analysis . . . . . . . . . . . . . .
2.3.3 Summary of the FEM Results . . . . . .
Mechanical Design . . . . . . . . . . . . . . . .
2.4.1 Instrument Structure . . . . . . . . . . .
2.4.2 Belt System . . . . . . . . . . . . . . . .
2.4.3 Submersed Structure . . . . . . . . . . .
2.4.4 The Rotor . . . . . . . . . . . . . . . . .
2.4.5 Yaw System . . . . . . . . . . . . . . . .
Instrumentation . . . . . . . . . . . . . . . . . .
2.5.1 The Drive System . . . . . . . . . . . . .
2.5.2 The Motor . . . . . . . . . . . . . . . . .
2.5.3 Torque cell . . . . . . . . . . . . . . . .
2.5.4 PIV system . . . . . . . . . . . . . . . .
2.5.5 DAQ Rio System . . . . . . . . . . . . .
3 Computational Fluid Dynamic Simulations
3.1 Modelling Approach . . . . . . . . . . . . . .
3.1.1 Porous disk . . . . . . . . . . . . . . .
3.1.2 Domain . . . . . . . . . . . . . . . . .
3.1.3 Boundary Conditions . . . . . . . . . .
3.2 Computational Model . . . . . . . . . . . . .
3.2.1 Governing Equations . . . . . . . . . .
3.2.2 Momentum Source Sink . . . . . . . .
3.2.3 CFX Boundary Conditions . . . . . . .
3.3 CFD Simulation Results . . . . . . . . . . . .
3.3.1 Unbounded Flow Validation . . . . . .
3.3.2 Bounded Flow Results . . . . . . . . .
3.3.3 Tunnel Wall Boundary Growth Effects
3.3.4 Reynolds Dependency Analysis . . . .
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vii
4.2
Blockage Correction Model Development . . . . . . . . . . . . . . . .
4.2.1 CFD Correction Factors . . . . . . . . . . . . . . . . . . . . .
5 Experimental Procedures and Testing Campaigns
5.1 Objectives of the experiment . . . . . . . . . . . . . . . .
5.1.1 Power output . . . . . . . . . . . . . . . . . . . .
5.2 Experiment Protocol . . . . . . . . . . . . . . . . . . . .
5.3 Experimental Blade Sets . . . . . . . . . . . . . . . . . .
5.4 Measurement Error Estimation . . . . . . . . . . . . . .
5.4.1 Error estimation . . . . . . . . . . . . . . . . . .
5.5 Initial Testing Campaign . . . . . . . . . . . . . . . . . .
5.6 Second Testing Campaign . . . . . . . . . . . . . . . . .
5.6.1 Operational Conditions . . . . . . . . . . . . . . .
5.6.2 Experimental Results . . . . . . . . . . . . . . . .
5.6.3 Surface Roughness and Reynolds Number Effects
5.6.4 Estimation of Blockage Effects . . . . . . . . . . .
6 Conclusions
6.1 Rig Design . . . . . . . . . . .
6.2 Computational Fluid Dynamic
6.3 Experimental Study . . . . . .
6.4 Future Work . . . . . . . . . .
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Simulations
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Bibliography
95
A Momentum Theory: The Actuator Disc Concept
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B Finite Element Analysis Modelling
B.1 Geometry and Material Properties .
B.2 Forces Applied to the System . . .
B.3 Maximum Deflection - Results . . .
B.4 Modal Analysis - Results . . . . . .
B.5 Mesh Refinement . . . . . . . . . .
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110
C PIV Theory
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viii
List of Tables
Table
Table
Table
Table
2.1
2.2
2.3
2.4
Table 3.1
Table 3.2
Table 3.3
Full size tidal turbine versus scaled model
Forces at the rotor plane . . . . . . . . .
Dimensions resulting from FEM analysis .
Characteristics of the candidate belts . .
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15
17
22
28
∆ CP (%) with respect theory value for different disc thickness
Cases for mesh dependency study . . . . . . . . . . . . . . .
∆ CP (%) with respect theory value for different mesh configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Maximum CP values . . . . . . . . . . . . . . . . . . . . . . .
Turbine size and flow conditions for additional RANS simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
60
Table 5.1
Table 5.2
Table 5.3
Pumping system frequencies and tunnel inflow velocity . . .
Uncertainties of measurement . . . . . . . . . . . . . . . . .
Pumping system frequencies and tunnel inflow velocity . . .
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Table
Table
Table
Table
Table
Configurations of study for modal analysis . . . . . . . .
Maximum deflections and stresses (Non-yawed condition)
Max.deflections and stresses at 30◦ yaw angle . . . . . . .
Maximum deflections and stresses at 45◦ yaw angle . . . .
Result of modal analysis - natural frequencies [Hz] . . . .
Table 3.4
Table 3.5
B.1
B.2
B.3
B.4
B.5
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ix
List of Figures
Figure 1.1
(a)
(b)
(c)
Figure 1.2
(a)
(b)
Tidal Turbine Industry . . . . . .
Tidal Generation Ltd . . . . . . . . .
Marine Current . . . . . . . . . . . .
Lunar Energy . . . . . . . . . . . . .
Actuator disk concept in open and
Unbounded domain . . . . . . . . . .
Bounded domain (e.g. water tunnel)
Figure 2.1
Figure 2.2
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
Figure
2.3
2.4
2.5
2.6
2.7
2.8
2.9
2.10
2.11
2.12
2.13
2.14
2.15
2.16
2.17
2.18
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bounded flows
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3
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3
3
6
6
6
Water tunnel facility . . . . . . . . . . . . . . . . . . . . . .
The energy extracting stream-tube of a wind turbine (adapted
from [1]) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Schematic of the testing rig . . . . . . . . . . . . . . . . . . .
FEM tube model of the testing rig . . . . . . . . . . . . . . .
Schematic operation . . . . . . . . . . . . . . . . . . . . . . .
Key components of the rig . . . . . . . . . . . . . . . . . . .
Components of the instrument structure . . . . . . . . . . . .
Rig for belt testing . . . . . . . . . . . . . . . . . . . . . . .
Submerged support structure . . . . . . . . . . . . . . . . . .
Model of fairings covering the submerged structure . . . . . .
Rotor assembly . . . . . . . . . . . . . . . . . . . . . . . . .
Yaw system operation . . . . . . . . . . . . . . . . . . . . . .
PIV system layout . . . . . . . . . . . . . . . . . . . . . . . .
Experiment system schematic . . . . . . . . . . . . . . . . .
Drive system . . . . . . . . . . . . . . . . . . . . . . . . . . .
Performance curve Parker Motor HV233 . . . . . . . . . . . .
Novatech installation schematic . . . . . . . . . . . . . . . .
General schematics of PIV system . . . . . . . . . . . . . . .
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x
Figure 2.19
Figure 2.20
CompactRio package . . . . . . . . . . . . . . . . . . . . . .
LabView interface . . . . . . . . . . . . . . . . . . . . . . . .
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44
Figure 3.1
Figure 3.2
Figure 3.3
Quarter domain water tunnel model (ANSYS CFX) . . . . .
CFX quarter domain boundary conditions . . . . . . . . . . .
CP v/s CT for turbulent flow conditions in bounded domain
with opening boundary conditions . . . . . . . . . . . . . . .
CP v/s CT for turbulent flow conditions in water tunnel domain
CP values for a wider range of Thrust Coefficients . . . . . .
Boundary layer effect for a rotor diameter 15 mm (9% blockage
ratio) referenced to tunnel conditions . . . . . . . . . . . . .
CP v/s CT , Unbounded domain . . . . . . . . . . . . . . . .
CP increment v/s blockage ratio at CT = 8/9 . . . . . . . . .
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Figure 3.4
Figure 3.5
Figure 3.6
Figure 3.7
Figure 3.8
Figure 4.1
Figure 4.2
Figure 4.3
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Actuator disk model in a closed tunnel section . . . . . . . .
Trend of CP v/s CT in water tunnel and unbounded domains
CFD-computed corrected velocity to inlet velocity ratio for
different blockage ratios and operational conditions . . . . . .
Figure 4.4
Comparison between analytical and CFD power coefficient
corrections (all values corrected to free-stream, CT referred
to tunnel conditions) . . . . . . . . . . . . . . . . . . . . . .
Figure 4.5
Correction curve for the experimental testing referenced to
tunnel conditions . . . . . . . . . . . . . . . . . . . . . . . .
(a) Ratio of corrected velocity to tunnel velocity v/s axial induction
factor for a 9% blockage ratio . . . . . . . . . . . . . . . . . . .
(b) Increment in power coefficient v/s axial induction factor for a 9%
blockage ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . .
71
Figure
Figure
Figure
Figure
Figure
Figure
Figure
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5.1
5.2
5.3
5.4
5.5
5.6
5.7
Frictional Torque - Dec. 2010 . . . . . . . . . . .
CP v/s λ Results Dec. 2010 . . . . . . . . . . .
α (deg) v/s r/R . . . . . . . . . . . . . . . . . .
Re v/s r/R . . . . . . . . . . . . . . . . . . . . .
CP v/s λ at low water tunnel velocity (rough) .
CP v/s λ at high water tunnel velocity (rough) .
CP v/s λ at high water tunnel velocity (smooth)
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xi
Figure 5.8
Figure
Figure
Figure
Figure
Figure
Figure
Figure
5.9
5.10
5.11
5.12
5.13
5.14
5.15
CP v/s λ at high water tunnel velocity, 1.0X and 1.5X smooth
blades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
CL v/s α, forced transition at 0.1 chord . . . . . . . . . . . .
CL v/s α, forced transition at 0.3 chord . . . . . . . . . . . .
CD v/s CL xtr=0.1 . . . . . . . . . . . . . . . . . . . . . . .
CD v/s CL xtr=0.3 . . . . . . . . . . . . . . . . . . . . . . .
CP v/s λ 1X rough surface blade - correction bounds . . . .
CP v/s λ 1X smooth surface blade - correction bounds . . . .
CP v/s λ 1.5X rough surface blade - correction bounds . . . .
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Figure A.1
An energy extracting actuator disk and stream-tube (adapted
from the Wind Energy Handbook [1]) . . . . . . . . . . . . . 101
Figure B.1
Figure B.2
Figure B.3
Rig structure modelling . . . . . . . . . . . . . . . . . . . . . 107
Rig structure modelling . . . . . . . . . . . . . . . . . . . . . 108
Mesh analysis (M odel10 ) . . . . . . . . . . . . . . . . . . . . 112
Figure C.1
Numerical processing flow-chart DPIV . . . . . . . . . . . . . 115
xii
Nomenclature
Chapter 1
V0
UF
Pwt
Punb
C
W
ui
pi
UC
CT,wt
CT,unb
CP,wt
CP,unb
y+
Glauert’s equivalent axial freestream velocity
Bahaj’s equivalent open speed
Power in the water tunnel domain
Power in the unbounded domain
Cross sectional area of the water tunnel
Cross sectional area at the far wake
Axial velocity at location i
Pressure at location i
Corrected axial velocity to free stream conditions
Thrust coefficient characteristic of water tunnel domain
Thrust coefficient characteristic of unbounded domain
Power coefficient characteristic of water tunnel domain
Power coefficient characteristic of unbounded domain
Non-dimensional wall distance
xiii
Chapter 2
CP
λ
ρ
Ω
P
R
U∞
U
U0
Rw
a
Re
A
T
γ
FX
FZ
σV M
σi
[K]
θi
[M ]
ωi2
ΩEi
L
c
D
Rec
ReD
Tf rictional
Thydro
Treact
Power coefficient
Tip speed ratio
Water density
Angular velocity
Power
Radius of the Rotor
Axial velocity of the undisturbed free stream
Stream velocity
Axial inflow velocity in the water tunnel
Radius of the wake expansion
Axial induction factor
Reynolds Number
Cross sectional area at the disc
Thrust force
Angle of Yaw
Maximum Thrust force aligned to the axis of the turbine
Maximum Thrust force orthogonal to the axis of the turbine
Von Mises stress
Stress in the i direction
Stiffness matrix
Mode shape vector
Mass matrix
Eigenvalue i
Natural frequency of a structure of mode i
Characteristic length
Chord length
Rotor disc diameter
Reynolds Number based on chord length
Reynolds Number based on rotor diameter length
Frictional torque
Hydrodynamic torque
Reaction torque
xiv
Chapter 3
χ
CT
U0
ρ
t
D
K −Ω
Re
u
p
τ
(SM )
u
ū
u0
K
UZ
US
popening
pspec
Un,wall
τw
Uinlet
Uspec,X
Uspec,Y
Uspec,Z
paverage,outlet
Uwall
CP
CT
a
y+
Atunnel
Momentum sink
Thrust coefficient
Axial inflow velocity in the water tunnel
Water density
Thickness of the disc
Diameter of the scaled rotor
Equation to model turbulence
Reynolds Number
vector velocity
pressure
stress tensor
External momentum sources
Turbulent Vector velocity
Mean velocity
Random velocity fluctuation
CFX Momentum Source Coefficient
Velocity in the Z axis
Flow speed in the streamwise direction
Pressure at the Opening boundary surface
Pressure specified at certain surface
Velocity normal to the wall
Shear stress
Velocity specified at inlet surface
X axis velocity component specified at inlet
Y axis velocity component specified at inlet
Z axis velocity component specified at inlet
Average pressure over the outlet surface
Vector velocity at the wall surface
Power coefficient
Thrust coefficient
Axial induction factor
Non-dimensional wall distance
Water tunnel cross sectional area
xv
Chapter 4
CP
CT
a
V0
U0
UC
UF
ui
pi
CP,unb
CP,wt
CT,unb
CT,wt
Pwt
Punb
C
W
Ucorr
K
Power coefficient
Thrust coefficient
Axial induction factor
Glauert’s equivalent axial freestream velocity
Axial inflow velocity in the water tunnel
Corrected axial velocity to free stream conditions
Bahaj’s equivalent open speed
Axial velocity at location i
Pressure at location i
Power coefficient characteristic of unbounded domain
Power coefficient characteristic of water tunnel domain
Thrust coefficient characteristic of unbounded domain
Thrust coefficient characteristic of water tunnel domain
Power in the water tunnel domain
Power in the unbounded domain
Cross sectional area of the water tunnel
Cross sectional area at the far wake
CFD corrected axial velocity
CFX Momentum Source Coefficient
xvi
Chapter 5
Pwt
τrotor
Ω
CP,wt
ρ
U∞
R
λ
α
CL
CD
r
U N C.RX
SX
M
UNC
Power in the water tunnel domain
Measured reaction torque
Angular velocity
Power coefficient in water tunnel before correction
Water density
Axial velocity of the undisturbed free stream
Radius of the Rotor
Tip speed ratio
Angle of attack
Lift coefficient
Drag coefficient
Local position along blade
Random uncertainty estimation of X measurement
Standard deviation of the sample X
Sample size
Total uncertainty estimates
xvii
ACKNOWLEDGEMENTS
I wish to thank all those who helped me to complete this project and turned this
graduate time into a great experience. Without their support this work may not have
been possible.
My sincere gratitude to my supervisor Dr. Curran Crawford, for his patience,
support, and guidance through all the stages in this learning process. I really appreciate the time Dr. Crawford spent helping me to develop understanding of my
subject of study and helping me to solve practical aspects of my work. I would like
to extend my thanks to Rodney Katz, Oleksandr Barannyk, and Patrick Chang for
their advice and hands-on help with the practical execution of my experiment; and
Heshan Fernando for his work on the rig design.
And last but not least, my deepest gratitude goes to my family and Patricio, for
their love and support over all these years.
xviii
DEDICATION
To Patricio, for his vision and his encouragement through this journey
Chapter 1
Introduction
As a result of the Kyoto Protocol and the Copenhagen International Conference on
Climate Change, several industrialized countries have committed to reduce Green
House Gas (GHG) emissions and to increase electricity generation using low-carbon
intensive technologies. Consequently, emerging economies have recognized the potential role of renewable energies within a portfolio of electric power generation projects.
Research on renewable energy technologies has become a priority in order to develop a
cost-competitive green technology capable of providing reliable and predictable access
to energy, and allowing countries to reach their GHG reduction targets.
In this context, kinetic turbines, as mechanical energy extracting devices, are a
choice for environmentally-friendly production of alternative energy in the near future.
Wind turbines, tidal turbines and in-stream turbines are the key devices being developed. Although wind turbines are considered a mature technology, already installed
in several locations and providing energy to the grid, there is still much research being
carried out to better understand the wakes of single devices and turbine arrays. Many
studies on blade profiles have been carried out in the aeronautic industry, however
to fully understand how blade geometry affects the flow downstream of the rotor, in
turn affecting the turbine performance, experimental studies on vortex wakes have
been recently performed [2]. A comprehensive summary of several experiments done
and numerical studies performed on wind turbines for both near and far wakes is
presented by Vermeer and Sorensen [3].
Regarding marine turbines, not much has been established as standard design yet
in the industry. The present designs for marine turbines are basically an adaption
of conventional wind turbines, taking into account the inherent differences of devices
2
harnessing the kinetic energy of marine currents instead of air. Comprehensive studies
and experiments are required in order to secure and strengthen the application of this
technology. As wind turbines are more familiar to the reader, a presentation of tidal
turbine technology is presented next, although the experimental rig and techniques
developed in this thesis are applicable to all forms of kinetic turbine testing.
1.1
Horizontal Axis Tidal Turbines
Energy from marine currents seems to be a reliable and perhaps more importantly
a predictable source of electricity generation [4]. The typical resource referred when
talking about marine turbines are the tides, caused by the gravitational forcing of
the sun and moon on the oceans. Two other water-based kinetic turbine applications
also exist: run-of-river turbines in freely flowing rivers, and ocean-based turbines
set in ocean flows largely driven by wind stress, such as the Gulf Stream, or ocean
circulation driven by surface heat and freshwater fluxes. In all cases, water-based
kinetic turbines offer a higher power density than other types of renewable sources
(such as wind). Since it is possible to identify the sites where sea flows are channelled
due to topographies, it makes possible to locally study the source itself in order to
better predict the energy output.
Since the design of Horizontal Axis Tidal Turbines (HATTs) is an emerging area,
and even if the majority of these devices present a conventional design setting a rotating shaft in line with the flowstream, it is possible to find as many different types of
turbines as companies getting into the market. HATTs development has widely benefited from the wind industry and their experience with axial rotor machines. In the
same way, several companies with tidal stream technologies under development have
been strongly influenced by the predominantly open three-bladed rotor design. Other
companies have moved to in-stream turbines, taking advantages of flow acceleration
[5].
Fig. 1.1 illustrates the mix of technological approaches. Subfigure (a) corresponds
to the Tidal Generation Ltd company. The turbine consists of a three-bladed, upstream pitch controlled rotor, with a drivetrain and power electronics inside the nacelle.A 500 kW prototype is currently operating at the European Marine Energy
Centre (EMEC) [6], with a commercial machine rating at 1 MW. Subfigure (b) is a
dual two-bladed rotor built by Marine Current Turbine, the biggest HATT installed
3
in the ocean (Strangford Narrow), generating 1.2 MW. Finally, subfigure (c) displays
the Lunar Energy ducted turbine. Ducted turbines have smaller rotor diameters and
a shroud that accelerates the incoming flow, with a 500 kW prototype not yet tested
in ocean, and a 1 MW device under development [5]. Not shown in figure, Nova
Scotia Power has installed a 1 MW in-stream tidal turbine in Minas Passage of the
Bay Fundy, to explore the feasibility of harnessing tidal energy on a commercial scale
[7].
(a) Tidal Generation Ltd
(b) Marine Current
(c) Lunar Energy
Figure 1.1: Tidal Turbine Industry
1.2
Experimental Kinetic Turbine Rotor Investigations
An important amount of knowledge from wind turbines and classical marine propellers
can be applied to the design and operational analysis of marine turbines [1, 8]. However, relevant differences inherent to flow characteristic and fluid properties of marine
turbines, such as density, high Reynolds number, viscosity, turbulence, cavitation, etc,
must be taken into account in the development processes of these machines. Continued experimental investigation is required to validate prediction codes and designs in
this field, as well as that of wind turbines, for which experimental data is also sparse.
4
1.2.1
Previous Test Campaigns
There have been efforts done to characterize the performance of marine extracting energy devices and evaluate the energy resources [9, 10]. The following section presents
a summary of the most relevant test campaign performed so far in this area.
Two physical tests were carried out at the University of Edinburgh [11, 12] for validation of numerical simulations of energy extraction based on the actuator disk concept. The testing considered several operational conditions for different disk porosities
with free surface. It was found good agreement between numerical simulations of wake
velocity and experimental data. This lead to the conclusion that numerical models
can outline first results regarding wake development downstream of turbines.
A contra-rotating tidal turbine of 0.8 m rotor diameter (1/30th scale) was designed
and tested at the University of Strathclyde, UK [13]. The results of this laboratory
testing were used for the design and construction of a prototype of 2.5 m diameter to
be tested in the open ocean, to finally become a grid-connected device.
