The Influence of Waves on Tidal Stream Turbine Arrays

238 Pages·2016·11.81 MB·English

The Influence of Waves on
Tidal Stream Turbine Arrays
A thesis submitted to The University of Manchester for the degree of
Doctor of Philosophy in the Faculty of Engineering and Physical
Sciences
Author:
Alexander Olczak
School of Mechanical, Aerospace and Civil Engineering
Contents
1 Introduction, Aims and Objectives 23
1.1 Tidal Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.2 Tidal Stream Energy . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.3 Tidal Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.4 Research Aims . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
1.5 Review of Research Approach . . . . . . . . . . . . . . . . . . . . 30
1.6 Characteristics of Tidal Stream Sites . . . . . . . . . . . . . . . . 31
1.6.1 Tidal Resource . . . . . . . . . . . . . . . . . . . . . . . . 31
1.6.2 Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.6.3 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . 32
1.6.4 Wave and Current Interaction . . . . . . . . . . . . . . . . 34
1.7 Research Objectives and Approach . . . . . . . . . . . . . . . . . 35
2 Tidal Energy Fundamentals 37
2.1 Tides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.2 Ocean Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.3 Linear Momentum Actuator Disk Theory . . . . . . . . . . . . . . 43
2.3.1 Actuator Disk Theory and Tidal Energy . . . . . . . . . . 44
2.3.2 Rotor Disk Theory . . . . . . . . . . . . . . . . . . . . . . 45
2.4 Blade Element Momentum Theory . . . . . . . . . . . . . . . . . 46
2.4.1 Tip Loss Correction . . . . . . . . . . . . . . . . . . . . . . 48
2.4.2 High Axial Corrections . . . . . . . . . . . . . . . . . . . . 49
2.5 Hydrodynamic Modelling . . . . . . . . . . . . . . . . . . . . . . . 50
2.5.1 CFD Turbulence Closure Models . . . . . . . . . . . . . . 52
2.5.2 CFD of Free Surface Waves . . . . . . . . . . . . . . . . . 54
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3 Single Turbine Wake Measurement in a Turbulent Flow with and
without Waves 56
3.1 Review of Wave-Current and Tidal Turbine Wake Experiments . . 57
3.1.1 Combined Wave-Current Flows . . . . . . . . . . . . . . . 57
3.1.2 Tidal Turbine Wakes . . . . . . . . . . . . . . . . . . . . . 58
3.2 Experimental Arrangement . . . . . . . . . . . . . . . . . . . . . . 60
3.3 Flow Profile, Waves and Turbulence . . . . . . . . . . . . . . . . . 61
3.3.1 Wave Conditions . . . . . . . . . . . . . . . . . . . . . . . 65
3.3.2 Combined Wave-Current Flow . . . . . . . . . . . . . . . . 69
3.4 Measurement of a Single Turbine Wake in Turbulent Flow . . . . 72
2
Contents
3.5 Measurement of a Single Turbine Wake in Combined Wave-Current
Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.5.1 Rotor Operation and Control in Waves . . . . . . . . . . . 76
3.5.2 Wake Profiles in Waves . . . . . . . . . . . . . . . . . . . . 78
3.5.3 Comparison of Waves with Similar Energy Density . . . . 79
3.5.4 Rate of Wake Recovery . . . . . . . . . . . . . . . . . . . . 82
3.6 Summary and Findings . . . . . . . . . . . . . . . . . . . . . . . . 84
4 CFD Models for Turbine Load and Wake Prediction 86
4.1 CFD Representation of Turbines . . . . . . . . . . . . . . . . . . . 87
4.2 Review of Previous Studies . . . . . . . . . . . . . . . . . . . . . . 89
4.3 Implementation of a RANS-BEM Method . . . . . . . . . . . . . 92
4.4 Mean Loads from RANS-BEM . . . . . . . . . . . . . . . . . . . . 94
4.5 Implementation of an Actuator Line Method . . . . . . . . . . . . 96
4.6 Mean Loads from RANS-BEM and Actuator Line Methods . . . . 100
4.7 Wake Generation using RANS-BEM and Actuator Line Methods . 102
4.8 RANS-BEM Single Wake . . . . . . . . . . . . . . . . . . . . . . . 105
4.8.1 Ambient Turbulence . . . . . . . . . . . . . . . . . . . . . 107
4.8.2 Blade Induced Turbulence . . . . . . . . . . . . . . . . . . 108
4.8.3 Evaluation of RANS BEM wake prediction . . . . . . . . . 110
4.8.4 Effect of Depth to Diameter Ratio . . . . . . . . . . . . . . 114
4.9 Actuator Line LES with SEM Onset Turbulence . . . . . . . . . . 115
4.10 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . 118
5 CFD of a Tidal Turbine in Waves 121
5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.2 Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
5.3 Simulating Waves in CFD . . . . . . . . . . . . . . . . . . . . . . 124
5.4 Turbine Control Methods . . . . . . . . . . . . . . . . . . . . . . . 127
5.4.1 Implementation of a Torque-Speed Control Method . . . . 128
5.4.2 Rotor Loading due to Sinusoidal Onset Flow . . . . . . . . 130
5.5 Rotor loading: Pulsatile Flow and VOF . . . . . . . . . . . . . . . 132
5.6 Turbine Wake in Turbulence Flow with Waves . . . . . . . . . . . 136
5.7 Summary and Findings . . . . . . . . . . . . . . . . . . . . . . . . 141
6 RANS-BEM Modelling of Tidal Turbine Arrays 143
6.1 Review of Experimental and Numerical Studies of Tidal Turbine
Arrays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
6.2 Experimental Comparison . . . . . . . . . . . . . . . . . . . . . . 146
6.3 RANS-BEM Array Simulations . . . . . . . . . . . . . . . . . . . 149
6.4 Single Row Array . . . . . . . . . . . . . . . . . . . . . . . . . . . 150
6.5 Multiple row arrays . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6.6 Torque Control Arrays . . . . . . . . . . . . . . . . . . . . . . . . 159
6.7 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . 160
7 Effect of Waves on a Tidal Turbine Row 162
7.1 Experimental Measurement of Five Turbine Row . . . . . . . . . . 163
7.1.1 Wake Measurements . . . . . . . . . . . . . . . . . . . . . 163
7.1.2 Waves Crossing Turbine Wakes: Experiments . . . . . . . 165
3
Contents
7.2 Prediction of Waves over Turbine Wakes . . . . . . . . . . . . . . 168
7.2.1 SWAN Model Configuration . . . . . . . . . . . . . . . . . 169
7.2.2 Model Arrangement for Five Disk Row . . . . . . . . . . . 170
7.2.3 SWAN Prediction: Five Disk Row . . . . . . . . . . . . . . 171
7.2.4 Location of Wave Generation Boundary . . . . . . . . . . 175
7.2.5 Proximity of Side Walls . . . . . . . . . . . . . . . . . . . 176
7.2.6 Influence of Wave Direction . . . . . . . . . . . . . . . . . 178
7.3 Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . 179
8 Conclusions and Recommendations for Future Work 182
8.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
8.2 Relevance to Industry and Research Community . . . . . . . . . . 188
8.3 Recommendations for Future Work . . . . . . . . . . . . . . . . . 189
Appendices 195
A Chapter 2: Tidal Energy Fundamentals 196
A.1 k ω SST Turbulence Model . . . . . . . . . . . . . . . . . . . . 196
−
B Chapter 3: Single Turbine Wake Measurement in a Turbulent
Flow with and without Waves 198
B.1 Method for Measuring the Phase Variation of Fricton Velocity in
Combined Wave-Current Flow . . . . . . . . . . . . . . . . . . . . 198
B.2 Effect of Tip-speed Ratio on Wake Generation . . . . . . . . . . . 200
C Chapter 4: CFD Models for Turbine Load and Wake Prediction201
C.1 Geometry and Performance Inputs for BEM . . . . . . . . . . . . 201
C.1.1 University of Manchester Rotor Geometry and Performance 201
C.1.2 Galloway (2014) Rotor Geometry and Performance . . . . 203
C.2 Bahaj et al. (2007b) Rotor Geometry and Performance . . . . . . 204
C.3 Effect of Gausian Smoothing Without Tiploss Correction Factors 205
C.4 Mesh Refinement Studies . . . . . . . . . . . . . . . . . . . . . . . 206
C.4.1 Mesh Refinment Study - Rotor Loads . . . . . . . . . . . . 206
C.4.2 Mesh Requirements for Wake Generation . . . . . . . . . . 207
D Chpater 5: CFD of a Tidal Turbine in Waves 209
D.1 Control Paramter for Constant torque RANS-BEM and Actuator
Line Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
D.2 Correction to Rotational Speed for Forced Oscilation Test . . . . 210
D.3 Rotor Loading due to Sinusoidal Onset Flow . . . . . . . . . . . . 212
E Chapter 6: RANS-BEM Modelling of Tidal Turbine Arrays 213
E.1 Disk Averaged Velocity Methods . . . . . . . . . . . . . . . . . . . 214