Related to industry development, a scaled model of a commercial turbine was
tested in a circulating channel at Southampton University to verify power output
prediction [14]. The horizontal axis turbine model had a 0.4 m diameter (1/30th
scale), and experimental data was acquired for varied channel flow speeds, blade
pitch angles, and rotor speed and yaw angle. The results obtained were compared to
a commercial Blade Element Momentum Theory (BEM) computer package, where if
was found that measured power output was higher than the simulated values for high
angles of attack. Moreover, Bahaj [15] carried out experimental studies on a 0.8 m
diameter Marine Current Turbine model in a cavitation tunnel and tank test. It was
found that interference between the twin rotors was not significant, providing also
useful information for the hydrodynamic design and experimental data for numerical
model simulations, such as CP vs λ performance curves.
Measurements on water surface elevation have also been performed to explore
blockage-type effects taking place around rotors. Investigation of a 0.4 m diameter
rotor shown exaggerated water level variation [16], however the author pointed out
that a reasonable variation in flow level and velocity should be expected in a full scale
array. This experimental investigation highlighted the relevance of estimating optimal
cross-sectional area versus power output of turbines (array) within a constrained
area, such as a channel. Another testing project to explore turbine interaction was
developed at University of Strathclyde [17]. Different array configurations of two-
5
bladed rotors of 25 cm diameter were tested at a towing tank having a maximum
velocity of 0.47 m/s. A significant power output reduction was found for in-line
turbine arrays, however an optimal array configuration was found that optimized
energy production, heading for an array efficiency of 100 %.
At this point, we can recognize that more experimental data is needed to validate
designs and simulations for emerging HATT. All types of kinetic turbine designs
(including wind turbines) can benefit from experimental studies.
1.2.2
Blockage effects
A common issue that arises in this type of experimental testing is that Reynolds
similitude is improved with larger scale models. Fortuitously, the behaviour of rotor
wake vorticity is relatively insensitive to Reynolds number [3]. However, for a larger
ratio of the rotor swept area to the tunnel section area, the greater the associated error
due to blockage. Consequently, larger models less accurately predict the performance
of the full scale turbine. Physically, the walls of the water tunnel constrain the
flow and cause an increment in the velocity around the rotor, compared to the inlet
velocity.
A simple model of the turbine takes the rotor as a thin disc plane that extracts
energy from the stream as the flow passes through it. This approach is known as
the actuator disc concept, and is explained in Appendix A. The energy extraction
done by the turbine implies a drop in static pressure in the area right after the disc
plane, which downstream causes a reduction in the velocity and cross sectional area
expansion of the streamtube through the rotor.
This situation is depicted in Fig. 1.2a, if the turbine is placed in an unbounded
domain. It is assumed that flow at constant pressure p0 surrounds the stream-tube
and the flow velocity remains undisturbed U0 everywhere outside the stream-tube
surrounding the disk. Conversely, if the turbine is placed in a constrained domain,
such as in a water tunnel section as shown in Fig. 1.2b, there is a change in the
velocity and pressure that surround the stream-tube compared to the far upstream
(undisturbed) conditions. This effect leads to higher forces and power outputs measured in the bounded domain relative to unbounded flow conditions around the real
machine. Conversely to propeller testing which create contracting wakes, this block-
6
Unbounded domain
Undisturbed
Velocity (Uo)
Uo
Uo
Velocity
across the
disc < Uo
Uo
Water tunnel section
po
Wake velocity << Uo
Undisturbed
Velocity (Uo)
Velocity > Uo
Velocity
across the
disc < Uo
Uo
Velocity > Uo
Wake velocity << Uo
po
po
Far Upstream
Disc
Far downstream
(a) Unbounded domain
Pressure ≠ po
Far Upstream
Disc
Far downstream
(b) Bounded domain (e.g. water tunnel)
Figure 1.2: Actuator disk concept in open and bounded flows
age is not negligible for kinetic turbines which extract energy from the flow and cause
flow expansion in the wake behind the rotor.
In the past decades, several efforts have been made to provide a suitable methodology to correct for wind and water tunnel blockage effects [18–20]. To date, these
methods have been based on the axial momentum theory representing this tunnel
interference by an equivalent free stream velocity. Analytical expressions correlating
this equivalent open flow velocity to thrust coefficient are used to correct the characteristic power coefficient, and consequently real power output [15, 18–21]. However,
the validity of these analytic corrections as the blockage ratio, the turbulence level,
and rotor loads increase, has not been clearly defined. These factors might affect
the flow field in the water tunnel used in the current work in such a way that the
assumptions from which the analytical corrections were derived are not longer valid.
Additionally, the need for a new post processing methodology arises when thrust data
is not available in the experimental testing. In the current work, due to the small
size of the rotors, it is impractical to measure with any accuracy the thrust force of
the rotor itself.
1.3
Motivation and Contributions
The purpose of this thesis research was to build a rig and develop associated testing
methods for the physical testing of scaled models of kinetic turbines in an existing
7
water tunnel facility. The experimental information generated by the testing could
then be used for turbine performance assessment, rotor design efforts, and validation
of numerical prediction codes. The rig was intentionally designed for small rotors,
so that many blade sets could quickly be produced using Fused Deposition Modeling
(FDM), a rapid prototyping technique producing Acrylonitrile-Butadiene-Stryrene
(ABS) or polycarbonate parts in 3D, thereby allowing the testing of a wide range of
rotors to produce a rich set of data. Any scaled model has limitations due to the scaled
physics of the facilities and rig, as well as the attainable accuracy of the instruments
used for measurement. This project therefore focused specifically on developing a
precision testing rig with the capability to properly scale operational conditions of
real machines.
The experimental study described in this work includes the use of Particle Image
Velocimetry (PIV) techniques to obtain quantitative information about the vector flow
field at the rotor plane and upstream/downstream. Flow measurements are obtained
at various rotor azimuthal positions at the same time that power measurement are
taken. The intention is to use this information in future studies in order to validate
potential flow and Computational Fluid Dynamics (CFD) simulations that resolve
wake features.
It is important to note that accurate thrust force measurements are not possible for
the size of the scale model built. Since PIV data will be available from the experiment
anyway, a novel actuator-disk CFD-PIV methodology was developed to post-process
the measured experimental data to properly account for tunnel blockage effects in the
absence of thrust measurements [22, 23].
Although not detailed in this thesis, the CFD simulation modelling approach was
also applied to a study [24] looking at recommended testing procedures for full-scale
turbines in-situ. In particular, the study looked at blockage effects in comparison between various modelling approaches including complete CFD with explicit resolution
of the blades. Recommendations were supplied to the authors of tidal turbine testing
standards currently in development related to acceptable testing parameters to avoid
erroneous performance estimates through testing in constrained conditions.
Unfortunately, the water tunnel PIV equipment was broken for an extended period covering the entire latter half of the thesis period, and therefore only an initial
mechanical measurement test campaign can be presented in this thesis as an initial
application of the rig. Progress was also delayed by a broken torque transducer which
8
had to be returned to the UK for servicing after a difficult fault-diagnosis process.
In addition, a problem with the driving stepper motor causing pull-out and severe
vibration that was only finally resolved by replacing the motor.
1.4
Thesis Outline
This thesis consist of five chapters, organized as follows. Chapter 2 details the mechanical design of the rig focused on ensuring accurate measurements could be taken
with the forces involved, and that PIV data could be gathered through a range of
operating conditions. Chapter 3 presents the CFD simulations used to study rotor
behaviour in unbounded and bounded domains, leading to the work presented in
Chapter 4 carried out to deal with tunnel blockage effects. Chapter 5 then presents
the initial experimental campaigns carried out to test the operation of the rig, in
the absence of PIV measurements due to protracted equipment breakdown. Finally,
Chapter 6 summaries the work and provides direction for follow-on use of the rig once
the PIV system is operational.
9
Chapter 2
Rig Design
This chapter describes the main aspects that were involved in the mechanical design
of an experimental apparatus for the investigation of the hydrodynamic performance
of kinetic turbines. The rig was initially developed with a view to testing HATT. The
model parameters were therefore sized to scale down a typical HATT device of 17 m
diameter full size, which is expected to generate about 1 MW if is placed in a free
stream of maximum velocity of 3 m/s when rotating at approximately 20 Revolutions
per Minute (RPM).
It is of particular interest to accurately estimate the dimensionless coefficients that
characterize the hydrodynamic performance of these types of turbines. The focus
of the experimental design is therefore on power output measurements. Obtaining
quantitative information of the flow field in the near wake, which is approximately
up to one rotor diameter downstream [3], is the other primary objective, as this
data can be used to directly validate CFD and potential-flow simulation codes. The
latter directly simulate vorticity (wake) evolution, making experimental validation
with PIV-derived wake trajectories very useful.
The final testing rig design enables measurement of the reaction torque of the rotor
under different inflow tunnel velocities and rotational speeds. The output power
can then be calculated as a function of the operational conditions. In addition,
the rig design leaves an area free from obstruction (undisturbed flow) in the near
wake downstream the rotor for the quantitative study of the flow field. Within this
undisturbed section, the velocity field will be estimated using PIV techniques, which
also provides the information required to post process the measured torque data and
to validate numerical prediction codes [23].
10
This chapter is comprised of the following sections:
• Section 2.1 introduces the water tunnel facility.
• Section 2.2 details the scaling parameters used to determine the appropriate
physical size for the models, an estimation of the forces in the system, and
testing requirements. These serve as a set of requirements for the mechanical
design of the scaled-model.
• Section 2.3 presents the Finite Element Method (FEM) for the mechanical rig
design, including static deflection and modal analyses carried out to determine
the minimum size of the main parts of the rig.
• Section 2.4 presents the mechanical rig design including a description of the
mechanical components, features, and capabilities of the finalized testing rig
design.
2.1
Water Tunnel Facility
The water tunnel shown in Fig. 2.1 utilized in the current study at the University of
Victoria (UVic) is a model 504 25 cm re-circulating type from Engineering Laboratory
Design, INC.
Figure 2.1: Water tunnel facility
It is composed of a test section, a filtering station in line, and a circulating pump
system with variable speed. The water tunnel has an interior cross sectional area of
11
45 cm width by 45 cm depth, and 2.5 m of working length. The sidewalls and floor
of the test section are fabricated of clear transparent acrylic. The tunnel usually is
typically operated with a free surface for ease of use, but an acrylic cover is available
to close the working section and allow for flow through the full section with slight
pressurization. A maximum flow speed of 2 m/s can be reached in this setup, and
1 m/s in the open configuration. For this experiment, the tunnel will operate fully
enclosed, so that higher flow speeds can be used, increasing the model Reynolds
numbers and providing higher forces to maximize the signal to noise ratio of the
measurements. The flow depth is also maximized to avoid free-surface and blockage
effects to the greatest extent possible in the testing facility.
2.2
Scaling Parameters
The analysis and design of HATTs is a new area of endeavour, however the basic
flow physics are quite similar to that of Horizontal Axis Wind Turbines (HAWTs).
Considering these similarities, it is possible to apply the simple momentum and blade
element theories used for wind turbines [3] to the modelling of tidal turbines and
power output estimation.
Wind turbine performance is typically described in a non-dimensional manner in
terms of the power coefficient CP as a function of the tip speed ratio λ. A Buckingham’s Pi theory applied to turbine parameters leads to the result that these two
dimensionless groups are the key non-dimensional parameters to define a rotor’s performance. λ is defined as the ratio of the rotor rotational speed times the blade tip
radius to the free-stream velocity, as shown in Eq. (2.1), where Ω is the rotor angular
velocity.
λ=
ΩR
U
(2.1)
The power coefficient CP is defined as the ratio of the power extracted to the
power available in the stream that goes through the rotor area, as shown in Eq. (2.2).
CP =
P
3 πR2
1/2ρU∞
(2.2)
12
where P is the power extracted by the rotor, ρ is the density of the fluid, U∞ is the
velocity of the undisturbed free stream, and R is the radius of the rotor. The theoretical maximum value for the power coefficient is given by the Betz limit, CP = 0.593
for conventional wind turbines [1]. Based on tidal and wind turbine similarities, this
expression will be utilized for the performance study of tidal turbines.
For the primary scaling parameter of the tidal turbine device, the tip speed ratio
λ will be used. Is well known in the wind industry that there is an optimal λ range,
for a given number of blades, that maximizes the power extraction of HAWTs. Thus,
for future design applications of HATTs it is desirable to identify and compare the
optimal operational range to that of HAWTs.
The scaled turbine will be tested across a range of tip speed ratios λ in the range
of 2-8 corresponding to maximum power production [1, 2, 15]. Since the maximum
inlet velocity in the tunnel facility U0 is 2 m/s, the turbine must have an angular
velocity high enough to fit the operational testing conditions. In other words, given
the operational testing conditions, the rotational speed of the scaled model will be
directly related to rotor diameter chosen for the model.
The Reynolds number is a dimensionless coefficient that quantifies the relative
importance of inertial forces relative to viscous forces. It is generally defined as given
in Eq. (2.3), where ρ is the density for the fluid, U stands for stream velocity, and L
for a characteristic length scale or dimension of the model being studied.
Re =
ρU L
µ
(2.3)
For this work, two Re are calculated based on different characteristic dimensions: a
Rec based on airfoil chord length (c) to characterize the airfoil section (see Chapter 5);
and a ReD based on rotor disc diameter (D) used in the CFD simulations in Chapter 3.
Equations (2.4) and Eq. (2.5) define Rec and ReD respectively.
Rec =
ρU c
µ
(2.4)
13
ReD =
ρU D
µ
(2.5)
Reynolds number similitude is impossible at the model scale desired for the water
tunnel facility, while Froude number scaling is not required as the water tunnel will
be operated in a fully-enclosed and pressurized mode with no free surface. Rec similitude is obviously important for proper scaling of effects local to the rotor blades, in
particular separation and lift/drag curve slopes for the airfoils. It should be noted
that in the case of bluff bodies, there is typically a distinctive CD -ReA 1 relationship
that has sharply defined ReA ranges. However, what is important to remember is that
for the streamlined airfoil shapes used in the experiments there is not as dramatic a
change in lift and drag characteristics with Rec . Of course there will be changes associated with varying Rec in terms of laminar or turbulent separation and associated
viscous and pressure drag, but these are more smoothly varying with Rec and the
drag coefficient of bluff bodies with ReA . In any case, the actual airfoil coefficients
seen at the small model scale will be determined in a separate experimental campaign
to properly account for varying Rec effects.
Additionally, the underlying assumption adopted is that once the flow has left the
blade and forms the wake, the evolution of the wake is Reynolds (ReD independent
[3]. It is the wake properties that dominate the flow conditions seen at the blade, and
hence the experiments will properly scale these velocities.
2.2.1
Rotor Size
In order to best represent the full-size turbine and minimize the errors associated with
scaling phenomena, it is desirable to have the largest model rotor size as possible, but
this also introduces errors due to physical blockages of the flow. Because rotor inflow
and the wake structures are mutually related [3], the performance of the rotor will be
affected by any changes in free wake expansion. Indeed, there is a trade off between
the larger models’ higher Reynolds numbers and the induced blockage errors. Thus,
the ratio of the the area swept by the rotor to testing tunnel area is a key variable to
choose.
1
Where A is the frontal area of the bluff body
14
In this section, a simple approach is used to determine the optimal size of the
turbine model. Based on the actuator disc concept [1], explained in Appendix A, the
rotor of the turbine is modelled as a thin disc that causes a drop in pressure as the
flow goes through it. In ideal conditions in an open flow, the kinetic turbine acts like
an extracting energy device, causing the flow to reduce its velocity when approaching
the disc. The disc exerts a pressure drop in the flow as it passes through the disk, and
downstream of the disc there is region that remains at reduced pressure and reduced
velocity, the so called the wake region. The theory assumes that eventually viscous
mixing returns the wake to the freestream velocity very far downstream.2 Because of
mass conservation, there is a flow expansion after the disc, as seen in Fig. 2.2.
Figure 2.2: The energy extracting stream-tube of a wind turbine (adapted from [1])
This approach makes it possible to obtain a simple expression that relates the
area of the streamtube required for the wake region, the rotor size, and the flow
speed variation induced by the disc on the free stream velocity. This induced velocity
in the stream wise direction is referred to as the axial induction factor a = 1 − ud /U∞ ,
where ud is the axial velocity at the disc location, and U∞ the undisturbed velocity
far upstream.
2
This is of course an assumption of an infinite domain to re-energize the downstream flow.
15
Equation (2.6) presents a simple correlation between the size of the rotor (R), the
radius of the wake (Rw ), and the axial induction factor a. This expression is derived
from equations Eq. (A.1), Eq. (A.2), and Eq. (A.8) detailed in Appendix A.
r
Rw =
R2 (1 − a)
1 − 2a
(2.6)
Equation Eq. (2.6) gives a rough reference to estimate the maximum rotor diameter of the model if we limit the wake tube radius expansion to the cross section
of the water tunnel facility. It is assumed that the turbine will operate at optimal
conditions to maximize output power, which corresponds to an axial induction factor
a equal to 1/3 in ideal, unbounded flow conditions [1]. For a tunnel section of cross
sectional area of 45x45 cm, the rotor radius obtained for the model turned out to be
approximately 15 cm.
Summarizing the scaling conditions, the following table Table 2.1 shows a comparison between the full scale turbine and the model for the HATT experiment.
Variables
Rotor diameter [m]
Maximum axial flow velocity [m/s]
Rotational speed [RPM]
Tip speed ratio λ
Typical blade chord Reynolds number [Rec ]
Full Size Turbine
Scaled Model
17.5
3
10 − 30
3 − 10
107
0.15
2
500 − 1500
2−9
105
Table 2.1: Full size tidal turbine versus scaled model
The full scale turbine operates with a maximum flow speed of 3 m/s3 , and the
tunnel facility has a maximum inlet flow speed of 2 m/s. It is seen that the range of
tip speed ratio λ is similar for both operational cases, but is not possible to match
the Reynolds number (Rec ).
The momentum theory was used as a first approach to determined the maximum
rotor size of the model, however the wall of the water tunnel produces several effects in
the scaled-model that are not found in an unbounded flowstream. Rae and Pope [25]
3
Although tidal flows can be above 5 m/s, 3 m/s is a typical tidal inflow velocity.
16
listed nine effects for the case of general wind tunnel testing. The two most important
factors related to experiments to study the wake structure [2, 26] and power output
measurement [15] are the so-called solid blockage and wake blockage. These two
blockage effects occur when the walls of the tunnel confine the flow around a model
in the test section, reducing the area through which the fluid must flow as compared
to the free unbounded conditions. This effect increases the velocity of the fluid as it
flows in the vicinity of the model, causing an increment in dynamic pressure which
affects all the hydrodynamic forces measured. This blockage effect adds error to the
measurements which must be corrected. A simple rule of thumb suggested by Rae
and Pope [25] indicates that the maximum ratio of frontal model to test-section cross
sectional area should be 7.5% to minimize errors. In Chapters 4 and 3 a more exact
method is presented to correct for the tunnel effects associated with wake blockage.
2.2.2
Force Estimation
Based on the momentum theory, the maximum thrust force at the rotor plane can
be estimated as the pressure drop across the rotor area times the rotor area [1]. If
the rotor axis is aligned with the incoming flow in steady conditions, the thrust force
can be expressed in terms of fluid density (ρ), undisturbed free stream velocity (U∞ ),
rotor area (A), and axial induction factor a, and the thrust force (T ) as given in
Eq. (2.7).
2
T = 2ρAU∞
a(1 − a)
(2.7)
Tidal turbines are not perfectly aligned with the flow direction and so maintain
steady yawed operational conditions most of the time. It has been determined for wind
turbines that the yawed rotor decreases its efficiency of energy production compared
to the non-yawed rotor [1], thus it is important to consider the assessment of yawed
rotor behaviour in terms of efficiency of energy generation.
The momentum theory has limited applications for force estimation in yawed
conditions, however this approach is good enough for the purposes of estimating the
maximum forces to be exerted on the rotor. If the rotor is held at an angle of yaw γ
to the steady fluid direction, the thrust force can be expressed in terms of the fluid
17
density (ρ), undisturbed free-stream velocity (U∞ ), rotor swept area (A), yawed angle
(γ) and axial induction factor(a) as in Eq. (2.8).
2
T = ρAU∞
2a(cos γ − a)
(2.8)
where the optimal condition is given for a = cos3 γ .
Appendix A provides more details about the momentum theory for a turbine
rotor in steady yawed conditions. The following Table 2.2 presents the summary of
the resultant maximum forces calculated at the rotor plane based on the actuator
disc concept. These were used as inputs to the FEM model developed next in §2.3.
FX represents the thrust force aligned to the axis of the turbine, and FZ the thrust
force orthogonal to the axis of the turbine.
Plane of the rotor w.r.t. the
inflow direction (degrees)
90
105
145
FX [N]
FZ [N]
31.32
28.22
11.08
0
7.56
11.08
Table 2.2: Forces at the rotor plane
Note that testing in a water tunnel leads to forces approximately an order of
magnitude higher than if the same-sized model was tested in a wind tunnel. This is
a result of the kinematic viscosity being an order of magnitude smaller for water, but
the density being three orders of magnitude larger, and assuming the model is run
at the same tip speed ratio but the wind tunnel speeds are an order of magnitude
larger than water tunnel speeds. These larger forces are advantageous in terms of
force measurement sensitivity for small-scale models, but are challenging in that as
described in §2.4 in order to control the rotor the instrument package must be out of
the tunnel to physically accommodate the required hardware. It is also interesting to
note, that given the same assumptions, the Reynolds number local to the blade chords
is approximately the same for wind and water tunnel-based testing of identically sized
rotors.