E.2 Percentage Difference RANS-BEM Array loading and Experiments 216
F Chapter 7: Effect of Waves on Tidal Turbine Arrays 217
F.1 Wake generation by porous disk and rotors . . . . . . . . . . . . . 217
F.2 SWAN - Wave Action Equation . . . . . . . . . . . . . . . . . . . 217
F.3 SWAN Mesh Refinement Study . . . . . . . . . . . . . . . . . . . 219
4
Contents
F.4 SWAN: Simulation used depth averaged flow-field direction from
RANS-BEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
F.5 Example of SWAN INPUT File . . . . . . . . . . . . . . . . . . . 221
5
List of Figures
1.1 Tidal energy systems . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.2 UK tides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.3 Types of tidal stream turbines . . . . . . . . . . . . . . . . . . . . 26
1.4 Prototype turbines operating within UK waters . . . . . . . . . . 27
1.5 Schematic outlining the research objectives. Turbine interaction
within an array subjected to and interacting with a propagating
wave field (left) and influence of waves on single device operating
and wake generation (right) . . . . . . . . . . . . . . . . . . . . . 29
1.6 Diagram of bed mounted ADCP . . . . . . . . . . . . . . . . . . . 33
2.1 Centrifugal and gravitational forces causing tidal flow . . . . . . . 38
2.2 Equilibrium tide . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.3 Spring and neap tides . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.4 Wave parameters for a single frequency wave . . . . . . . . . . . . 40
2.5 Dispersion of linear waves . . . . . . . . . . . . . . . . . . . . . . 41
2.6 Depth decay of maximum and minimum wave particle velocity from
linear wave theory. . . . . . . . . . . . . . . . . . . . . . . . . . . 42
2.7 Blade element momentum theory . . . . . . . . . . . . . . . . . . 47
3.1 Tidal turbine experimental scale wake generation . . . . . . . . . 59
3.2 Photo of the University of Manchester combined wave-current flume 61
3.3 Wave-current flume arrangement . . . . . . . . . . . . . . . . . . 62
3.4 Streamwise velocity profile in near bed region (z/d) . . . . . . . . 63
3.5 Depth variation of flow properties measured at rotor plane . . . . 64
3.6 Depth profiles of streamwise velocity and turbulence intensity at
mid-span at mid-span(Y = 0) and downstream distances of X=0D,
X=4D, X=8D and X=12D . . . . . . . . . . . . . . . . . . . . . . 65
3.7 Lateral variation of onset flow . . . . . . . . . . . . . . . . . . . . 66
3.8 Filtering to remove high frequency signal on measurements of
surface elevation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.9 Spectra of wave amplitude. kd = 3.13 Wave III . . . . . . . . . . 68
3.10 Spectra of wave amplitude. kd = 1 Wave III . . . . . . . . . . . . 68
3.11 Spatial variation of wave energy (m ) recorded for 30 minutes . . 69
0
3.12 Modification of streamwise vertical velocity profile of by waves . . 70
3.13 Variation of phase averaged bed-friction velocity (U∗) during a
wave for kd = 1 wave III . . . . . . . . . . . . . . . . . . . . . . . 70
3.14 Vertical profile of total flow kinetic energy for combined wave
current-flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6
List of Figures
3.15 Thrust and power coefficient variation with tip-speed ratio for
full scale turbine BEMT prediction of laboratory scale rotor and
experiment measurements of laboratory scale rotor . . . . . . . . 72
3.16 Supporting structure used for rotor and disk experiments . . . . . 73
3.17 Sketch of streamwise velocity profile showing recovery of single
turbine wake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.18 Lateral profiles of velocity deficit in current only flow . . . . . . . 75
3.19 Vertical profiles of velocity deficit in current only flow . . . . . . . 75
3.20 Empirically obtained relationships for far wake recovery in steady
flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.21 Mean thrust coefficient and tip-speed ratio for combined wave-
current tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.22 Recorded time series of rotational speed and force for kd = 1 wave II 77