18
2.3
Finite Element Method (FEM) Modelling
The testing rig basically consists of a three-bladed rotor attached to a main horizontal
shaft which drives the rotor, driven by a belt carried up through a vertical support
tube. The horizontal and vertical tubes that compose the support-structure are made
of aluminum tubing and are submerged in the water tunnel so that the motor and
instruments of the system are placed outside the water, on top of the cover of the water
tunnel, as shown Fig. 2.3. The scaled rotor has a diameter of approximately 15 cm,
and it will be placed at half of the water tunnel height (25 cm). Since the vertical
tube (main upright) should be positioned as far downstream of the rotor location as
possible, in order to minimize the disturbance in the near wake, the length of the
horizontal tubing (the sting) was expected to be between the 20 and 30 cm. This
corresponds to a number of complete wake revolutions downstream of the rotor that
could be characterized using PIV.
Several configurations of lengths, diameter and wall thicknesses for the tubing
support-structure were evaluated using ANSYS 11.0 in order to determine the minimum possible sizes for the tubes. A structural static analysis was performed on the
loaded structure to estimate the maximum deflections. The intent was to have a rigid
structure so that aero and hydrodynamic validation could be carried out without
confusing the picture with coupled aero/hydro-elastic deformations. In addition, a
modal analysis was performed to obtain the natural frequencies in order to compare
with the external frequency imposed on the system by the rotor rotation. Details
of the FEM modelling, such as geometry and property materials, can be found in
Appendix B.
Once the minimum allowable sizes for the main tube components were determined,
the mechanical components of the model were chosen based on testing requirement
and availability in the market. The detailed drawings needed for fabrication, summarized in the §2.4, were developed by a co-op student, Heshan Fernando [27].
2.3.1
Failure Criteria and Maximum Deflection
The maximum deflection accepted for the final design is restricted to 1.5 mm for
yawed conditions, and limited to a maximum value of 1 mm for the case of the rotor
plane facing the inflow orthogonally. The von Mises stresses available in ANSYS [28]
were used in the evaluation of failure for the tubing-material. The von Mises stress is
19
5
4
2
1 Three blades rotor
2
Horizontal tube (1):
Shaft housing
3
Horizontal tube (2):
Pulley housing
4
Vertical tube (3): Belt
housing
5
Rotating plate , motor,
pulley and torque cell.
3
1
Cross section of tunnel facility
Figure 2.3: Schematic of the testing rig
essentially an equivalent tensile stress value computed from the stress tensor that can
be compared to the yield strength of the material to predict yielding under a specific
loading condition [29].
The von Mises stress (σV M ) is related to the principal stresses (σ1 ,σ2 , and σ3 ) by
the following expression:
1 p
σV M = √
(σ1 − σ2 )2 (σ2 − σ3 )2 (σ3 − σ1 )2
2
(2.9)
The yield strength of pure aluminum is 7-11 MPa, while aluminum alloys have
yield strengths ranging from 200 MPa to 600 MPa. For this model a value of 200 MPa
was used as the design yield strength.
20
2.3.2
Modal Analysis
A modal analysis was performed to determine the natural frequencies and mode
shapes of the support structure [30]. The purpose of this analysis was to determine
vibration characteristics of the testing rig structure in order to avoid coupling with the
spinning turbine blades while performing the experiments. In this particular model,
neither pres-stress nor damping was computed.
The basic equation solved in typical modal analysis without damping is the classical eigenvalue problem:
[K]θi = ωi2 [M ]θi
(2.10)
where [K] is the stiffness matrix of the structure, θi is the eigenvector (mode shape)
of mode i, [M ] is the mass matrix, and ωi is the eigenvalue (natural frequency) of
mode i. The modal analysis is solved using the consistent mass matrix. The natural
frequencies and mode shapes are equivalent to the solution of an eigenvalue problem.
Depending on the computation of damping and the resulting system matrices the
numerical effort to solve the eigenvalue problem may vary.
ANSYS provides a number of different eigenvalue solver options [31]. To solve the
eigenvalue problem the Block Lanczos Method was chosen. It is a fast and robust
algorithm and used for most applications as the default solver. It is recommended
when finding many modes, or when the model consists of mainly solid elements [28].
2.3.3
Summary of the
FEM
Results
Ten different configurations of tube length and wall thickness were defined and computed in the analysis (M odel1 to M odel10 ). Table B.1 in Appendix B presents the
detailed dimension for the 10 configurations, where T ube1 is the horizontal tube that
houses the rotating shaft; T ube3 is the vertical tube that houses the vertical belt; and
T ube2 is the short tube that houses the pulley and connects T ube1 to T ube3 as shown
in Fig. 2.4.
T ube3 did not vary its length since the rotor must be placed at the half-height of
the tunnel depth, however wall thicknesses between 0.058 in and 0.12 in are considered
in the analysis. The same was true for tube2 of length 5 cm and thickness between
21
Y
X
Vertical
Tube 3
Z
Rotor swept area
Inflow
Horizontal
Tube 1
Horizontal
Tube 2
Figure 2.4: FEM tube model of the testing rig
0.058 and 0.12 in. T ube1 varied its length between 20 and 30 cm and wall thickness
between 0.058 and 0.12 in.
The results of the static analyses are provided in Appendix B, displayed in Table B.2 to Table B.5. In the first model simulations, only four of the ten models
(M odel7 , M odel8 , M odel9 , and M odel10 ) achieved maximum deflections within the
threshold value set up for the design. Based on this static analysis, the minimum
diameter for the horizontal tube that houses the spinning shaft (T ube1 , the sting)
was 1/2 in with a minimum wall thickness of 0.065 in. The minimum diameter of the
vertical tube that houses the belt (T ube3 ) was found to be 3/4 in with a minimum
wall thickness of 0.12 in; and the minimum diameter of the shortest tube that houses
the pulley (tube2 ) is 3/4 in with a minimum wall thickness of 0.065 in.
The modal analysis was then computed for the selected models, and the first 10
modes extracted for the system composed of the three tubes and a mass representing
the rotor, as shown in Appendix B, Fig. B.1.
22
External forcing vibration frequency will be applied to the system due to the rotating set of blades, during the testing. The rotor will spin in the range of 500 to
1500 RPM, which means frequencies in the range of 8.33 and 25 rev/s. To avoid vibration coupling, the natural frequencies obtained in this modal analysis were compared
to the frequencies associated with the operational conditions of the rotor. Details of
this analysis is presented in Appendix B, where in Table B.5 it is seen that natural
frequencies are higher than the external frequencies for M odel5 to M odel10 . Since
at the time this modal analysis was done the final design was not yet finished, the
most robust and heavier structure (M odel10 ) was chosen for determining the minimum diameters and wall thickness of the tubes that compose the structure. The
modal analysis results of M odel10 allowed variation in the rig design without the risk
of increasing significantly the mass of the system and consequently decreasing the
characteristic vibration frequency of the structure.
The maximum length of T ube1 , and recommended minimum thickness and diameter for all the tubes that composed the rig structure are summarized in Table 2.3.
Dimension
T ube1
T ube2
T ube3
Length [mm]
Diameter [in]
Thickness [in]
20
0.75
0.12
25
0.75
0.12
5
0.12
0.12
Table 2.3: Dimensions resulting from FEM analysis
2.4
Mechanical Design
This section presents a summarized description of the mechanical components that
compose the rig mechanical design. Detailed information is found in Fernando’s report
[27].
There were four main objectives that the testing rig design had to meet:
1. It must fit into a existing facility: the water tunnel of cross sectional area of 45
by 45 cm and height of 25 cm.
23
2. The driving system should provide speed control in order to measure power
output for different operational controlled conditions.
It is important to notice that frictional forces are not negligible for this model
size. The mechanical components of the rig, such as seals, bearings, belt, shaft,
etc, exert frictional forces and torque (Tf rictional ) on the system, which could
be of the same order of magnitude as the hydrodynamic torque expected to be
measured from the rotor. Moreover, depending on the operational conditions it
is possible that the frictional torque is greater than the hydrodynamic torque
exerted by the fluid on the rotor. To better understating of this situation,
Fig. 2.5 shows a schematic of the externally applied torques identified in the rig
system.
The instrument load cell is attached to the case of the motor which runs the
system. The motor drives the belt which in turn drives the rotating shaft and
the rotor attached to it. Thydro is the hydrodynamic torque exerted by the flowstream on the system, Tf rictional is the torque due to static and dynamic frictional
forces of the mechanical components, and Treaction is the reaction torque at
the motor, read by the load cell, corresponding to the difference between of
hydrodynamic and frictional torque, Treaction = Thydro − Tf rictional .
Summarizing, a motor/generator (as opposed to simply a generator) is required
to overcome friction and to properly control the turbine when Tf rictional > Thydro .
Additionally, accurate control of the angular position of the rotor was required
for PIV post-processing phase/azimuthal correlation between blade and wake
positions.
3. The rig must have an area behind the spinning rotor where the disturbance
of the flow, due to the supports, is minimal. A distance of one to two rotor
diameters was imposed as a requirement for the horizontal tube that houses the
rotating shaft for this purpose.
4. The rig must allow testing in yawed flow conditions. For that, a yaw system is
required up to 45◦ , ideally maintaining the rotor in the center of the tunnel to
avoid wall interference effects.
The main components of the final design are shown in Fig. 2.6. The top plates,
located on top of the cover of the water tunnel (as shown in Fig. 2.3) contain the
24
Torque Cell
Motor
Treaction
Belt
Rotor
Shaft
Thydro
Tfrictional
Figure 2.5: Schematic operation
instrument structure and the yaw system. The instrument structure consist of a
torque cell and the stepper motor that drives the system. The yaw system consists of
two plates attached to the hatch that can rotate and adjust position of the submersed
structure. The submersed structure is composed of several parts: the horizontal
rotating shaft and its housing tube, the rotor, the fairings that reduce the disturbance
of the flow, and the belt system and its corresponding housing tubes. The motor
drives the belt system which is connected to the rotating shaft which in turn drives
and controls the speed of the rotor.
2.4.1
Instrument Structure
Figure 2.7 presents a schematic of the instrument structure.
25
Instrument Structure
Belt Drive
Yaw System
Fairings
Submerged Structure
Figure 2.6: Key components of the rig
Plates and posts compose the structure that houses the motor and torque cell.
The torque cell is attached to one plate; the motor is attached to the torque cell and a
flexible coupler attaches the output shaft of the motor to the pulley shafts that drives
the belt system. Bearings are used to minimize the friction, and a clamp attaches
the vertical tube support of the submerged structure to the instrument structure.
Since the measurements must be very precise, alignment is critical for this design.
The plates and posts are accurately machined to meet these requirements. Holes are
made on the plate that accurately mate with bosses machined on the posts. Further
details of the motor and instruments are provided in Chapter 5.
2.4.2
Belt System
In order to minimize the friction of the rotating components, a belt was chosen to drive
the submerged rotating shaft (which runs the rotor). This option has less friction than
26
Stepper Motor
Coupler
Torque-cell
Clamp
Housing
Figure 2.7: Components of the instrument structure
using a rotating gear system. The spinning rotor will reach high rotational speed, up
to 1500 RPM, which can lead to additional vibration in the system. To check this
design choice, a rig for belt testing was fabricated before carrying out the final design
of the testing rig.
To asses two different belt options, and to check the level of vibration of the system
in the range of rotational speeds considered for the final experiment, belt testing was
performed in this early design stage. The belts were ordered from SDP/SI products;
Table 2.4 present the characteristic of the two belt tested [32]. Pulleys were also
ordered from SDP/SI, each type corresponding to the belt model.
The rig designed for the belt testing had a support structure made of two plywood platforms and two aluminum posts, as shown in Figure 2.8. The mechanical
components for the testing were the motor, the belt, two pulleys (one attached to
the output shaft of the motor and the other located in the lower platform), and a
bearing system that houses a free-spinning shaft located in the lower platform. Is was
27
Figure 2.8: Rig for belt testing
possible to adjust the location of the motor in the vertical plane by fastening four
screws, which provided the tension required for the belt to work properly. The test
was run for rotational speeds in the range of 60 RPM to 1500 RPM.
As a result of this testing, vibrations were noticed only at very low speeds, below
500 RPM. The belt type MXL ran smother than the belt type GT3; this may be
because belt type GT3 was found to be stiffer than belt type MXL. In addition, the
pulley corresponding to belt GT3 used a set screw to attach to the output shaft of
the motor, what caused slight damage to the shaft, whereas pulley of belt MXL had
a clamp. In conclusion, belt MXL was chosen for the final testing rig.
28
Model number
Material body
Material
cord
MXL A6G16-350025
GT3 A6R53M250060
polyurethane
nylon covered fiberglass reinforced
polyester
polyester
Pitch
length
[in]
28
29.5
No of.
grooves
350
250
Table 2.4: Characteristics of the candidate belts
2.4.3
Submersed Structure
The submerged structure is composed of a rotor, a sting, a connecting part, a vertical
tube, and a set of fairings, as shown Figure 2.9. The aim of this particular design
was to make the components of this structure as small as possible to avoid blockage
effects and flow disturbances. In addition, the sting had to be as long as possible in
order to provide an undisturbed area behind the rotor for the PIV images to be taken.
The sting is the part that houses the rotating shaft which is attached to the rotor.
This assembly part is made of aluminum tube of 0.75 in external diameter, and has
two press-fitted pieces at each end, one of them containing threads that attach this
structure to the connecting piece.
The connecting piece connects the sting assembly and the vertical tube which
suspends the submerged structure from the rig-plates. This connecting piece is made
of aluminum and has an overall outside diameter of 2 in. It was not possible to make
this piece smaller since it has to provide sufficient room to locate the pulley that
drives the shaft inside this connecting piece. For the sting assembly to be attached
and aligned to this connecting piece, a bore and threads were designed in the front
part.
There is a vertical tube that houses the belt which compose the rig drive system.
The vertical tube, made of stainless steal of 1.25 in diameter, connects the submerged
structure to the upper instrument structure, and keeps the sting assembly at the
center of the vertical tunnel cross-section. A flange is welded at the bottom of the
tube to secure it by screws to the connecting piece.
The blades and hub that composed the three-blade rotor design are fabricated in
the SSDLs lab, using the FDM machine as described in section next.
29
Vertical Tube with
Rounded Flange
1.25” Stainless
Steel)
Sting Assembly
0.75”)
Three blades
Rotor ( 15 cm)
Connecting Piece
Threaded
connection
Figure 2.9: Submerged support structure
In addition to all the structural parts that compose the underwater structure,
there are fairings incorporated into the rig design with the purpose of reducing flow
turbulence and drag as the water passes the submerged assembly.
As shown in Figure 2.10, there are two main fairings: one covers the vertical tube
and the other covers the connecting piece. The vertical fairing slides over the vertical
tube; the tolerances in this design also allow aligning the fairing to the flow for the
yawed position of the rig. The fairing which covers the connecting pieces is fabricated
as two split halves. Tolerances in the design allow the fairing part to slide over the
sting and rear part of the connecting piece, and help to keep the fairings attached to
the structure. The split parts clip together in the middle, and they are also secured
by the vertical fairing which slides over a vertical extrusion of the connecting piece
fairing.
An important consideration in the rig design was to ensure the drive system worked
under dry conditions. Different type of seals were used to prevent water from leaking
30
Fairings
Figure 2.10: Model of fairings covering the submerged structure
inside the underwater structure. O-rings and grooves were placed between two mating
surfaces or press-fitted pieces, and lip seals were used to prevent water entering around
the rotating surfaces like the rotating shaft in the sting.
Finally, notice that three axial bearings were used in this design to align and
minimize the friction for the rotating shaft. There are two bearings on the sting, and
a third bearing placed in the rear part of the connecting piece
2.4.4
The Rotor
A 3D material printer available in the Sustainable System Development Lab (SSDL)
using FDM techniques was utilized for building the rotor blades (and a number of
fairings and other parts of the rig). This technology allows construction in-house
of several parts in a short period of time. Then, different blade profiles and sizes
can be tried in the ongoing and future experiments. A wide range of thermoplastics with different mechanical properties can be used as printing material; ABS and
Polycarbonate (PC) thermoplastics were available for building the parts.
Depending on the material employed, it is possible to accurately manufacture
small parts by extruding material into layers as thin as 0.005 in thickness (T10 tip).
31
For the first set of blades the material used was PC, and the T12 tip was used which
creates a layer 0.007 in thick. Build time and part finish are proportional to the tip
size used.
The 3D printer, a Fortus 400mc, works with the Insight software. This application,
installed on the user’s work station, allows setting up the properties of the parts to
be printed, such as surface smoothness, layer path, filling spaces, void volume, etc.
Figure 2.11: Rotor assembly
Figure 2.11 shows the blades and hub parts that were made separately and then
assembled together. The upstream end of the rotating shaft has a boss to prevent
the hub part from touching the sting assembly (Fig. 2.9) and to align the hub part
with the submerged structure. It also has threads allowing the hub-part to be secured
against the shaft.
The three blades have identical profile, are about 70 mm long, 25 mm wide at the
root, and 7 mm wide at the tip of the blade. The root part has a circular plate plane
orthogonal to the span-wise axis, which is used to keep the blade clamped between
the two-half hub parts. The hub part is composed of two cylindrical parts meant to
clamp the blades and to provide pitch adjustment. A hexagonal nut is used to secure
the hub against the shaft boss. The nose cone is attached to the hub part covering
the hex-nut.
32
The initial set of blades built correspond to a NACA63(2)-4XX airfoil profile, with
21 % thickness, and a twist angle of 15◦ . This relatively large thickness airfoil was
used to ensure blade rigidity.
2.4.5
Yaw System
The yaw system works due to the motion of two concentric planes of rotation: the
plane of the instrument structure plate, and the circular rotating plate. The former
has an axis of rotation about the vertical support tube, and the latter about the water
tunnel cover cutout hole.
As shown in Fig. 2.6, the vertical tube which holds the submerged assembly is
clamped to the instrument structure. This instrument structure is placed above the
circular rotating plate, and secured to the plate by screws. The circular rotating plate
is seated on a hole made in the cover of the water tunnel, and is kept attached to the
hatch by six clamping pieces and 24 screws.
Figure 2.12 demonstrates the yaw motion for the rig. The starting point in shown
in the scheme number 1 of the reference figure. First the circular plate rotates,
generating rotation of the the instrument structure, the vertical tube clamped to it,
and all the submerged structure attached, as shown in part 2 of the figure. Then,
the angle of the sting can be adjusted by rotating the instrument structures plate, as
shows part 3 of the figure. In such a way, it is possible to get different yaw angles
but keep the rotor at the center of the cross-section of the water tunnel.
Marks for the degree movements are included for both the rotating circular plate
as well as the base plate of the instrument structure. The maximum yaw angle
obtainable with the original rig design, with a sting of 13.25 in length, is about 23◦ .
It is possible to reach 45◦ if the sting assembly is replaced for a shorter one of 7.42 in
length. In the end, two different sting assemblies were built allowing different yaw
capabilities for the final testing rig. At present, the yaw system is actuated manually
and fixed during testing. In the future, this system could be automated to enable
dynamic yaw event testing.
33
Figure 2.12: Yaw system operation
2.5
Instrumentation
The general layout of the complete rig and PIV system is depicted in Fig. 2.13.4 There
are two acrylic hatches that cover the water tunnel at the upper surface allowing the
section to operate closed instead of having a free surface. As described in §2.4.3, the
whole instrument and drive system is kept outside the water tunnel. The rotor is
located at the center of the section to minimize wall effect over the measurements.
The DPIV system is comprised of a camera and a laser sheet, and will be used
to illuminate a horizontal plane and capture the particle images in the near wake.
The area of interest is located behind the rotor up to a few diameters downstream.
4
The terms Digital Particle Image Velocimetry (DPIV) and PIV as used in this thesis both
strictly refer to a DPIV system, as the images are digitally acquired and processed.
34
Front View
Side View
Laser
system
Laser
sheet
Area of interest
Camera
Camera
Vector velocity field
Figure 2.13: PIV system layout
The X-Y plane is parallel to the bottom and roof of the water tunnel, the flow is
in the X axis direction, from left to right, and the Z-axis points upward. The laser
sheet illumination is the X-Y plane, and the camera is located perpendicular to the
illumination plane looking upwards. This general layout is meant to avoid, or at least
minimize, shadows in the wake. When illuminating the same plane from the bottom,
the vertical tube, that contains the shaft, will probably generate shadows in the area
of study. On the other hand, this vertical tube will be positioned as far aft the rotor
as is possible in order to minimize the disturbance in the near wake.
The interactions among the components of the integrated electric system that
control the experiment are shown in Fig. 2.14. The main components of the integrated
system are:
• The rotor itself, imparting torque on the shaft. This torque is transmitted to
the drive system by the rotating shaft and belt system.
• The drive system, which runs the rotor, comprised of a stepper motor and the
E-AC Driver.
35
• The Data Acquisition System (DAQ) system is composed of the instrument to
measure the torque of the motor, the loadcell, and by the control and data acquisition system, the NI CompactRio hardware. The CompactRio technology
is a real time acquisition system which allows control of the drive system, triggers the PIV system to start, and stores all the information acquired. LabView,
installed on a user computer, provides a user interface for the DAQ system.
Through this software it is possible to display the information being acquired
and command the motor velocity and direction, and to start and stop the system.
• The PIV system is an independent piece of hardware with its own controller
system and storage capacity. It cannot be commanded by the CompactRio
directly to take a picture, but it can be triggered to start operation. It is
composed of a laser, a digital camera, and operating software, LaVision. The
laser system was the component that was broken during most of the thesis
period and precluded operation of the PIV for the trial runs of the rig discussed
in Chapter 5.
2.5.1
The Drive System
In order to meet the objectives of the experiment, it was important to have control
over the operational conditions of the turbine. It was also desirable to be able to
control the rotational position of the rotor, and minimize the number of components
and electric equipment working within the system.
Stepper motors allow precise positioning and speed control without the use of
encoder or feedback sensors. The stepper motor and the drive selected allows the
shaft to move only a set number of degrees when each pulse is delivered by the drive.
The stepper motor HV233 and the E-AC 120 V AC Microstepping Drive from Parker
were chosen as the drive system, as shown in Fig. 2.15. The E-AC Microstepping
Drive can be plugged directly into the standard mains supply (ranging between 95 to
132 V AC), and can be integrated to the Compact Rio technology control.
BEM simulation runs for comparison to the experimental results were typically
done setting an angular accuracy of 5 ◦ . Consequently, providing rotor control with
the best angular accuracy is desirable for measurement and comparison. In others
words, given the accuracy required on angular position, a restriction on the minimum
36
Data Acquisition
•Torque Cell
•Compact Rio System
Drive
System
•Motor
•E-AC Drive
Gear components of
the
Experiment Set Up
Rotor
RIG
Data interface
•LabView Software
•USER programing
PIV System
•Laser
•Camera
•LaVision Software
Figure 2.14: Experiment system schematic
resolution was set up for the drive system selection in order to meet these requirements. The drive system chosen satisfied the technical conditions specified, having
a resolution of 50, 800 steps per revolution, with an error of 3 % to 5 % per step
non-cumulative from one step to another, an accuracy of 5.003 ◦ can be reached, with
an error of +/− 0.000354 ◦ .
Figure 2.16 shows the performance curve of the motor obtained for the rig, a double
shaft HV-233 stepper motor. It provides the maximum torque estimated (0.9 Nm)
for operation at 500 RPMs (8.3 revolutions per second) and a wide range of rotational
speeds.
2.5.2
The Motor
A motor device is essential to control operational conditions, to keep the λ value
within the range established. Also, the testing rig has an inherent friction due to
the belt components and bearings, and thus a motor device is necessary to overcome
frictional losses. In such a manner, the motor is working as a device that can absorb
37
Figure 2.15: Drive system
and provide power, and that allows the net torque of the rotor minus all the losses in
the drivetrain to be determined.
In retrospect, while the stepper motor is advantageous in providing speed and
position control without feedback, two issues were found in practise. In order to
attain the required torques, the coils were connected in series, but this caused the
motor to overheat when run longer than 10-20 minutes. In addition, the first motor
obtained had some flaw that caused stalling even in no-load conditions. The situation
was hard to address, even after multiple attempts at ensuring alignment of matings
surfaces, etc. Again, this greatly delayed the experiments, and eventually lead to
replacement of the first motor. Perhaps a better approach for future rigs would be
a servomotor with encoder feedback positions, although high-accuracy encoders for
fine knowledge and control of azimuthal position could be challenging to obtain.
2.5.3
Torque cell
Notice that for small scale models, accurate force measurement is extremely difficult
to achieve due to the level of noise in the signals, thus only torque measurement was
feasibly for this study. Thrust force measurement was considered, but was considered
impractical given the other constraints of the system and the primary requirement
for excellent torque and azimuthal position control.
The Novatech F 326-Z 1 Nm loadcell was chosen to measure the reaction torque of
the motor. This type of loadcell fits between a motor and its mounting structure act-
38
HV233
Figure 2.16: Performance curve Parker Motor HV233
ing as a coupling. Novatech proposed two options for the F326-Z mounting, Fig. 2.17,
for this rig. The configurations suggested are meant to support the motor weight and
remove any extraneous forces and bending moments, if the mounting structure and
bearings for shaft supports are properly aligned. At one side of the loadcell, four
screws are used to fasten the motor to the torque cell structure so that the motor’s
torque is transmitted to the F 326. This flanged mounted motor torque transducer
has a hole through the axial centre of the structure, which allows the motor shaft
to pass through it. On the other side of the loadcell another four screws are used
to fasten the loadcell to the instrument rig structure. The rig instrument structure
follows the first scheme of Fig. 2.17 (single shaft mounting), but utilizing a double
shaft motor as described in §2.4. The reaction torque is therefore measured between
the case and mounting (earth) structure.
With respect to the torque range measurement and its resolution, the loadcell has
the capability to measure torques ranging -1 Nm to +1 Nm, and read values as small
as the minimum expected torque for the experiment, which is 0.01 Nm, providing the
DAQ electronics components can handle the small signal of 60 µV.
The F 326-Z loadcell has a nominal output of 0.6 mV/V, which basically determined the selection of DAQ CompactRio module in charge of torque measurement.
Given the minimum torque value to be read (i.e 0.01 Nm), and a 10 volt excitation
voltage for the torque cell, this specific DAQ module must be capable of reading a
small signal of 60 µV.
39
Figure 2.17: Novatech installation schematic
For this reason we looked at a 16 bit minimum DAQ module for torque measurement. A module of less bits of resolution would not be capable to handle that small
voltage value, and hence it would not provide enough resolution for measurement.
During initial testing, one or more leads internal to the load cell broke for some
reason. The loadcell was not overloaded, and hence the structure was intact and only
the leads required reattachment by the manufacturer. However, as the vendor was in
the UK, this breakdown again set the project back.
2.5.4
PIV system
The acquisition of the vector velocity field that characterizes the near wake will be
done using DPIV, which is the most suitable flow visualization technique for the
measurement of velocity fields over a two-dimensional region of flow [33]. PIV is
an optical method used to obtain instantaneous velocity measurements, and since
40
optical measurements avoid the need for Pitot tubes, hotwires or other physical flow
measurement probes which cause disturbance of the flow field, this method has the
advantage of being a non intrusive measurement technique.
The fluid is seeded with tracer particles which are supposed to cause negligible
distortion of the fluid flow. These particles have to be carefully chosen depending
of the type of fluid and motion to follow the flow dynamics. For this particular
experiment, Mearlin Supersparkle particles were available with mean diameters in
the range of 5 to 7 µm and silver in colour. The specific gravity of these particles is
larger than specific gravity of water, thus they are deposited on the bottom of the
channel when the water tunnel is off. However, it is possible to infer from others’
experiments carried out in the same tunnel facility and having the same type of
particles [34], that the flow speed considered for this particular experiment is high
enough to keep the particles following the motion of the flow field.
Optics
Double pulse
laser
Laser sheet
Seeded
flow
Lens
(camera)
t
t+ t
Sensor plane
(in camera)
Figure 2.18: General schematics of PIV system
Notice that it is the motion of these tracer particles that makes visible the fluid
motion. By recording the position of them at different instances of time, is possible
41
to determine the displacement of the particles in this time interval, and to calculate
its velocity, and eventually build up the flow velocity field.
To capture the image of displacement of the tracers, typically DPIV uses digital
cameras with frame rates on the order of 15 - 30 Frames per Second (FPS). To
freeze the movement of the particles at specific time, a laser pulse of light is used
to illuminate the plane of motion. In this way, the sensor of the digital camera is
able to capture the movement of the small particles. Finally, the images taken are
processed in a computer to reconstruct the whole velocity field. The schematics of
this technique is presented in Fig. 2.18.
There are some factors relevant the DPIV measurement technique, such as timing
of the camera shooting, laser pulse, and the size of the interrogation cell. For instance,
to get accurate measurements it is crucial to synchronize the camera shutters and laser
pulse. Also, the size of the interrogation cell (typically size 6x6 pixels) will depend
on the conditions of the flow to be measured. Ideally there are between 3 and 15
particles per area of interrogation. Thus depending on the seeding density, the size of
the seeding particle, and the velocity of the flow field, there is a cell size that satisfies
that ideal condition and this must be set up for each particular experiment event
(a trial and error process). More detailed information about PIV theory is given in
Appendix C.
For this particular experiment, in an attempt to reconstitute the 3D velocity fields,
PIV images are intended to be taken for a set of different azimuthal planes, each one
representing a cross-section of the wake [2]. It is important to notice that PIV images
are basically 2D, in this case taken at the plane parallel to the inflow velocity. The set
of azimuthal planes are obtained by triggering the camera to take single 2D pictures
at different timings relative to the rotor, in such a way that each picture will capture
the instantaneous flow velocity corresponding to the vertical position of the blades
set at different angles. This will also allow for azimuthally averaged flow quantities
to be computed.
The available PIV equipment in the Fluid Lab consisted of a high speed digital
camera, a Quantronix Nd:YLF laser, and a PC with hardware for DPIV image data
acquisition. For the experiment, the task is to the synchronize the PIV recording
equipment with a defined angular position of the rotor, in order to obtain flow photographs at any predetermined position of the blades. This was the primary reason
for selection of a stepper motor, and a control system able to trigger the PIV image
42
recording.
The Darwin-Duo laser series, a 25 mJ Nd:YLF dual diode-pumped type, can be
externally triggered via TTL Inputs in such way that the PIV hardware starts the
laser operation. At each input signal, the laser provide two laser pulses, having a
pulse width of 120 ns and a frequency ranging between 0.1 to 10 kHz. This allows
control of the time intervals between each of them with a resolution of 25 ns, and a
timing jitter below 2 ns.
The laser optics provides a planar light sheet to illuminate the particles in the
region of interest. The digital camera is a HighSpeedStar HSS − 5 CMOS sensor
with frames rates up to 250 kHz, a maximum resolution of 1024x1024 pixel for a
frame rate of 3 kHz and below, and a minimum interframe time of 2 µs.
The images taken are sent to the software LaVision DaVis 7.2 for data processing.
Within the software the recorded images are evaluated by cross-correlating pairs of
frame, each containing single exposure of the group of markers (This PIV technique
is detailed in Appendix C).
Basically, the required settings for recording images are previously set up in the
DPIV PC Hardware, such as pixel size, frequency of image capture, etc. There is a
time delay between the starting time of the laser and the moment the camera capture
the first picture. Thus, there is also a set time delay before the camera starts in order
to synchronize with the laser pulses. Finally, the external trigger starts the DPIV
hardware, which triggers the laser and the image acquisition.
Ideally the whole system can be programed to capture an image every turn of the
rotor at specific position. However, because of the high rotation speed of the scale
model rotor, it is probable that the camera must be set up to capture the images
every two or three turns. The final frequency and operation of this integrated system
must be adjusted in a trial an error exercise once the PIV system is again operational.
2.5.5
DAQ Rio System
The NI CompactRio package was selected as a combined control and DAQ system.
This technology is portable, it communicates over the network, contains a real-time
processor, a reconfigurable field-programmable gate array (FPGA), and a variety of
analog and digital input/output modules to cover the requirements for the experi-
43
ments. Each of the NI modules of the CRio package connects directly to sensors,
motors, etc, to customize the system architecture.
Figure 2.19: CompactRio package
The National Instruments (NI) package acquired for the experiment,Fig. 2.19, is
mainly composed of:
• NI cRio-9022, an embedded real time controller with 533 MHz processor, 2 GB
storage for logging data, and 256 MB of memory RAM.
• NI 9401 module, an 8 channel TTL digital input/output signal component. This
module outputs the digital signal to trigger the DPIV system.
• NI 9237 24 bit module for load/pressure/strain/torque measurements. The
selection of this module is due to its capability and resolution to read the
torque cell output voltage measured for the smallest value of torque expected,
0.010 Nm. Thus, for a 10 volt excitation voltage, a 60 µV signal has to be
handled for the NI module. This task is accomplished by this 24 bits resolution module. The NI 9237 can also output up to 10 V excitation, and has four
simultaneous input sampled at up to 50 kS/s per channel, allowing for future
expansion.
• NI 9201 8 channel analog input module, which reads the output analog signal
of each laser pulse fired.
44
• NI 9512 stepper drive interface module. This module is probably the most
complex of the package. It has its own power supply, and acts as the controller
of the drive system. This module makes if possible to control rotation speed and
direction of the motor when running, without the need to stop the movement.
It also allows moving the rotor in discrete steps.
• NI LabView software, a graphical tool developed by NI can be installed in the
user’s laptop for designing, prototyping, and deploying embedded applications.
The control software for the entire system was implemented in LabView. Figure 2.20 depicts a screen shot of the developed LabView interface software. The
figure displays the basic functions programmed such as velocity control, data
recording onset, PIV triggering option, data position display, torque measured
display, etc.
Figure 2.20: LabView interface
45
Chapter 3
Computational Fluid Dynamic
Simulations
This CFD study focuses on providing information that can be used to properly correct
the data acquired in the experiment performed in the water tunnel, which is known
to be affected by blockage due to the walls of the tunnel facility, as described next
in Chapter 4. Since the experimental data obtained must be corrected to unbounded
flow conditions (see §4.1), a key point presented in this CFD chapter is the unbounded
model domain validation. The study also included ReD dependency analysis to verify
the validity of the simulations results for a range flow conditions.
This chapter has two main sections which describe the computational modelling
approach used to represent the fluid phenomena of kinetic turbines operating in water
tunnel and free stream conditions. The first section presents the conceptualization
of the turbine and physical domain in such a way that can be translated into a
simple computational model. In this context, the rotor has been conceptualized as a
continuous plane that extracts energy from the flow. Suitable boundary conditions
have been set up to the model in order to represent both scenarios, the water tunnel
and open flow conditions. The second section of this chapter presents the details of
the computational tools used for these purposes. Note that this second section is an
overview description of the mathematical equations employed in the ANSYS CFX
tool, but is not an exhaustive text on CFD.
46
3.1
3.1.1
Modelling Approach
Porous disk
Several approaches have been used to model the aerodynamics of horizontal axis
wind turbines [3]. Regarding the near wake, the porous or actuator disk technique
has been widely utilized in numerical models, as well in experimental testing applied
to horizontal tidal stream turbines [12, 35]. This porous disk model has the advantage
of requiring a reduced mesh density compared to other available numerical models for
CFD simulations [3, 35]. Thus, it is computationally less expensive, and it is utilized
to simulate the blockage effects in this study.
Because this method conceptualizes the rotor as a plane which extracts energy
from the flow, a drawback of this model is that the blades of the turbine are not
directly simulated. However, considering the objectives of these CFD simulations,
this approach is adequate to meet the study purposes.
The total pressure drop that the actuator disk area exerts on the fluid is represented by a unidirectional momentum loss, or thrust force per volume unit, χ applied
at the disk volume. For the CFD simulations, this momentum loss is rewritten in
terms of the thrust coefficient (CT ), the upstream axial inlet velocity (U0 ), the water
density (ρ), and the thickness of the disk (t), as presented in Eq. (3.3). Equation (3.3)
is obtained by equating the thrust force from Eq. (3.1) and Eq. (3.2), as follows:
1
T = ρAU02 CT
2
χAt = T
χ=
3.1.2
1
ρU02 CT
2
t
(3.1)
(3.2)
(3.3)
Domain
The simulations were run over two different computational domains. The first domain
accounted for the unbounded conditions where no wall prevents the streamlines from
expanding freely. The second computational domain models the water tunnel, which
allows for comparison between experimental and full scale conditions.
Defining D (15 cm) as the diameter of the scaled rotor being tested, the rectangular water tunnel computational domain has a cross-sectional area of 3Dx3D and
47
a length of 15D, and the disc is placed 5D downstream of the inlet centred in the
tunnel section, corresponding to the experimental setup. The unbounded rectangular
computational domain is defined with a section of 6Dx6D, 25D long, and the disk
located 5D downstream from the inlet. For both cases, a structured mesh was generated using ICEM, applying O-grid and blocking topology features that facilitate the
manipulation of the grid for a 3D model.
As detailed in the boundary conditions section next, symmetry is applied to the
original model described, which allows the simulations to be run over a quarterdomain as shows scheme in Fig. 3.1.
Figure 3.1: Quarter domain water tunnel model (ANSYS CFX)
By computing simulation results for four different rotor sizes, the effects of blockage ratio were explored, where blockage ratio is defined as the ratio of rotor swept
area to tunnel section area (A/Atunnel ). The thickness of the disc was fixed at 0.5%
of the rotor diameter (0.005D) in all cases.
48
3.1.3
Boundary Conditions
A uniform axial velocity of 2 m/s was set up at the inlet of the domains. This
boundary condition is physically driven by the pump in the water tunnel, and also
represents the operational expected flow velocity in the open water. At the outlet, an
average static pressure was defined, with relative pressure equal to zero. Specifying
an average static pressure over the whole outlet allows the pressure variable to vary
locally over the outlet boundary such that the average pressure is constrained to a
specific value. Physically, this may be the situation of the experiment with a higher
velocity at the centre of the section and lower near the wall region. Additionally, this
boundary condition configuration is listed as the most numerically robust option in
Ansys CFX [36].
At the actuator disk a unidirectional momentum loss χ (referring to Eq. (3.3))
was applied to account for the pressure drop for each CT value computed. Since
a quarter domain was used, two symmetry planes were applied, in the vertical and
horizontal planes respectively. These boundary conditions were also active for the
area of the disc in contact with these symmetry planes. For the unbounded domain,
an opening boundary condition, allowing fluid to cross the boundary surface but
keeping a constant pressure value at the boundary, was applied to the walls. For the
water tunnel domain, the base case considers a free-slip wall condition.
Even though free-slip conditions at the walls were previously defined as a boundary condition in order to compare the CFD results to the analytical expressions for
blockage discussed in §3.3, additional simulations were run to investigate the effects
of the boundary layer growth within the tunnel. A minimum number of 10 nodes
within the boundary layer is suggested by the ANSYS CFX Guidelines [37] for the
near-wall turbulence model to work properly. For a turbulent boundary layer on a
flat plate in similar flow and fluid conditions, the viscous sublayer thickness should
be less than 1 mm [38]. Thus, to include the effects of viscous losses at the boundary,
a mesh having 10 nodes within this first 1 mm layer was generated from the wall to
properly computed the boundary layer [36]. The q
dimensionless wall distance is known
u∗ y
as y+ = ν where the friction velocity is u∗ = τρw and tw is the wall shear stress.
In the simulations run, y+ was approximately 10.
The water tunnel used for testing has a very low turbulence level (approximately
1%) which was used in the simulation inputs. Both laminar and turbulent flows were
computed. The Reynolds Average Navier-Stokes (RANS) equations were solved for
49
steady and incompressible flow, using a finite-volume method, and the K −Ω equation
was used to model the turbulence, as described next in §3.2.1.
3.2
Computational Model
The academic version 12.0 of the commercial package ANSYS CFX was used for the
three-dimensional CFD simulations, and the structured mesh over the domain was
generated using ANSYS ICEM.
The Navier-Stokes equations for mass-flow and momentum can be discretized and
solved numerically using diverse solution methods. The CFX package corresponds
to a particular CFD code based on a finite volume technique [39] in which the fluid
region of interest is split into smaller sub-regions, so called control volumes. This
subdivision allows an iterative solution of the set of partial differential equations for
each small sub-region. Finally, an approximate solution of the variables of study is
obtained, point by point, over the entire flow field domain.
3.2.1
Governing Equations
The basic equations of fluid mechanics, for describing the fluid motion, are the NavierStokes equations, Eq. (3.4) and Eq. (3.5), where ρ is the fluid density, u the vector
velocity, p the pressure, τ the stress tensor, and SM the additional scalar term representing a momentum source (refer to section next 3.2.2). Equation (3.4) is known
as the continuity equations, and Eq. (3.5) is called the momentum equation. These
general N-S equations are valid for both turbulent and non-turbulent flows, steady
and non steady conditions. The energy equations were not required, as the change in
fluid properties with temperature are negligible in the cases under investigation.
−
∂ρ
+ ∇(ρu) = 0
∂t
(3.4)
∂(ρu)
+ ∇(ρu ⊗ u) = −∇p + ∇ · τ + SM
(3.5)
∂t
The fluid conditions that characterize the experiments performed in the water
tunnel makes it necessary to incorporate turbulence in the CFD model. Turbulence
occurs when the inertia forces in the fluid become important relative to viscous forces
−
50
(i.e. higher Reynolds numbers). In CFD modelling turbulent flows can be thought of
as an average characteristic, with an additional random fluctuation superimposed in
time and space. Thus, the turbulent flow can be statistically modelled for example as
an instantaneous velocity expressed as the sum of the mean velocity and a fluctuating
component Eq. (3.6), where the mean velocity is estimated as expressed in Eq. (3.7).
u = ū + u0
Z 1+∆t
1
udt
ū =
∆t t
(3.6)
(3.7)
This statistical technique is applied to the Navier-Stokes equations producing the
RANS equations. For this particular model the governing equation for the turbulent
and incompressible flow are the RANS equations. The averaged quantities are substituted into the general transport equations and rearranged, resulting in Eqs. (3.8)
and (3.9):
−
−
∂ρ
+ ∇(ρu) = 0
∂t
∂(ρu)
+ ∇(ρu ⊗ u) = −∇p + ∇ · (τ − ρu ⊗ ·u) + SM
∂t
(3.8)
(3.9)
where the terms ρu ⊗ ·u have the same structure as the viscous stress tensor and
are called Reynolds Stresses, however these terms arises from a non-linear convective
term contribution of the fluctuating velocities to the change of the averages ones. The
Reynold stress tensor incorporates additional unknown variables to be solved in the
CFD model, generating a closure problem.
Since this study considers stationary flow conditions, the varying-time terms in
Eq. (3.8) and Eq. (3.9) become zero. Notice that ANSYS CFX is an iterative solver
which approaches the solution of the set of partial differential equations over a set
of iterations. The solver therefore uses a timestep for iteration process, used only to
under-relax the governing equations.
In order to achieve closure for equation Eq. (3.9), turbulence models are introduced to compute the Reynolds stresses and fluxes. Depending on the assumptions
of these models, there are two main types available in CFX: eddy viscosity models
and Reynolds stress models [36]. For this study, to achieve closure, the K − Ω model
51
was used, which is part of the family of eddy viscosity two-equation turbulent models.
This model has become a widely used turbulence model [40], which can predict effects
for both free shear flows (which is the case of the wake behind the rotor in this study)
and wall-bounded boundary layer flows with reasonable accuracy provided a good
detailed mesh is used, as indicated in §3.1.3 [36]. Considering the simulations comprises both free-slip and non-slip boundarie condition set ups, this turbulence model
is suitable for the whole range of flow conditions. In addition, CFX has been run
in a laminar model (i.e. with Reynolds averaging) for comparison to the turbulence
model results.
3.2.2
Momentum Source Sink
In ANSYS CFX, sources allow for adding additional terms to the set of equations
being solved by CFX with the purpose of modelling an additional physical process.
In this case, the pressure drop, caused by the disc, is introduced by setting a general
momentum source sink in the streamwise direction, over the disc volume (thin plane).
Note that this type of source does not introduce any additional mass but it does model
flow resistance.
This momentum source sink is specified in terms of a momentum loss value per
unit of volume in a specific direction, and setting up a value equal to zero in all
others directions. Convergence is improved when the source is a function of velocity
[36]. The source is linearized by setting a momentum source coefficient K. Note that
this momentum source coefficient K is equivalent to the unidirectional momentum
loss (thrust force per volume unit) χ defined in Eq. (3.3), therefore this χ value is
calculated as function of the variables characteristic of each running, and introduced
in the CFX model.
Finally, ANSYS CXF solves Eq. (3.10) within the system of equations for the Z
coordinate component direction (components in the X and Y axis directions were set
up as zero).
−
∂p
= KUZ
∂Z
(3.10)
52
3.2.3
CFX Boundary Conditions
The set of boundary conditions established in this model were already stated in §3.1.3,
and therefore this section explains the tools available in ANSYS CFX for applying
the boundary conditions depicted in Fig. 3.2.
Figure 3.2: CFX quarter domain boundary conditions
To simulate an open boundary condition, representing the unbounded domain,
the Opening Boundary was applied to the walls [41]. This CFX boundary condition
allows fluid to enter and exit the domain, and a constant pressure is kept at the
boundary surface, as shown Eq. (3.11).
popening = pspec
(3.11)
For the water tunnel domain, the Wall Boundary Free Slip was applied to the walls.
For this case the velocity normal to the wall and the wall shear stress are both set to
zero, whereas the velocity component parallel to the wall has the velocity computed
for the fluid flow at that location. No fluid is allowed to cross the surface domain.
Summarizing, for the constrained domain with free slip condition: Un,wall = 0 and
τw = 0.
53
Since a quarter domain was defined in the model, two boundary symmetry planes
were applied to the vertical (Y axis) and horizontal (X axis) respectively. This
boundary condition provided a plane of both geometric and flow symmetry.
The recommended general configuration of boundary conditions provided by the
ANSYS CFX Solver Modelling Guide [36] indicated that setting velocity flow at the
inlet and static pressure at the outlet is the most robust configuration. Thus, a
Cartesian velocity component inlet boundary was set up at the boundary surface,
having a uniform finite value in the direction normal to the surface (Z axis) and zero
in the X and Y axis, as Eq. (3.12) states.
Uinlet = Uspec,X + Uspec,Y + Uspec,Z = 0 + 0 + Uspec,Z
(3.12)
For the outlet surface, the static pressure outlet boundary was applied. A relative
average pressure equal to zero was maintained fixed at the outlet surface, as Eq. (3.13)
states.
paverage,outlet = pspec
(3.13)
In the additional simulations run to investigate the effects of the boundary layer
growth within the tunnel, the Wall No slip boundary condition was applied to the
wall surfaces. In these cases the velocity of the fluid is set to zero at the wall. Then,
the boundary condition for the velocity turned is Uwall = 0.
3.3
CFD Simulation Results
The results from the CFD simulations are presented in this section, where theory
stands for the values of the simple momentum theory without corrections.
Four different rotor sizes were computed in the CFD simulations, corresponding
to 5.5%, 9%, 20%, and 55% blockage ratios, where the blockage ratio was defined as
the ratio of the rotor swept area to the cross-sectional area of the tunnel (A/C). A
volume-weighted average axial induction factor was computed over the disk volume
for each run. The power coefficient CP was then computed as a function of the thrust
coefficient CT , which is an input to the simulations, and the axial induction factor,
as stated in Eq. (3.14):
CP = CT (1 − a)
(3.14)
54
3.3.1
Unbounded Flow Validation
The results for the power coefficient, for both laminar and turbulent flow simulations,
for unbounded conditions, were found to have good agreement with respect to the
standard actuator disc theory presented in Appendix A up to CT values of 0.8 (see
Figure 3.3). For higher values of CT , the difference between the simulations and
analytic theory becomes larger, as expected, due to the absence of a high thrust
coefficient model in simple momentum theory. Also, in terms of power coefficient,
there is no significant difference between the results obtained for laminar and low
turbulence level flow simulations.
Theory
Laminar 55% blockage ratio
K-Omega 55% blockage ratio
Laminar 5.5% blockage ratio
K-Omega 5.5% blockage ratio
CP
0.6
0.4
0.2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
CT
Figure 3.3: CP v/s CT for turbulent flow conditions in bounded domain with opening
boundary conditions
Referring to Fig. 3.3, the results from the smallest and larger disc sizes computed
(i.e. 5.5% and 55%) were used to check the opening boundary condition influence.
As the two results are quite similar, the ability of the opening boundary condition to
unduly influence the results for unbounded conditions is verified.
As part of the unbounded flow validation results, a disk thickness and mesh dependency study were also performed. For the disk thickness analysis, four width values
were computed, referred to the disc of 15 cm diameter. These four values correspond
55
to a thicknesses of 5%, 1%, 0.5%, and 0.25% of the disc diameter respectively. The CP
was computed for the four cases and the results compared to the CP values expected
from theory (Appendix A). Table 3.1 presents the difference between the computed
CP and the theory value, for each disc thickness case, over a range of CT values.
CT
0.1
0.3
0.5
0.7
0.9
5 % diameter
0.06
0.24
0.52
1.19
3.28
%
%
%
%
%
1 % diameter
0.06
0.23
0.52
1.15
3.18
%
%
%
%
%
0.5 % diameter
0.06
0.22
0.49
1.07
3.02
%
%
%
%
%
0.25 % diameter
0.06
0.22
0.49
1.07
3.01
%
%
%
%
%
Table 3.1: ∆ CP (%) with respect theory value for different disc thickness
From this study, a disc thickness of 0.5 % of disc diameter was found to be
appropriate for the simulations, since at this width value the difference in CP values
with respect the theory became almost constant. Decreasing the disc thickness further
did not increase the accuracy of the results but did increase the simulation run times.
Regarding the mesh dependency study, a similar approach was used to determine
the best mesh configuration based on a tradeoff between speed and accuracy. A
structured mesh was defined for the unbounded domain. Since the main changes in
the velocity vector occur in the axial plane (perpendicular to the rotor plane), the
mesh of the sections aligned with the rotor plane was kept constant upstream and
downstream of the rotor, and only the mesh comprising the elements perpendicular
to the disc plane were changed to explore mesh dependency. The mesh in the axial
plane was defined starting with the smallest element sizes at the disc plane and then
increasing the element size upstream and downstream perpendicular to the disc plane.
The mesh inflation ratio at the disc proximity was set to a value of 1.1.
Four cases were run, as detailed in Table 3.2, and the results in terms of the
difference between CP from simulations and theoretical expected values are presented
in Table 3.3.
Based on the result obtained for the different configurations, presented in Table 3.3, the mesh with 40 elements upstream and 50 elements downstream was found
56
Case No
Elements upstream
Elements downstream
Total mesh elements
1
2
3
4
20
40
80
100
25
50
100
125
95,885
178,910
344,960
427,985
Table 3.2: Cases for mesh dependency study
CT
Case 1
Case 2
Case 3
Case 4
0.1
0.5
0.7
0.9
0.10
0.57
1.13
3.16
0.06
0.49
1.07
3.02
0.06
0.49
1.07
3.01
0.06
0.48
1.07
3.01
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
Table 3.3: ∆ CP (%) with respect theory value for different mesh configurations
to be good enough for the purpose of the study. The finest mesh slightly increases
the accuracy of the results at the expense of greatly increased running time.
Regarding convergence, the RANS equations were solved with Root Mean Square
(RMS) velocity residual levels of 1E-05, within the maximum number of iterations
set for the solver, and a maximum momentum residual of 1E-04. Increasing the
number of iterations was not found to modify the results, and so the solution was
considered converged for the purposes of this study. Note that an RMS of 1E-05
indicates adequate convergence for most engineering applications [37].
3.3.2
Bounded Flow Results
Figure 3.4 shows the results for power coefficient and thrust coefficient in turbulent
flow conditions, for the water tunnel domain. It is seen that for CT values higher than
0.3, the increment in power coefficient with respect to the simple momentum theory
(Chapter A)for unbounded flows becomes noticeable, especially for the larger rotors.
It is found that as the blockage ratio increases, a higher maximum value of power
coefficient is obtained, which occurs at a higher CT value, as depicted in Fig. 3.5.
57
Theory
20% Blockage ratio
5.5% Blockage ratio
9% Blockage ratio
55% Blockage ratio
CP
1.00
0.80
0.60
0.40
0.20
0.00
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CT
Figure 3.4: CP v/s CT for turbulent flow conditions in water tunnel domain
Note that optimal rotor performance for free-stream conditions occurs at a CT value
of approximately 0.89, thus these differences become important. This effect was also
mentioned by Garret, in the study of the efficiency of a tidal turbine operating in
its optimum conditions [42]. Table 3.4 presents the maximum value of the power
coefficient found for each blockage ratio in the CFD simulations.
Notice that as the blockage in the tunnel is increased, extra power needs to be
added to flow. Physically this is made possible in the experiments by extra pressure
being provided by the pump system to keep a constant flow rate at the inlet of the
water tunnel while performing the experiments. In a real tidal channel, increased
blockage would in fact retard the overall flow through the channel. Therefore Fig. 3.5
should not be interpreted as indicated that very high blockage ratios are advantageous
(there will be a unique optimum for each channel [42]).
3.3.3
Tunnel Wall Boundary Growth Effects
The effect of boundary layer growth was explored for a blockage ratio of 9%, which
represents the scaled rotor size within the water tunnel facility. The results are shown
in Fig. 3.6. For the case in which a no-slip condition was defined at the wall boundary,
58
Theory
20% Blockage ratio
5.5% Blockage ratio
9% Blockage ratio
55% Blockage ratio
CP
3.00
2.50
2.00
1.50
1.00
0.50
0.00
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
CT
Figure 3.5: CP values for a wider range of Thrust Coefficients
an increment in power coefficient was found with respect to the case where free slip
condition was defined at the wall. This effect can be explained by a reduction in
the water tunnel section caused by the growth of the boundary layer. The increment
in power coefficient is not significant in this particular case, reaching a value of 2%
for a thrust coefficient of 0.9. The simplification of not resolving the boundary layer
helped to reduce the long run-times of the simulations, and focused the investigation
on the blockage effects for a given domain size, as discuss in Chapter 4. In any case,
this extra increment in power due to wall boundary growth effects can be eventually
Blockage ratio
Max. CP
CT
5.5%
9%
20%
55%
0.682
0.727
0.929
2.835
1.1
1.2
1.6
6
Table 3.4: Maximum CP values
59
incorporated to the final axial induction factor a-CP correction curve.
Free slip condition at the wall
CP
Non-slip condition (B.Layer)
0.80
0.60
0.40
0.20
0.00
0.1
0.3
0.5
0.7
0.9
1.1
1.3
CT
Figure 3.6: Boundary layer effect for a rotor diameter 15 mm (9% blockage ratio)
referenced to tunnel conditions
3.3.4
Reynolds Dependency Analysis
A set of simulations for turbines of different diameters and flow speeds were run to
explore the Reynolds wake dependency effects over a wider range of ReD . These
simulations, as detailed in Table 3.5, resulted in practical ReD ranging from 2x105
to 2x107 , where ReD is defined based on disc diameter. The intent of these simulations was to explore any Reynolds number effects in the viscous wake to verify the
assumptions of ReD independence in the CFD simulations.1 Clearly the actuator disc
simulations ignore any blade chord Reynolds number effects, which are known to be
important, but are a separate consideration to the wake dependency on ReD .
Simulations for each case detailed in Table 3.5 were run for different blockage
ratios. The change in power coefficient as defined in Eq. (4.4) was computed for each
case. Figure 3.7 presents the results for the power coefficient to thrust coefficient
1
It is commonly asserted that wake dynamics are ReD in experimental campaigns.
60
Turbine diameter [m]
Inlet velocity [m/s]
ReD
0.15
0.15
1
10
2
150
3
3
2x105
2x107
2x106
2x107
Table 3.5: Turbine size and flow conditions for additional RANS simulations
relationship in turbulent flow conditions for the unbounded domain. For thrust coefficients up to 0.8 good agreement can be observed for the power coefficient with
respect the theory, for the whole range of Re. Also, there is no noticeable difference
between the power coefficient values obtained in the simulations for Re ranging from
105 to 107 .
Figure 3.8 shows the increment in power coefficient with respect the unbounded
domain at CT = 8/9, as the blockage ratio varies, for different ReD conditions. There
is an expected positive trend; as the blockage ratio increases, the increment in CP also
becomes greater. With respect to the values of CP obtained for the same blockage
ratio and different Re numbers, there is only a subtle difference between the values,
less than 2 % in terms of CP increment that becomes noticeable at larger blockages
ratio values, such as 60 %. These results support the assumption that the mismatch
between full-scale and model scale Reynolds number do not affect wake development,
as these CFD simulations only simulate the wake behaviour.
61
CP Theory
Re 2x10^7 (Disc 15 cm)
Re 2x10^7 (Disc 10 m)
Re 2x10^5 (Disc 15 cm)
Re 2x10^6 (Disc 1 m)
CP
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.2
0.4
CT
0.6
0.8
1
Figure 3.7: CP v/s CT , Unbounded domain
Re 2x10^7 (Disc 10 m)
Re 2x10^7 (Disc 15 cm)
Re 2x10^5 (Disc 15 cm)
Re 2x10^6 (Disc 1 m)
∆ CP
35%
30%
25%
20%
15%
10%
5%
0%
0%
10%
20%
30%
40%
50%
60%
Blockage ratio [%]
Figure 3.8: CP increment v/s blockage ratio at CT = 8/9
62
Chapter 4
Tunnel Blockage Correction
Models
It is desirable in experimental testing to have larger scale models to achieve Reynolds
(Rec ) similitude. However, for a large ratio of rotor swept area to tunnel cross-section
area, the walls of the water tunnel constrain the flow and increase the velocities
around the rotor. This in turn increases the forces and torques compared to open
water conditions, as depicted in Fig. 1.2, Chapter 1. Thus, the values acquired from
experiments performed in tunnel facilities must be corrected to unbounded conditions,
to accurately predict the performance of full size turbines. Available methodologies
for correcting results handle the tunnel interference by determining an equivalent free
stream velocity, and correlating this value to thrust coefficient to finally correct the
measured power coefficient.
Hence, standard blockage correction techniques require measurement of rotor
thrust to correct power coefficients for bounded testing domains. Due to the small
forces and compact nature of the testing rig developed in this thesis, accurate thrust
measurement is not possible. This chapter therefore presents a methodology that utilizes the velocity field data at the rotor plane obtained from the water tunnel test and
CFD simulations based on the actuator disk concept to account for blockage without
the requirement for thrust data. The velocity can be obtained with PIV or other techniques, however PIV data is to be simultaneously utilized for wake characterization
and to estimated the average velocity at the disc plane, and so was made the basis of
the new correction technique.
In essence, the correction technique uses PIV measurements to compute an average
63
axial induction factor that can be related to the characteristic power coefficient. From
CFD simulations, the increment in CP is predicted for a given set of operational conditions that represents the water tunnel setup. These CFD values then provide a a-CP
correction curve to be utilized for processing the experiment test data. Furthermore,
to investigate the validity of the conventional analytical expressions, a comparison is
made between analytical and CFD correction results for different operational conditions and blockage ratios.
4.1
Thrust Based Analytical Models
One of the first tunnel correction methods was developed for propeller testing by
Glauert [20] in the late 1920’s. Glauert introduced the concept of equivalent free air
speed V 0 which would produce the same velocity at the disc, thrust and torque on the
rotor as those observed in the tunnel for the corresponding tunnel datum velocity U0 .
In that model, the real and scale machines both rotate at the same angular velocity
thus giving different tip-speed ratios for free and tunnel conditions. For propellers,
the equivalent free stream velocity is normally less than the tunnel datum velocity,
whereas for energy extracting devices, such as wind and tidal turbines, this equivalent
freestream velocity is larger than the tunnel datum speed.
To find the equivalent free velocity V 0 , based on the actuator disk approach, the
principles of momentum balance, force balance, and continuity are applied to the case
of the device rotating in the tunnel. Finally, an analytical expression correlating V 0 ,
inflow tunnel velocity U0 , relative rotor/tunnel size, and thrust coefficient CT is found
and used to correct the testing data to unbounded conditions. This method, based
on the axial momentum theory, is still widely used and has been adapted for wind
turbine experimental testing corrections [19], accounting for negative thrust (relative
to propellers which in Glauert’s theory have positive thrust).
An improvement to the Glauert method was recently developed by Mikkelsen and
Sorensen for wind turbines [21, 43]. This method is also based on the axial momentum
theory and the concept of equivalent free stream velocity of Glauert [20], but a new
solution was presented to account for the wall blockage effects of flow expansion. This
method has the advantage of working with non-dimensional variables and obtaining
the corrected free stream velocity UC in a more straightforward procedure but still
64
requiring thrust measurements. Moreover, this methodology resolved the singularity
inherent in Glauert’s correction for a thrust coefficient of -1.
Regarding tidal turbines, as yet little has been developed to account for wall interference in experimental testing. One good reference is provided by Bahaj [15] who
derived an analytical blockage correction for wake expansion applicable to experimental testing of tidal turbines. This analytical correction was derived using an actuator
disk model to represent the rotor of the turbine, and applying the principles of continuity and momentum and force balance on the water between the far upstream
and far downstream at the tunnel facility. An equivalent water speed UF , similar to
the equivalent free stream velocity V 0 determined by Glauert [20], was obtained by
applying an iterative procedure. Finally, experimental power and thrust coefficients,
as well as tip speed ratios are corrected as a function of the ratio of equivalent open
water speed to water tunnel velocity. The method is very similar to those developed
for wind turbines.
4.1.1
Momentum Based Model
The three analytic reference models cited above represent the propeller [20] or turbine
[15, 21, 43] by a disk plane that causes a uniform pressure drop as the flow goes across
it [1]. The flow field is assumed to be inviscid, irrotational, and incompressible over
the entire domain. Two separate regions are clearly defined as shown in Fig. 4.1; the
region inside the streamtube and the region between the streamtube and the walls of
the tunnel.
Far upstream, the flow is characterized by a uniform axial inlet velocity U0 and a
pressure p0 . A stream tube with upstream area smaller than the disc bounds the flow
through the disk. As the flow approaches the disk, its velocity slows down, which
also causes expansion of the streamtube. This induced velocity can be described
by a speed variation factor a = 1 − Uu10 called the axial induction factor. At the
disk plane, a pressure drop (p+ − p− ) is exerted to account for energy extraction,
and as a result of this the downstream flow inside the streamtube, called the wake,
proceeds with reduced pressure and reduced velocity, compared to the flow outside
the streamtube. In the far wake, it is assumed that the pressure has risen to match the
flow pressure outside the bounding streamline, and the wake has fully expanded. Very
far downstream viscous mixing combines exterior and interior flows. Refer to Fig. 4.1,
65
u3
Uo
p3
-T u1
p+ p-
Uo
A
u2
p2 = p3
W
C
po
Figure 4.1: Actuator disk model in a closed tunnel section
at the far wake p2 = p3 < p0 and u2 < u3 . Clearly the distinct wake expansion then
mixing regions are an approximation to reality, but this standard theory has been
shown to be a reasonable analytic model.
Unlike what this simple theory dictates and from which the analytical corrections
[15, 20, 21, 43] were obtained, while performing experimental testing in a water tunnel,
the viscosity and the turbulence in the fluid will produce - to a greater or lesser
degree depending on the flow conditions - lateral flow mixing between the wake and
the region outside the streamtube. Additionally, the larger the blockage ratio and
the rotor load, the larger the increment in the axial induction factor, which leads to
smaller velocities in the wake and higher velocities downstream outside the streamtube
which eventually will cause the flow to mix into the streamtube. Also, for higher
thrust loads, a region with flow recirculation becomes visible within the wake. These
effects are accounted for in standard the BEM theory used to analyze rotors through
empirical CT models, as the simple momentum formulations of BEM theory break
down. Therefore, depending on the operational conditions of the turbine being tested,
and the relative rotor size to the tunnel cross sectional area, analytical expressions may
66
not give accurate corrections. This uncertainty motivates the current investigation to
determine the blockage ratio range in which analytical corrections can be satisfactorily
applied without incurring significant errors. In addition, rationalized bounds on model
size and testing thrust values are required.
4.2
Blockage Correction Model Development
The models presented by Glauert [20], Mikkelsen and Sorensen [21, 43], and Bahaj
[15], provide a correlation between CT and the ratio of equivalent open velocity (UC ) to
tunnel velocity. This accounts for the change in loading and induced velocities, due to
wall interference in a testing tunnel, and can be used to correct the experimental data.
Once the theoretical corrected velocity is determined, by solving any of the methods
previously identified, the corrections to the experimental characteristic coefficients
are a straightforward mathematical calculation.
For a given CT obtained from thrust measurement in the test tunnel, there is a
corresponding correction factor that should be applied to get the equivalent characteristic coefficient in open conditions. Corrections for the power and thrust coefficients
and the tip speed ratio λ, as noted in reference [15] are:
U0
UC
3
U0
= CT,wt
UC
U0
= λwt
UC
2
CP,unb = CP,wt
CT,unb
λunb
(4.1)
(4.2)
(4.3)
where U0 is the actual inlet velocity in the experiments, UC is the velocity corrected
to freestream conditions, CP,unb , CT,wt , and λu nb correspond to the power coefficient,
thrust coefficient and tip speed ratio for unbounded domain, and CT,unb , CP,wt , and
λw t correspond to the power coefficient, thrust coefficient, and tip speed ratio obtained
in the tunnel facility.
It is important to notice that a difficulty arises in this process when thrust data
is not being acquired during testing. To address this issue, in the current work, CFD
simulations are used to estimate the corrected free stream velocity and to also provide
67
a correction curve relating the available experimental data and the corrected velocity,
as described in the following paragraphs.
Figure 4.2 shows the trend curve for CP versus CT for both domains, the water
tunnel and the unbounded region. ∆ is defined as the difference between the water
tunnel-power coefficient CP,wt and the unbounded-power coefficient CP,unb , for a given
CT value , as shown in Eq. (4.4). Note that CT is referenced to actual conditions in
both domains.
∆ = CP,wt − CP,unb
(4.4)
CP
Water tunnel
CP,wt
∆
CP,unb
Unbounded
domain
CT
Figure 4.2: Trend of CP v/s CT in water tunnel and unbounded domains
Thus, the power coefficients in the water tunnel and unbounded domains for a
given thrust coefficient can be expressed as in Eq. (4.5) and in Eq. (4.6), where Pwt
and Punb are the power extracted by the rotor in the water tunnel and unbounded
domain respectively.
68
CP,wt =
Pwt
1
ρAU03
2
(4.5)
CP,unb =
Punb
1
ρAU03
2
(4.6)
Since CP,wt > CP,unb , for a given CT value, it is clear that Pwt 6= Punb as defined
in Eq. (4.5) and Eq. (4.6). However, it is possible to define a corrected freestream
velocity UC that will produce the same thrust force at the rotor in the unbounded
domain as in the water tunnel, for a given velocity u1 across the disk, and when the
turbine is assumed to keep the same angular velocity [20]. Therefore, at these similar
conditions in the bounded and unbounded domains, the same torque and power are
generated.
For this corrected freestream velocity UC , the power in the water tunnel is the
0
0
same as the power in the unbounded domain Pwt = Punb
, where Punb
is the equivalent
power that the rotor would extract while running at the same rotational speed inserted
in a flow stream having a speed equal to the corrected free stream velocity UC [20].
Consequently, CP,unb can be rewritten as in Eq. (4.7), where CP,wt is found to be
proportional to CP,unb by a factor K 3 , as shown in Eq. (4.8). From CFD simulations,
the power coefficient for both the unbounded and water tunnel conditions can be
obtained for a range of thrust coefficients. Then, replacing the corresponding values
of CP,unb and CP,wt in Eq. (4.8) a correction factor K 3 , correlating power and thrust
coefficient, is estimated. Also, from CFD simulations an average axial induction factor
is computed for both the unbounded and tunnel domain, for the range of CT values.
As a result, there is a corresponding power coefficient CP , an axial induction factor
a, and a correction factor K 3 associated with each given thrust coefficient CT . In
such way, a curve correlating axial induction factor and thrust coefficient is obtained,
providing the final axial induction factor/power coefficient correction curve that will
be utilized in the data correction for the experimental testing.
0
Punb
1
ρAUC3
2
3
UC
= CP,unb
= CP,unb K 3
U0
CP,unb =
CP,wt
(4.7)
(4.8)
69
4.2.1
CFD Correction Factors
Using the same CFD models presented in Chapter 3 and Eq. (4.8), the ratio of corrected free-stream velocity to tunnel inlet velocity is found for a range of thrust
coefficients, in turbulent flow, and for different blockage ratios. The results are depicted in Fig. 4.3. As expected, the equivalent open velocity (UC ) is larger than the
inlet velocity (U0 ). Additionally, the corrected velocity increases as the rotor load
is increased (CT ) and this later effect is positively correlated to the blockage ratio.
Figure 4.3 only shown results to CT =1.0, since for the experiment the blockage ratio
is about 9% and this gives a corrected CT of 0.9, which is basically the maximum
power condition from theory.
9% blockage ratio
20% blockage ratio
55% blockage ratio
5.5% blockage ratio
UC / Uo
1.15
1.10
1.05
1.00
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
CT in tunnel
Figure 4.3: CFD-computed corrected velocity to inlet velocity ratio for different blockage ratios and operational conditions
Figure 4.4 shows a comparison between the analytical corrections in §4.1 and the
new CFD corrections applied to the power coefficient data simulated for the water
tunnel domain. The corrections were made utilizing the information presented in
Fig. 4.3 and the relation stated in Eq. (4.8). A good agreement is found between
both correction models for the smaller values of blockage ratio, corresponding to
5.5% and 9%, whereas for the highest blockage ratio of 55%, a noticeable difference
70
appears between the analytical and CFD corrections. At the Betz limit condition,
the analytical expressions seem to overestimate the corrections by 7% and 20%, for a
blockage ratio of 20% and 55% respectively.
Finally, a correction curve based on axial induction factor a-CP is obtained for
a 9% blockage ratio that will be utilized to correct the experimental data. The
correction curve is depicted in Fig. 4.5b which provides information related to the
power coefficient increment expected for a given axial induction factor. Given that
the novel CFD correction method appears valid for higher blockage rations, future
experimental campaigns will include larger rotors with higher blockage to validate
this approach. For these cases, additional CFD data for higher CT could be used to
generate extended correction curves. The use of larger rotors would of course alleviate
on-blade Reynolds Rec number effects as well as provide higher forces which could
improve the signal-to-noise ratios of the torque measurements. Typically, optimal
operational conditions occur at an axial induction factor of 0.3, thus a potential 20%
increment in CP can be predicted for the experimental data, as seen in Fig. 4.5.
71
Theory
Analytical correction
CFD correction
CP
0.80
5.5 % blockage ratio
0.60
0.40
0.20
0.00
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
CT
CP
0.80
9 % blockage ratio
0.60
0.40
0.20
0.00
0.1
0.2 0.3
0.4 0.5
0.6
0.7 0.8
0.9 1.0
0.6
0.7
0.9
CT
CP
0.80
20 % blockage ratio
0.60
0.40
0.20
0.00
0.1
0.2
0.3
0.4
0.5
CT
0.8
1.0
CP
0.80
55 % blockage ratio
0.60
0.40
0.20
0.00
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
CT
Figure 4.4: Comparison between analytical and CFD power coefficient corrections
(all values corrected to free-stream, CT referred to tunnel conditions)
72
UC/U0
1.06
1.05
1.04
1.03
1.02
1.01
1
0
0.1
0.2
0.3
Axial induction factor in tunnel
(a) Ratio of corrected velocity to tunnel velocity v/s axial induction factor for
a 9% blockage ratio
∆ CP (%)
20%
15%
10%
5%
0%
0
0.1
0.2
0.3
Axial induction factor in tunnel
(b) Increment in power coefficient v/s axial induction factor for a 9% blockage
ratio
Figure 4.5: Correction curve for the experimental testing referenced to tunnel conditions
73
Chapter 5
Experimental Procedures and
Testing Campaigns
The ultimate goal of the experimental rig developed in this thesis is to enable testing
of a wide range of model rotors. These scaled models of HATTs and HAWTs will be
tested in a pressurized water tunnel at UVic in order to obtain characteristic power
coefficients and to address the need for detailed rotor wake measurements that will
be used to validate numerical prediction models.
The rig is specifically designed for the water tunnel having a cross sectional area
of 45 x 45 cm, with a maximum flow speed of 2 m/s. The nominal rotor diameter
designed for is 15 cm, so that the rotor swept area to the water tunnel section will be
approximately 9% to limit blockage effects as discussed in previous chapters. However,
as noted in Chapter 4, it will be possible to use larger rotors and correct for blockage
effects a posteriori. The inlet velocity of the water tunnel is limited to 2 m/s. In order
to maximize the blade Reynolds number, and to obtain different tip speed ratios, the
rotational speed will be therefore be varied. The velocity field in the near wake behind
the rotor will be acquired using PIVs technique with digital technology [44, 45].
This chapter first describes the specific objectives of the experimental campaigns
to be conducted with the rig. The experiment protocol utilized to carry out experiments is described next, followed by results from the first set of results obtained from
the rig. The initial set of results presented in §5.5 (obtained by the author) turned
out to be not useful due to a number of difficulties realized after the test campaign.
The final set of results presented here were obtained by another co-op student, Peter
Root, with post-processing by the author.
74
5.1
Objectives of the experiment
The two specific objectives of this experimental rig are power output estimation and
the acquisition of the velocity field in the near wake behind the rotor, for different
operational conditions. Based on the power output estimation, the power coefficient
characteristic of the model run under different rotor speeds and inflow velocity in the
testing facility can be obtained. This characteristic is the fundamental performance
metric of any rotor. The vector velocity obtained in the near wake will provide
quantitative information to validate predictive codes. Additionally, as discussed in
Chapter 4, the same PIV data can be used to correct CP values obtained from the
experimental data.
5.1.1
Power output
For the power output estimation, the reaction torque of the motor driving the rotor
is measured. Having measured this reaction torque, the power output characteristic
of the model Pwt is estimated as follows:
Pwt = τrotor Ω
(5.1)
where τrotor is the measured reaction torque, and Ω is the angular velocity of the
rotor. Once the power output is computed for a diverse range of rotational speeds,
the power coefficient characteristic of the model is calculated as shown in Eq. (5.2).
CP,wt =
Pwt
3 πR2
1/2ρU∞
(5.2)
where CP,wt is power coefficient characteristic of the model running in the water
tunnel, ρ is the density of the water, and R the radius of the rotor.
The operational conditions can be expressed as defined in Eq. (2.1), where λ
relates the rotor speed and the tunnel inflow velocity, both characteristic factors of
the experiment being carried out. Notice that, later on, this experimental data must
be corrected to unbounded conditions as detailed in Chapter 4.
75
5.2
Experiment Protocol
The experiment will run the turbine placed inside a closed section water tunnel over
a range of rotational speeds. In such a way, it is possible to obtain a set of torque
measurements for a wide range of operational conditions. The results can then be
calculated and corrected for CP and λ to defined the characteristic curve of the rotor.
The first stage in the experiment, once the rig is placed into position with the
desired yaw condition for the particular test, is to fill the water tunnel until the
section is slightly pressurized. The pressurization is just enough to prevent air to
come into the tunnel while running the tunnel and the turbine.
Second, since the torque measurements are the net result of the forces on the
blades and the friction in the drivetrain of the rig, as discussed in §2.4, an important
step is to quantify the torque due to friction. This must be done without the rotor
blades installed, and a dummy hub installed instead of the rotor. The shaft is then
driven through the complete range of rotor speeds, and a correlation found between
friction torque and rotor speed. This friction torque will include bearing friction, the
dynamic seal on the shaft, and the belt system. The tests are run with the water
tunnel off, as the freestream fluid motion is unlikely to influence the frictions values
obtained (this has been verified experimentally). This frictional torque can then be
included in the final calculation of hydrodynamic torque, in order to isolate just the
component of torque due to the rotor. This friction estimation should be performed
every time the rotor is installed in the tunnel, and ideally before each round of testing.
Third, before starting up the rotor with the blades re-installed (the water tunnel
must be re-pressurized as well), the water tunnel is turned on and its flow speed is
gradually increased until reaching the value chosen for the set of measurements. Then,
the motor is run between 1 and 22 Revolutions per Second (RPS) for the data to be
acquired within that range. Notice that, as discussed in §2.4, the motor will operate as
a motor or generator depending on the net friction in the system, leading to turbine or
propeller operational conditions. This stage can be repeated for a number of different
inflow velocities in the water tunnel. The flow velocity is controlled by adjusting the
frequency of the pump system of water tunnel recirculation, as Table 5.1 shows. Note
that the advertised maximum flow speeds in some cases caused air leakage into the
tunnel, making it difficult for the tunnel to operate without air entrainment. This
can be avoided through additional pressurization (adding water) to the tunnel during
76
operation.
Finally, the water tunnel is turned off and the friction measurement is repeated.
It is important to open the drainage valve of the water tunnel when decreasing the
flow speed, otherwise the testing section is flooded and water will leak between the
sealed surfaces in contact with the top of the tank.
Frequency [Hz]
15
25.5
35
Tunnel inflow velocity [m/s]
0.6
0.9
1.3
Table 5.1: Pumping system frequencies and tunnel inflow velocity
5.3
Experimental Blade Sets
The blade sets used in these experiments had simple linear chord and twist distributions. The baseline blades used NACA63(2)-421 airfoil profiles. Inboard the blades
blended to a circular profile for attachment to the hub, which had a diameter of
19 mm. Over the active airfoil section of the blade, the chord tapered from 25 mm to
7 mm, and the blade was twisted 15 deg toward stall from zero pitch at the root. The
overall pitch angle of the blades in the rotors of the experiments was defined relative
to the pitch of the root section, with zero pitch aligning the root section in the plane
of rotation of the rotor.
For comparison to simulations, aero or hydrofoil properties at low Reynolds numbers can be input to the simulations, enabling comparison of the larger flow field
conditions and power outputs which are the primary area of interest for simulation
validation work. The blades produced for the rig using FDM technology (see §2.4.4)
inherently have a moderate surface roughness. Previous studies have shown that
fixed trip strips on the order of 0.25% chord located in the first 25% of the chord
can avoid the laminar separation type behaviour that limit airfoil performance at
Reynolds numbers around 1 × 104 to 1 × 105 [46]. The trip serves to prematurely
trigger turbulent transition, and this more energetic boundary layer is then able to
navigate the adverse pressure gradient on the airfoil without separation. In some cases
77
full transition may not occur at the trip strip, but reattachment can be facilitated
through laminar-turbulent transition over a laminar separation bubble.
Based on literature from the FDM manufacturer1 , the typical surface roughness Ra
for the finest T10 tips (0.127 mm inch) is 0.015 mm. For typical chord lengths for the
rig’s blades around 10-30 mm, the surface roughness is on the order of 0.15% to 0.05%
chord, but distributed over the entire blade surface. The natural as-produced surface
roughness is therefore expected to be in the proper range to promote transition to
turbulence and hence achieve reasonable airfoil performance without massive laminar
separation regions or large laminar separation bubbles.
5.4
Measurement Error Estimation
Defining the error of a measurement as the difference between the measured value
and the true value of the variable to be measured, in experiments we can identify two
main categories of errors: systematic errors and random errors. Systematic errors
are fixed or bias errors; they are consistent and repeatable. It is assumed that if the
same measuring system is used in the same manner, and several measurements are
taken, the error will be the same each time. Random error are the scatter in the data
measured caused by a lack of repeatability in the output of the measuring system.
The random error in a single measurement corresponds to the difference between a
single reading and the average of all reading.
Notice that normally is not possible to know the error level in an experiment.
However, the uncertainty interval of the measurement can be estimated. The uncertainty is defined as an estimation of the limits of error in the measurement [47].
Any experimental measurement will include some degree of uncertainty due to lack
of accuracy in the data acquisition equipment, random variation in the measurand,
sample size, etc.
Random uncertainty can be estimated using the expression given in Eq. (5.3):
SX
U N C.RX = ±t √
M
(5.3)
where U N C.RX is the random uncertainty estimation of the X measurement, SX is
the standard deviation of the sample, M is the sample size, and t is equal to 2 for
1
www.fortus.com
78
a sample size larger than 30 and a confidence level of 95 %. Notice that random
uncertainty trends to zero as the sample size increases.
Systematic uncertainty does not depend on the sample size. In a particular variable measured systematic uncertainties will remain constant if the experiment is repeated under the same conditions. These fixed errors can be estimated but not
eliminated from the measurement process.
In this study, uncertainty estimates were done to demonstrate the validity of the
results, and took into account the imprecision of the measurement (i.e. random
uncertainty) and an estimated maximum fixed error (i.e. systematic uncertainty) in
the torque data acquired.
Regarding PIV uncertainty, the main sources of error are related to the particle
displacement calculation. These errors mainly result from not choosing the most appropriate method to extract the displacement peak from the correlation function, or
for distortion of the correlation function [48]. Low seeding density, velocity gradients,
interrogation cell resolution, etc. can cause errors in locating particles’ position from
the images and errors in velocity calculation. Fortily and Strykowsky [48] presented
a procedure that allows quantification of the bias and precision errors of DPIV in an
attempt to correct the systematic error presented in the mean displacement measurements. However, no PIV data was acquired in this experiment thus, no uncertainty
analysis was be done for this measurand. As a reference, a similar experiment what
tested a scale model of a vertical turbine [49] in the same tunnel facility estimated the
total error in velocity was less than 2 %. However, values for spatial and temporal
resolution, appropriate for the operational conditions of this experiment, are needed
to more accurately estimate these errors.
5.4.1
Error estimation
In DAQ measurement systems there are several error sources, so called elemental error sources, generating either a random or systematic uncertainty. These elemental
errors can be arranged in 5 categories as ASME suggests [47]: calibration uncertainties, data-acquisition uncertainties, data-reduction uncertainties, uncertainties due to
method and other uncertainties. This grouping has the sole purpose of identifying
and comparing uncertainties in measurements. In the end the elemental uncertainties
79
are combined by using the square root of the sum of the squares (RSS) to obtain the
total uncertainty [47].
The standard calibration process done at the factory is intended to minimize
resulting systematic errors, however there are some residual errors, leading to systematic uncertainties. Example of these calibration uncertainties are hysteresis and
nonlinearity. In the experiment performed, there are two instruments involved: the
torque cell and the NI 9237 module for torque measurement (§2.5).
Table 5.2 presents a summary of the sources of elemental error and uncertainties of
the measurements associated with each instrument, based on technical specifications
provided by the vendor.
Instrument
Elemental Error
Torque Cell Non linearity
Torque Cell Repeatibility
Torque Cell Hysteresis
NI 9237
Gain error
Uncertainty (%)
0.1
0.05
0.04
0.2
Table 5.2: Uncertainties of measurement
Systematic and random uncertainty are combined by using the square root of the
sum of the squares (RSS) to obtain the total uncertainty. Notice that, because of
the large size of the sample (i.e. greater than 10, 000), the random uncertainty is
estimated to be zero. Then, the total uncertainty estimates result in approximated ±
0.23%, obtained as in Eq. (5.4), where UNC is the total uncertainty estimate. This
means a maximum possible error of ± 0.0023 Nm for any given measurement. As
this error level is so small, error bars are not shown on any of the results plots, as
they are too small to be seen.
UNC =
√
0.12 + 0.052 + 0.042 + 0.22
(5.4)
80
5.5
Initial Testing Campaign
For the first testing campaign, the submerged structure was aligned with the incoming
flow, thus no yaw condition was included. The frictional torque was measured for
several rotational speeds up to 22 RPS in the water tunnel turned off. The data
acquired were voltage values, which were then converted to torque values by simply
multiplying the raw data with the conversion factor given by the vendor of the load
cell as function of the excitation voltage. Then, the turbine measurements were done
for three different water tunnel speeds: 0.6 m/s, 0.9 m/s, and 1.3 m/s, with turbine
rotational speed ranging between 1 RPS and 22 RPS.
Frictional Torque [Nm]
2.5E-03
2.0E-03
1.5E-03
1.0E-03
y = 2E-05x + 0.0013
R² = 0.1113
5.0E-04
0.0E+00
0
5
10
15
20
25
Rotational Speed [Hz]
Figure 5.1: Frictional Torque - Dec. 2010
Notice that two forms of friction are present, static and dynamic friction. There
is an initial threshold static torque value that must be applied to start the shaft
rotating. Beyond that point, dynamic friction occurs. Since it was expected that the
dynamic frictional would vary with the rotational speed of the shaft, the frictional
torque was measured for different rotational speeds. A linear curve was then fit to
the frictional data in a least-squares sense, in order to get an analytical expression
to included in the final calculation of hydrodynamic torque. The frictional torque is
81
plotted in Fig. 5.1. In this first set of runs, frictional torque turned out to be of the
same order of magnitude as the turbine torque for rotational speeds up to 12 RPS.
CP
0.6 m/s
0.9 m/s
1.3 m/s
0,0
0
5
10
15
20
-0,2
-0,4
-0,6
-0,8
-1,0
-1,2
-1,4
-1,6
Figure 5.2: CP v/s λ Results Dec. 2010
The blades of the rotor were then installed at 0◦ pitch angle relative to the blade
roots. Unfortunately, as seen in Fig. 5.2, the measurements obtained in this first campaign were not useful in terms of characterizing turbine performance. Negative CP
values obtained confirmed the rotor was adding energy to the flow, not extracting as
expected for turbine rotor behaviour. The rotor operating as a propeller is explained
due to misalignment of the blade root, which resulted in a large negative pitch at
the tip and consequently, negative angles of attack accelerating the flow downstream
(propeller) rather than retarding it (turbine). This illustrates the utility of the motor/generator approach, so both turbine and propeller can be tested at constant λ.
5.6
Second Testing Campaign
As a result of the lessons learning during the first testing campaign by the author,
a second testing campaign was performed by a co-op student, Peter Root, who redesigned the blade roots and achieved proper pitch alignment. The tests were re-run
82
with 1X and 1.5X blades, [50], again with NACA63(2)-4XX airfoil profiles. where
the size scaling is defined in terms of chord and blade radius length. The 1.0X and
1.5X blade size designations refer to linearly scaled blades, with the 1.0X blade size
corresponding to blades of 75 mm radius length, root chord of 25 mm and tip chord
of 7 mm. The overall twist of the blade was kept constant.
Different flow conditions, blade sizes and surface roughness effects were explored
in this set of experiments. Measurement were taken at a combination of low tunnel
velocity (0.6 to 1.3 m/s) and high tunnel velocity (1.5 to 1.9 m/s); ‘smooth’ and
‘rough’ blade surfaces, for both the 1.0X and 1.5X blade sizes.
The ‘rough’ blades were produced using T12 FDM tips (see §2.4.4), while the
‘smooth’ blades were produced using T10 tips. The 1.5X blade was obtained by
scaling the 1.0X blade up by 50%. Also, BEM simulations were run following the
methodology developed by Crawford [51], to be used for experimental results comparison. The BEM code used is typical of design codes used for kinetic turbines. Lift
and drag 2D airfoil coefficients were estimated using the XFoil software2 [52], with
forced transition at two chord locations, 10 %c and 30 %c. Forced transition was used
to reflect the flow conditions on the rough blade surfaces, and because free-transition
was found to predict massive separation at the lower Reynolds numbers tested, even
though overall rotor performance was not indicative of massive separation.
5.6.1
Operational Conditions
Figures 5.3 and 5.4 illustrate the α and Re operational range respectively, along
the blade, for both the 1.0X and 1.5X sized blades. The results are from the BEM
simulations where α is defined as the angle of attack determined form the incident
resultant velocity in the cross-sectional plane of the airfoil.
This second test campaign also faced inconsistent results for power and CP values.
It was first found that signal to noise ratio is low for the slow tunnel speeds, because
torque values measured were quite close to friction torque levels. This can be improved
by increasing inflow speeds [50]. Thus, the following test runs were performed with the
tunnel running at 1.5 m/s, 1.7 m/s and 1.9 m/s tunnel inflow velocity, corresponding
to 40, 45, and 50 Hz pumping frequencies, respectively, as indicated in Table 5.3.
2
XFoil solves a coupled inviscid-viscid problem with boundary layer equations for 2D airfoils.
This allows for good prediction of lift/drag performance across a range of Reynolds numbers, up to
conditions nearing stall where the approach becomes invalid as gross separation occurs.
83
1X blades
α
1.5X blades
50
45
40
35
30
25
20
15
10
5
0
0.0
0.2
0.4
0.6
0.8
1.0
r/R
Figure 5.3: α (deg) v/s r/R
5.6.2
Experimental Results
Figures 5.5 and 5.6 show the results obtained for the 1.0 X blade size, rough surface,
and operating over different ranges of water tunnel speeds. BEM simulations results,
for both forced transition location xtr=0.1 and xtr=0.3, are also plotted as references.
Fig. 5.7 plotted the performance curve obtained for the 1.0X blade with smooth
surfaces at high water tunnel speeds.
The scatter in the data measured at the low flow speed conditions is noticeable in
Fig. 5.5, compared to that occurring at higher water tunnel speeds for both smooth
Frequency [Hz]
40
45
50
Tunnel inflow velocity [m/s]
1.5
1.7
1.9
Table 5.3: Pumping system frequencies and tunnel inflow velocity
84
Re
1X Blades
1.5X Blades
8.E+04
7.E+04
6.E+04
5.E+04
4.E+04
3.E+04
2.E+04
1.E+04
0.E+00
0.0
0.2
0.4
0.6
0.8
1.0
r/R
Figure 5.4: Re v/s r/R
and rough blade surfaces. Also, measurements from high tunnel velocities with rough
surfaces seems to have better performance curve agreement with BEM simulations
than the experimental data for smooth-surfaced blades. The smooth surface blade
results show lower CP peaks compared to the rough surface data, at the same conditions. There is also a clear shift in the CP vs. λ characteristic between the BEM
simulations and the experimental results. The differences are likely related to Re
number effects on the blade section characteristics, however the shift in performance
curves with respect to expected simulation results are not fully explained by his comparison.
5.6.3
Surface Roughness and Reynolds Number Effects
In order to explore and understand discrepancies due to Re and surface roughness,
Fig. 5.8 plots the results for the 1.0X and 1.5X blade sizes, both smooth surfaces, at
higher tunnel speeds.
It is instructive to look at the airfoil behaviour for an explanation. Figures 5.9
and 5.10 present predicted 2D lift coefficients over a range of angles of attack at
85
CP
1X rough 1.3 m/s
1X rough 0.9 m/s
1X rough 0.6 m/s
BEM 1X xrt03 1.3 m/s
BEM 1X xrt03 0.9 m/s
BEM 1X xrt03 0.6 m/s
BEM 1X xrt01 1.3 m/s
BEM 1X xrt01 0.9 m/s
BEM 1X xrt01 0.6 m/s
0,4
0,3
0,2
0,1
0
-0,1
0
1
2
3
4
-0,2
-0,3
Figure 5.5: CP v/s λ at low water tunnel velocity (rough)
different Re, for transition forced at 10 % and 30 % chord respectively. Here xtr is
defined as the location for forced transition in terms of percentage of the chord length
starting from the leading edge of the airfoil section. At a Re of 1 × 105 , there is a
bump in the curve between 12 degree and 14 degree data because the transition point
moves upstream of the 0.3c fixed transition point. The flow over the airfoil becomes
turbulent earlier, delaying laminar separation, thus reducing drag and increasing lift.
Then, for even higher angles of attack, turbulent separation grows and drag increases.
This situation is depicted in Figs. 5.11 and 5.12, at xtr = 0.1 and xtr = 0.3.
These predicted airfoil performance curves explain to some degree the higher CP
values for the rough blades surface compared to the smooth blades. As shown in
Figs. 5.3 and 5.4, the operational Re are in the 3 × 104 to 7 × 104 range and generally
below stall. Over those ranges, the 0.1c transition location curves (representative of
rough blades) generally have better performance in terms of drag compared to the
0.3c transition location curves (representative of smooth blades). Therefore, although
the BEM results to not predict large differences between bladesets, the experimental
data suggests that the airfoil performance is quite sensitive over this Reynolds number range, and to the surface roughness. The better performance of the smooth 1.5X
86
CP
1X rough 1.9 m/s
1X rough 1.7 m/s
1X rough 1.5 m/s
BEM 1X xrt03 1.9 m/s
BEM 1X xrt03 1.7 m/s
BEM 1X xrt03 1.5 m/s
BEM 1X xrt01 1.9 m/s
BEM 1X xrt01 1.7 m/s
BEM 1X xrt01 1.5 m/s
0,4
0,3
0,2
0,1
0
-0,1
0
1
2
3
4
-0,2
-0,3
Figure 5.6: CP v/s λ at high water tunnel velocity (rough)
blades relative to the smooth 1X blades indicate a significant Re effect, given the
surfaces have similar roughness. Comparing the rough and smooth 1X blade results
in Figs. 5.6 and 5.7 respectively, the rough results are clearly superior in terms of performance, again lending support to the hypothesis that rougher blade delay laminar
separation effects and enhance performance at these low Re numbers.
5.6.4
Estimation of Blockage Effects
It is also important to notice that increasing blade size lead to improved full size
turbine representation (larger Re), but also affects the measurements due to wake
expansion, and hence blockage effects must be explored too. Unfortunately, there was
no PIV data available to make a proper correction to experimental data accounting
for the induced velocity using the procedures developed in Chapter 4. However, a
rough CFD correction can be made, based on the methodology presented in Chapter 4,
considering lower and high thrust loads exerted by the rotor.
For the 15 cm rotor diameter (1.0X blade)the blockage ratio is about 9%. Two
correction factors K = UC /U0 are taken from the CFD simulations, Fig. 4.3, the first
for a low CT (e.g. 0.1) and the second for a high CT values (e.g. 1.0). In such a
87
CP
1X smooth 1.9 m/s
1X smooth 1.7 m/s
1X smooth 1.5 m/s
BEM 1X xrt03 1.9 m/s
BEM 1X xrt03 1.7 m/s
BEM 1X xrt03 1.5 m/s
BEM 1X xrt01 1.9 m/s
BEM 1X xrt01 1.7 m/s
BEM 1X xrt01 1.5 m/s
0,4
0,3
0,2
0,1
0
-0,1
0
1
2
3
4
-0,2
-0,3
Figure 5.7: CP v/s λ at high water tunnel velocity (smooth)
way, CFD correction bounds are plotted in Figs. 5.13 to 5.15 over the experimental
data for the 1.0X rough blade surface, the 1.0X smooth blade surface, and the 1.5X
smooth blade surface, for the water tunnel running at 50 Hz (1.7 m/s flow velocity).
These bounds on the corrections that should be applied to the data in the absence
of PIV data. This is true even at the relatively small 9% blockage ratio. It also
appears that some of the discrepancy between the 1X and 1.5X blades in Fig. 5.8 can
be explained by the higher blockage for the 1.5X blades not being accounted for in
the absence of PIV data . This suggests that the Rec effects may not be as dramatic
as initially suggested by the uncorrected performance curves.
88
1X smooth 1.9 m/s
1.5X smooth 1.9 m/s
BEM 1X xrt01 1.9 m/s
BEM 1.5X xrt01 1.9 m/s
CP
1X smooth 1.7 m/s
1.5X smooth 1.7 m/s
BEM 1X xrt01 1.7 m/s
BEM 1.5 xrt01 1.7 m/s
1X smooth 1.5 m/s
1.5X smooth 1.5 m/s
BEM 1X xrt01 1.5 m/s
BEM 1.5X xrt01 1.5 m/s
0,35
0,3
0,25
0,2
0,15
0,1
0,05
0
-0,05 0
1
2
3
4
-0,1
Figure 5.8: CP v/s λ at high water tunnel velocity, 1.0X and 1.5X smooth blades
CL
Re 5E+05
Re 1E+05
Re 5E+04
Re 3E+04
Re 2E+04
Re 1E+04
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.2 0
5
10
15
-0.4
α
Figure 5.9: CL v/s α, forced transition at 0.1 chord
89
CL
Re 5E+05
Re 1E+05
Re 5E+04
Re 3E+04
Re 2E+04
Re 1E+04
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.2 0
5
10
15
-0.4
α
Figure 5.10: CL v/s α, forced transition at 0.3 chord
CL
Re 5E+05
Re 1E+05
Re 5E+04
Re 3E+04
Re 2E+04
Re 1E+04
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.20.00
-0.4
0.05
0.10
0.15
CD
Figure 5.11: CD v/s CL xtr=0.1
0.20
90
CL
Re 5E+05
Re 1E+05
Re 5E+04
Re 3E+04
Re 2E+04
Re 1E+04
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.20.00
0.05
0.10
0.15
0.20
-0.4
CD
Figure 5.12: CD v/s CL xtr=0.3
BEM 1X xrt03 1.7 m/s
BEM 1X xrt01 1.7 m/s
1X rough 1.7 m/s
CFD corrected value (CT=0.1)
CFD correcte value (CT=1.0)
CP
0,4
0,3
0,2
0,1
0
-0,1
0
1
2
3
4
-0,2
-0,3
Figure 5.13: CP v/s λ 1X rough surface blade - correction bounds
91
BEM 1X xrt03 1.7 m/s
BEM 1X xrt01 1.7 m/s
1X smooth 1.7 m/s
CFD corrected value (CT=0.1)
CFD correcte value (CT=1.0)
CP
0,4
0,3
0,2
0,1
0
-0,1
0
1
2
3
4
-0,2
-0,3
Figure 5.14: CP v/s λ 1X smooth surface blade - correction bounds
BEM 1.5X xrt03 1.7 m/s
BEM 1.5X xrt01 1.7 m/s
1.5X smooth 1.7 m/s
CFD corrected value (CT=0.1)
CFD correcte value (CT=1.0)
CP
0,4
0,3
0,2
0,1
0
-0,1
0
1
2
3
4
-0,2
-0,3
Figure 5.15: CP v/s λ 1.5X rough surface blade - correction bounds
92
Chapter 6
Conclusions
Although it was not possible to complete final testing using PIV equipment during
the course of this thesis, a number of achievements were made. A rotor rig was
designed and tested, which when coupled with PIV measurements will provide highaccuracy data using small-scale blade sets, enabling a large testing campaign. A set
of testing procedures were developed, including a PIV-based correction routine, that
will enable proper post-processing of the results to account for blockage effects. The
initial set of experiments has also highlighted the key areas needing refinement to
enable comparison of simulation and experimental results.
6.1
Rig Design
The design of the test rig was a comprehensive task, which included consideration of
scaling issues to achieve appropriate scale models that maximize chord Re without
compromising the reliability of the experimental data acquired because of blockage
effects. FEM modelling of the structure was completed to avoid coupling of vibrations
in the system and deformations of the rig support and sting beyond limits predefined.
The mechanical design itself meet several conditions both required and desirable for
testing purposes. The features of the rig are that it: minimizes the disturbance of
flow, allowing testing in yawed flow conditions up to 45 ◦ , and providing control over
operational conditions; it has an interchangeable hub that allows varying size rotors;
and it is a rig that can be added to by other SSDL researchers as future requirements
arises. Most notably, the rig could be improved by automation of the yaw system for
future tests.
93
6.2
Computational Fluid Dynamic Simulations
This research developed a methodology for wall interference corrections, based on CFD
simulations, that can be applied to find a correction curve for the experimental data
acquired in tunnel testing facilities. This curve correlates the average axial induction
factor (a) and the power coefficient (CP ) in the water tunnel, and an explicit curve
a-∆CP is derived to correct the dimensionless water tunnel power coefficient (CP,wt )
to freestream conditions.
An interesting outcome is that CFD results and analytical expressions present
good agreement (less than 5% difference) for blockages ratios up to 10%. For higher
ratios of swept rotor area to tunnel section, analytical expressions - based on the axial
momentum theory - seem to underestimate the power coefficient in the water tunnel,
which leads to higher analytical correction factors compared to that obtained from
CFD simulations.
The results of the wake Reynolds dependency study show the simulations turned
out to be Reynolds independent, which allow extrapolating the results of the model
to real operation conditions of the full size turbine.
6.3
Experimental Study
An experiment protocol was developed to acquire torque measurements for different
operational conditions in order to finally obtain the performance curve of tip speed
ratio to characteristic power coefficient.
Two testing campaigns have been carried out so far. The first set of experimental
data revealed an error in the alignment of the blade root. The rotor was operating
as a propeller rather than a turbine; hence, it was not possible to use the acquired
information to characterized the turbine behaviour. However, the testing capability
of the rig was successfully verified, and the data acquisition hardware allowed for
controlled operational conditions as needed.
The second testing campaign provided more useful results. As first insight, measurements at low torque seems to be easily disturbed by other signals. Comparison of
data for each blade set across a range of higher water tunnel speeds show consistent
results. Comparison between blade sets of different sizes and similar roughness do
however likely show some Re dependency, however the bounds on the tunnel blockage
94
corrections to the data indicate that this effect may be dominant over Re dependency.
In any case, the CP results of smooth blade surfaces are lower than CP values obtained
from rough blades. Also, the best performance curves from simulation correspond to
rough blades at higher water tunnel velocities. It is clear that blade surface is a key
factor in the blade performance. Roughness significantly affects flow separation onset
on the airfoil profile, causing an earlier transition to turbulence and drag reduction
for angles of attack up to approximately 14 degree at 1E + 05 Re.
6.4
Future Work
It is obvious from the results presented in this thesis that in order to compare simulation and experimental results, the low Reynolds number performance of the airfoils
to be used on the blade sets must be ascertained. The effect of roughness, including manufacturing procedures and setup, must be a part of the characterization. To
this end, the additional experimental apparatus under construction in the SSDL is
required to experimentally measure 2D airfoil performance, as analysis codes such as
XFoil have ambiguous parameters and must be validated to use predictively.
Obviously the next step in the rig testing campaign is to integrated the PIV system,
and acquire simultaneous torque and PIV data. With this extra data, the mechanical
data can be properly corrected. Furthermore, the wake structure information will be
invaluable in validating rotor computation models, once accurate 2D airfoil data is
obtained. In the longer term, new blade designs can be constructed and tested on
the rig to validate performance of a wide range of kinetic turbine designs.
95
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100
Appendix A
Momentum Theory: The Actuator
Disc Concept
Figure Fig. A.1 illustrates the actuator disc concept, where the disc represents a
rotor with an infinitive number of blades. The upstream flow gradually slows down
its velocity when approaching the disc, and reaches a lower value as it arrives at the
disc. Just before the disc, there is a stream-tube expansion as a result of the flow
retardation and, since no work has been on the flow yet, the static pressure in the
fluid rises to absorb the decrease in kinetic energy. At the disc plane work is done on
−
the fluid, resulting in a static pressure drop (p+
d − pd ) as the fluid passes through the
disc. The fluid then proceeds downstream with reduced speed and static pressure; this
region of the flow is called the wake. Eventually, far downstream, it is assumed that
pressure equilibrium is achieved as the wake achieves full expansion and the static
pressure in the wake returns to the original upstream value. In the standard theory, a
streamtube is assumed to exist downstream of the rotor separating the external flow
and the flow through the rotor. In the very far wake, it is assumed that mixing across
the streamtube boundary returns the wake flow back to the uniform inflow velocity.
Within the boundaries of the streamlines, the rise in static pressure is at the
expense of the kinetic energy and so causes a further slowing down of the flow.
The flow expansion is due to mass flow conservation, see Eq. (A.1). Because there
is a reduction in the velocity, the cross sectional area must increase since the mass
flow rate must be the same everywhere along the stream-tube.
101
Figure A.1: An energy extracting actuator disk and stream-tube (adapted from the
Wind Energy Handbook [1])
ρA∞ U∞ = ρAd Ud = ρAw Uw
(A.1)
where ρ is the fluid density; A, U are the cross sectional area and the fluid velocity
at the respective locations. The symbols ∞, d, and w, stand for the undisturbed flow
far upstream, the disc position, and the far wake respectively.
Near the disc, the actuator disc reduces the velocity of the free-stream as the
presence of the rotor is felt by the flow. This variation can be expressed in terms of
the free-stream velocity U∞ and the so called axial induction factor a as shown in
Eq. (A.2):
Ud = U∞ (1 − a)
(A.2)
102
The flow inside the boundaries of the stream-tube that passes though the disc
experiences a rate of change in momentum, as given in Eq. (A.3) which is essentially
given by the change in velocity times the mass flow rate. Notice that in this simplified
model the force that causes this change in momentum comes entirely from the pressure
difference across the actuator disc, as given by the right hand side of Eq. (A.3).
Thought of another way, the momentum deficit is absorbed by the momentum sink
representing the rotor in the CFD simulations (§3.2.2).
−
(U∞ − Uw )ρAd Ud = (p+
d − pd )Ad
(A.3)
Then, substituting Eq. (A.2) into the Ud term in left side of Eq. (A.3) we obtain
Eq. (A.4):
−
(U∞ − Uw )ρAd U∞ (1 − a) = (p+
d − pd )Ad
(A.4)
Applying Bernoulli’s equations at both sections of the stream-tube, upstream and
downstream, with respect to the actuator disc plane, we can obtain the pressure difference across the disc. It is important to notice that the total energy is different
upstream and downstream, thus two separate equations, Eq. (A.5) and Eq. (A.6),
are required to obtain this pressure difference approaching from upstream and downstream respectively.
The general Bernoulli’s equations for steady conditions states that the total energy
in a streamline flow remains constant if no work is done on or by the fluid. For this
study the flow is assumed to be incompressible (ρ∞ = ρd = ρw = ρ), and the disc is
perpendicular to the flow.
Therefore, in the upstream section Bernoulli’s equation results in:
2
2
p+
d = 1/2ρ(U∞ − Ud ) + p∞
(A.5)
Between the disc and the downstream station we obtain:
2
2
p−
d = 1/2ρ(Uw − Ud ) + p∞
(A.6)
103
Next, subtracting equations Eq. (A.5) and Eq. (A.6) we obtain Eq. (A.7):
−
2
2
p+
d − pd = 1/2ρ(U∞ − Uw )
(A.7)
Finally, substituting Eq. (A.7) and Eq. (A.2) into Eq. (A.4), we obtain that the relation between the velocity downstream far in the wake and the upstream undisturbed
velocity in terms of the axial induction factor a as shown Eq. (A.8):
Uw = (1 − 2a)U∞
(A.8)
The thrust force T can be computed from the pressure drop times the disc surface
−
area Ad as T = (p+
d − pd )Ad . From Eq. (A.4) and Eq. (A.8), we can rewrite the thrust
force in terms of the undisturbed upstream velocity U∞ , the density ρ, an the axial
induction factor (a) as given in Eq. (A.9):
−
2
T = (p+
d − pd )Ad = 2ρAd U∞ a(1 − a)
(A.9)
Then, the rate of work done by the thrust force times the local flow velocity at the
disc Ud is defined in Eq. (A.10) (equation obtained from Eq. (A.9) and Eq. (A.2)),
which indeed represents the useful power extraction from the air.1
3
T Ud = 2ρAd U∞
a(1 − a)2
(A.10)
Finally, the useful power extracted (P = T Ud )can be non-dimensionalized to give
a power coefficient CP as defined in Eq. (A.11), where the denominator represents
the available power in the flow without disc. The equation is finally written in terms
of the axial induction factor for the actuator disc theory.
CP =
1
etc.
3
2ρAd U∞
a(1 − a)2
= 4a(1 − a)2
3 A
1/2ρU∞
d
(A.11)
Note that T U∞ is the total work done on the flow by the disc including all wake mixing losses,
104
In similar manner, the force on the actuator disc (thrust force) is non-dimensionalized,
and expressed in terms of the axial induction factor, to give a thrust coefficient CT :
CT = 4a(1 − a)
(A.12)
These quantities can also be defined using results from CFD and experimentally
determined quantities as:
P
3 A
1/2ρU∞
d
T
CT =
2 A
1/2ρU∞
d
CP =
(A.13)
(A.14)
The development of the analytic tunnel blockage correction models referred to
in Chapter 4 is based on this theoretical approach and its limiting assumptions. For
example, the maximum achievable value of power coefficient turns out to be 0.593, for
a = 1/3, commonly referred to as the Betz limit. Recall that the actuator disc model
considers the stream-tube to be completely surrounded by flow at constant pressure,
with no lateral mixing between the external and internal regions. In addition, if the
streamtube is expanding, there must be a net axial pressure force on the sides of the
streamtube, but this is ignored in the simple analytic actuator disc theory. As shown
in the CFD simulations for unbounded domain in §3.3.1 these assumptions are only
approximately true, and so the simple analytic theory must be treated with caution,
including instances when correction factors (e.g. for high thrust/induction cases) are
employed.
105
Appendix B
Finite Element Analysis Modelling
As described in Chapter 2, the experimental setup consists of a three-bladed rotor
attached to a main shaft which is driven by an electric motor mounted on a platform
above enclosed water tunnel. To connect the rotor to the motor (generator) a belt
carried up through a vertical support tube which connects to the main body of the
turbine. The main upright body (tube3 )and the horizontal bodies (tube1 and tube2 )
are made of alloy aluminum tubing. This appendix describes, step by step, the
methodology followed and required in the FEM analysis.
B.1
Geometry and Material Properties
The submerged structure of the testing rig, shown in Fig. 2.3 in Chapter 2, is mainly
made of high-strength aluminum (alloy 2024) tubes. This structure can be modelled
as three tubes of different length, diameter, and thickness, joined by rigid connections
as shown in Fig. 2.3. This scheme is a simplification of the structure that satisfied
the purposes of the FEM performed using ANSYS 11.0. The detailed dimensions of
each tube is presented in Table B.1.
The density and modulus of elasticity of the aluminum are about one third of the
respectively values of the steel. It is ductile and easily machined, which is why it
was chosen for this particular design. A Young’s modulus of 70 GPa, a density of
2700 kg and a Poisson’s modulus of 0.35 are considered as properties for this particular
structural model.
The yield strength of pure aluminum is 7 MPa to 11 MPa, while aluminum alloys
have yield strengths ranging from 200 MPa to 600 MPa. For this model a value of
Variables
Length tube1 cm
Diameter tube1 in
Wall thickness tube1 in
Length tube2 cm
Diameter tube2 in
Wall thickness tube2 in
Length tube3 cm
Diameter tube3 in
Wall thickness tube3 in
Model 3 Model 4 Model 5 Model 6 Model 7 Model 8
30
30
30
30
30
20
0.5
0.5
0.5
0.5
0.75
0.5
0.058
0.065
0.065
0.12
0.12
0.065
5
5
5
5
5
5
0.75
0.75
0.75
0.75
0.75
0.75
0.058
0.065
0.065
0.12
0.12
0.065
25
25
25
25
25
25
0.75
0.75
0.75
1
1
0.75
0.058
0.12
0.12
0.12
0.12
0.12
Table B.1: Configurations of study for modal analysis
Model 1 Model 2
30
30
0.5
0.5
0.058
0.058
5
5
0.75
0.75
0.058
0.058
25
25
0.75
0.75
0.058
0.12
Model 9 Model 10
20
20
0.5
0.75
0.12
0.12
5
5
0.75
0.75
0.12
0.12
25
25
1
1
0.12
0.12
106
107
200 MPa is used as yield strength, typical of the 6061 aluminum available in the
machine shop.
The origin is located at key point 1. The tubes are defined in Ansys by keypoints
and lines as shown in Fig. B.1. The three tubes are connected by flanges at keypoints
2 and 3, and the rotor is located at keypoint 1.
Figure B.1: Rig structure modelling
The seven keypoints defined six line-elements on the model; the properties associated with each type of tubing are set up on each of the six lines. A linear isotropic
model is selected for the aluminum material. For the nodal analysis the mass associated to the flanges connection at node 2, 3 and 7 is neglected, however the mass of
the rotor at the nose of the structure will be included for the modal analysis as a mass
point located in node 1. Nodes 5 and 6 are defined for support of a streamline-plate
that will avoid excessive disturbance and forces on the vertical tube. For this analysis, no forces will be applied to these two keypoints, the design of the streamlined
component is not yet defined. With respect the boundary conditions, displacement
and rotation about all axes are zero at keypoint 7, which connect the tubes-structure
with a platform located outside the water tunnel.
108
B.2
Forces Applied to the System
Referring to Fig. B.2 the tubing-structure will support the rotor located at key point
1, and then the force exerted by the fluid flow at the rotating set of blades will be
directly transmitted to the tubing structure. When the rotor is aligned with the
horizontal tubing and the plane of the rotor faces the flow orthogonally, the force
at node 1 is a vector acting along in the X direction only: FX as shown scheme.
The system will also operate in yawed conditions in the XZ plane. Only the plane
of the rotor is modified, and then the tubing structure keeps it location. The force
applied on node 1 will be a vector with components acting in the X and Z axis. No
yaw is exerted in the YZ plane. Forces applied on any other node are neglected in
this model. For the static analysis, the maximum possible value of these forces it is
applied.
Figure B.2: Rig structure modelling
The resultant maximum forces are summarized in Table 2.2.
Since the forces are both aligned on the rotor axis and yawed in the plane XZ,
displacement in X, Y, and Z direction can occur. A three dimensional analysis was
109
performed, and thus an element with 3D capabilities (axial, torsion and bending in
X,Y and Z directions) was used to model the tubes. In addition, a mass element was
chosen to represent the rotor attached to the horizontal tubing 1.
PIPE16 Element was selected for the tubes. PIPE16 is a uniaxial element with
tension-compression, torsion, and bending capabilities. The element has six degrees
of freedom at two nodes: translations in the nodal x, y, and z directions and rotations about the nodal x, y, and z axes. This element is based on the 3-D beam
element (BEAM4), and includes simplifications due to its symmetry and standard
pipe geometry [28].
For the element input data, it was required to include the pipe outer diameter
and wall thickness, as detailed in Table B.1. The density of the material, elasticity
and Poison’s ratio was already defined in material properties for aluminum material.
The element mass is calculated from the pipe wall material.
To represent the mass associated with the rotor, the MASS21 element is available
in ANSYS. MASS21 is a point element having up to six degrees of freedom: displacement in the X, Y and Z direction and rotation about the nodal X, Y and Z axes. The
mass element is defined by a single node; in this case associated to keypoint 1, and
having a mass of 30 gr.
B.3
Maximum Deflection - Results
The maximum deflection and stresses were computed for the forces estimated at the
rotor plane for both, the yawed and non-yawed condition (see Table 2.2 in Chapter 2.
The following Table B.2 shows the maximum deflections and the maximum stresses
(von Misses) computed when the inflow is aligned with the axis of the turbine.
Observing the system loaded in the axial turbine direction only, which is the stiffer
condition of the structure, models 1 to 4 already experienced deflections of 1 mm or
larger. Consequently, those first four configuration were no longer considered for the
yawed condition analysis. Tables B.3 and B.5 present the maximum deflection of the
structure and maximum von Mises stresses computed for the yawed conditions of 30◦
and 45◦ respectively.
110
Case
M odel1
M odel2
M odel3
M odel4
M odel5
M odel6
M odel7
M odel8
M odel9
M odel10
Max.deflections [mm]
1.63
0.997
7.31
0.997
0.374
0.374
0.374
0.764
0.286
0.286
Max.Stress [MPa]
24
14.7
68.40
14.7
7.31
7.31
7.31
14.7
7.31
7.31
Table B.2: Maximum deflections and stresses (Non-yawed condition)
Case
M odel5
M odel6
M odel7
M odel8
M odel9
M odel10
Max.deflections [mm]
1.5
1.228
0.645
1.064
0.506
0.358
Max.Stress [MPa]
6.91
6.91
6.91
13.5
6.57
6.57
Table B.3: Max.deflections and stresses at 30◦ yaw angle
B.4
Modal Analysis - Results
Results of the modal analysis for models 5 to 10 are presented in Table B.5:
B.5
Mesh Refinement
The structure was defined by 7 keypoints; six element lines Pipe 16 and one element
MASS 21 at node and keypoint 1. Different elements size were computed to study
the effect of the number of elements in results of the model.
In general terms, a fine mesh allows the definition of small ”sub elements” to get
good values of the distribution of stresses along the total length of each element. In
such a way the solution and stress values will be more precise, and it is possible to
111
Case
M odel5
M odel6
M odel7
M odel8
M odel9
M odel10
Max.deflections [mm]
2.155
1.736
0.817
1.219
0.646
0.378
Max.Stress [MPa]
4
3.84
3.84
6.69
3.37
3.37
Table B.4: Maximum deflections and stresses at 45◦ yaw angle
Mode
M ode1
M ode2
M ode3
M ode4
M ode5
M ode6
M ode7
M ode8
M ode9
M ode10
M odel5
55
576
204
263
543
555
1, 446
1, 466
1, 785
1, 885
M odel6
56
59
184
235
506
523
1, 333
1, 374
1, 743
1, 797
M odel7
69
76
196
237
713
742
1, 627
1, 635
2, 087
2, 204
M odel8
74
82
175
215
897
951
1, 385
1, 407
2, 650
3, 014
M odel9
97
105
217
274
947
1, 002
1, 684
1, 774
2, 549
3, 031
M odel10
108
117
260
289
1, 292
1, 293
1, 818
1, 874
3, 360
3, 677
Table B.5: Result of modal analysis - natural frequencies [Hz]
identify areas with higher critical tensile stresses in the structure. Specially, when
there are distributed loads applied to the system, and the purpose of the analysis is
to resolve peak bending stresses, the node point should be near the real location of
the peak value, otherwise the linear bending moment can be underestimated. In this
particular model there is only one point load. Even if the maximum displacement
obtained will be not affected by the mesh size, since a modal analysis was also performed, it was important to obtain accurate solutions for the peak stresses, so mesh
refinement was performed.
Note that the maximum number of nodes that the Academic Version of Ansys
11.0 allows is 32, 000. Thus, the smallest possible element for this model has a length
of 0.025 mm.
112
For the mesh analysis, a modal analysis was performed over the M odel1 0 configuration, with the mass element added at key point 1, considering different element
sizes for the mesh. The first 20 modes of each coarser mesh of element sizes 100 mm,
10 mm, 1 mm, and 0.1 m were compared to the modes obtained for the finest possible
mesh of element size 0.025 mm.
Figure B.2 show the differences between the frequency results obtained for each
coarser (100 mm, 10 mm, 1 mm, and 0.1 mm) mesh and the finest possible mesh
allowed by software limitations. It was found that an element of 0.1 mm size provides
accurate enough results compared against to the results obtained for the finest mesh.
Thus, this 0.1 mm element size is used to compute the static and modal analysis for
the different set of configurations.
Mesh_100_mm
Mesh_1_mm
0.001%
0.00%
-5.00% 0
5
10
15
20
25
-10.00%
-15.00%
-20.00%
Difference (%)
Difference (%)
5.00%
-25.00%
0.000%
-0.001% 0
5
20
25
20
25
-0.002%
-0.003%
-0.003%
Modes
Mesh_0.1_mm
Mesh_10_mm
0.05%
0.100%
5
10
15
-0.10%
-0.15%
-0.20%
-0.25%
20
25
Difference (%)
Difference (%)
15
-0.002%
Modes
0.00%
-0.05% 0
10
-0.001%
0.080%
0.060%
0.040%
0.020%
0.000%
0
Modes
5
10
Modes
Figure B.3: Mesh analysis (M odel10 )
15
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Appendix C
PIV Theory
The fundamental premise of the PIV technique is that instantaneous fluid velocities
can be evaluated by recording the position of images produced by small markers,
suspended in the fluid, at consecutive intervals time. This concept assumes that the
small particles follow the fluid motion, with minimal lag, and do not modify the fluid
properties. Solid particles are often employed as markers, either in liquid or gas fluid
flow.
In a typical arrangement of a PIV system, the fluid being studied is illuminated
by a pulsed light sheet. A photograph or video device is located in the plane perpendicular to the sheet to capture the light reflected by the particles seeded in the fluid
that follow the flow motion. Finally, the information is transferred to a computer to
be analyzed [53].
By controlling the pulse light and the continuity of the image recording (frame)
several representations of pulse code and framing can be obtained, for example multiframe/single-pulse, etc. The relevance of the pulse code is to provide images of
the location of the particles in an interval of time ∆t that allows calculating the
displacement of the particles for a particular flow condition. The separation of the
pulses ∆t of light in addition to light intensity are the factors that rule the range of
velocity possible to be measured, and the sharpness of the particle picture obtained
[53].
Two distinct operation modes are possible in this technique: the autocorrelation mode where two or more instantaneous image patters created by the tracers is
recorded in the same frame; and the cross-correlation mode, in which the individual
instantaneous patterns are kept in separate frames. The time separation between
114
exposures is chosen in such a way that the markers will have moved only a few diameters, far enough to resolve their motion, but less than the smallest fluid macro
scale. The distance between the multiple-exposed images from one marker, which is
proportional to the fluid motion, can be obtained by using standard image processing
techniques [33].
In digital particle image velocimetry (DPIV) the information of two consecutive
digital images through an interrogation window at a specific area is used, and the local
spatial cross-correlation is performed computationally. The mean observed spatial
displacement between the particles of the twin images can be predicted with a linear
model. The input to the system is the first sampled region f (m, n); the output of the
system is the twin image taken in a posterior ∆t time, g(m, n). The mathematical
expression that describes the output function as a result of the displacement function
applied to the input data is given by the following Eq. (C.1), which is basically the
spatial discrete convolution of f (m, n) and the spatial shifting function s(m, n);
g(m, n) = [
∞
∞
X
X
(s(k − m, l − n)f (k, l))] + d(m, n)
(C.1)
k=−∞ l=−∞
The displacement function can be obtained by finding the best match between
the images in a statistical sense. This is achieved by calculating the discrete crosscorrelation function Φf,g (m, n) of the sampled regions, as is written in the following
Eq. (C.2);
P∞
P∞
f (k, l) · (g(k + m, l + n))
k=−∞
P∞ l=−∞
P∞
P∞
Φf,g (m, n) = P∞
k=−∞
l=−∞ f (k, l)
k=−∞
l=−∞ g(k, l)
(C.2)
Basically, the cross-correlation function statistically quantifies the degree of match
between the two samples for a given shift. When a significant number of particles
have a strong linear relationship with its twin image shifted, a value of 1 is expected
from the cross-correlation. Among the peaks correlation values observed, the highest
one represents the strongest match. The maximum cross-correlation value matches
the position of the displacement function [45].
The cross-correlation of two functions is equivalent to a complex conjugate multiplication of their Fourier transforms, and the cross-correlation process can be accel-
115
erating by applying a Fast Fourier Transformation (FFT) [45]. The figure Fig. C.1,
taken from Digital Particle Image Velocimetry [45] shows the last version of the technique presented by Willert and Gharib (1991). In this enhanced process, the crosscorrelation is computed over the spatial frequency domain, where Fourier transform
were first performed to both of the images digitally recorded.
Figure C.1: Numerical processing flow-chart DPIV
By implementing this FFT the number of computations is greatly reduced. To
obtain the cross-correlation peak, a parabolic or exponential curve is adjusted around
to the highest element initially estimated for the two dimensional array. Finally, once
the image displacement have been determined, by using the magnification factor
between the image plane and the object plane it is possible to calculate the particle
displacement, and then the velocity of the flow.
To deal with the inherent restriction in the resolution and ambiguity in the DPIV
measurement, the particle image size, the size of the interrogation window, local
velocity gradients, the number of particles within the sampling window, the apparatus
performance, quantization effects, and computational errors are factors that must be
taken into account when performing the analysis. For example, an increase in seeding
densities has a positive effect in the certainty in the measurement. There are two main
factors that lead to inaccuracy in the displacement measurement: the intrinsic error of
the peak correlation estimation considering three points; and the presence of gradient
velocity in the flow field that is not appropriated taking into account [45].
116
In the experiment carried out by Willert and Gharib [45], which studied the temporal evolution of a vortex ring, the displacement vector obtained shows areas of high
velocity gradients near the center of the core. These gradients will bias the crosscorrelation peak. To avoid this effect, a possible solution is to lessen the sampling
window for the analysis, but this action will also affect the spatial resolution because
the lower density seeding of the images taken [2]. Then, the way to deal with this
problem is to remove the doubtful data which could lead to misinterpretation, and
some vectors for each data set must be interpolated with the associated loss of information. Also, a convolution filtering (low pass spatial filter) could be applied to the
data, which eliminates the high frequency jitter associated with the different location
estimates of the cross-correlation peak, with no information lost. The validation of
the measurements is so far the most difficult and laborious duty within this whole
process [45].
Several types of errors can be found in velocity measurement in DPIV; however,
the interesting point is the errors in the particle displacement calculation. This error can be the result of not choosing the most appropriate method to extract the
displacement peak from the correlation function, or for distortion of the correlation
function, for example due to velocity gradient [48]. Fortily and Strykowsky (2000)
presented a procedure that allows quantifying the bias and precision errors of DPIV
in an attempt to correct the systematic error presented in the mean displacement
measurements.
In this procedure [48], to resolve the directional ambiguity two digital images at
each pulse separation were taken within this region a wide range of flow gradients are
presented, and the digital images are processing with the different algorithms available
in the software package that is being utilized for the experiment. Firstly, images must
be taken for non-flow conditions, several uniform displacement images are generated
by varying the mirror speed and pulse separation, in this fashion a wide range of
displacement and a detailed measurement of the sub-pixel displacement region are
obtained. For example, if the sampling windows size has 128x128 pixels, and the
images are interrogated on a spatial grid of 30x10 displacement measurements over the
image domain, then 300 displacement vectors can be obtained for each image. If the
interrogation windows are large, the displacement peaks results clearly taller than the
noise peaks, at each image. Finally, the bias error can be calculated as the difference
between the displacement measured and the displacement generated (at each pulse
117
separation), which represents the error in the average displacement measured. This
calibration process is suggested to find the best mathematical algorithm option, for
the particular experimental set up, within the available methods available in the
software in use.
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