3.23 Mean, maximum and minimum thrust coefficient for each wave
condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3.24 Vertical profiles of velocity deficit X = 2D downstream for increas-
ing wave heights . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.25 Vertical profiles of velocity deficit X = 4D downstream for increas-
ing wave heights . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.26 Vertical profiles of velocity deficit and FKE . . . . . . . . . . . . . 80
3.27 Centreline measurement of velocity deficit in wake centre from
X = 1.5D to X = 12D downstream . . . . . . . . . . . . . . . . . 82
3.28 Near and far wake decay rate for combined wave-current flow . . . 83
4.1 Meshes for tidal turbine CFD methods . . . . . . . . . . . . . . . 87
4.2 Methods for turbine representation within CFD . . . . . . . . . . 88
4.3 RANS-BEM process diagram . . . . . . . . . . . . . . . . . . . . 92
4.4 Source region of mesh showing polar mesh and non-permeable hub 93
4.5 Radial distributions of BEM inputs, computed forces and resultant
flow-field at tip-speed ratio, λ = 6, for the Galloway (2014) turbine 95
4.6 Comparison of power and thrust coefficients with tip-speed ratio to
tow-tank experiments (Galloway, 2014) with and without tip-loss
corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.7 Schematic showing Actuator Line method . . . . . . . . . . . . . 97
4.8 Size of Gaussian force distribution (G ) . . . . . . . . . . . . . . . 99
s
4.9 Effect of smoothing length (r ) on an Actuator Line simulation . 100
1/2
4.10 Effect of smoothing length (r ) on rotor loads obtained from
1/2
Actuator Line simulation . . . . . . . . . . . . . . . . . . . . . . . 101
4.11 Comparison of mean rotor loads from RANS-BEM and Actuator
Line to experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 101
4.12 Effect of blockage on rotor loads for the Galloway (2014) turbine . 102
4.13 Power and thrust variation with tip-speed ratio for University of
Manchester turbine . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.14 Instantaneous streamwise velocity (u ) at rotor plane (X=0) . . . 104
x
4.15 Iso-surface of Q-Criterion . . . . . . . . . . . . . . . . . . . . . . . 104
4.16 Vertical profiles of velocity deficit within centre of wake (y = 0) . 106
4.17 Lateral profiles of velocity deficit through centre of wake (z = d/2) 106
7
List of Figures
4.18 Lateral profiles of turbulent kinetic energy through centre of wake
(z = d/2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.19 Influence of inlet turbulence intensity (TI) on wake recovery . . . 107
4.20 Centreline profiles of velocity deficit and turbulence kinetic energy
shown influence of inlet turbulence length scale (L) on wake recovery107
4.21 Transverse profiles of turbulent kinetic energy and velocity deficit
showing application and effect of sources of tip-generated turbulence109
4.22 Lateral profiles of velocity deficit within centre of wake (z = d/2) 111
4.23 Lateral profiles of turbulent kinetic energy within centre of wake
(z = d/2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.24 Wake characteristics in the YZ plane at X=0.5D downstream.
Experiments (left), RANS-BEM - Inlet Turb. (centre) and Tip-
Turb. (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.25 Wake characteristics in the YZ plane at X=1.5D downstream.
Experiments (left), RANS-BEM - Inlet Turb. (centre) and Tip-
Turb (right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
4.26 Downstream variation of near wake rotation U (X) . . . . . . . . 114
θ
4.27 Effect of depth diameter ratio (d/D) on transition to far wake . . 115
4.28 Actuator Line simulation with onset turbulence . . . . . . . . . . 116
4.29 Centreline mean flow and turbulence characteristics from open
channel simulations with SEM onset flow . . . . . . . . . . . . . . 117
4.30 Vertical velocity profile at rotor plane for SEM open channel flow 118
4.31 Vertical velocity profiles within wake for Actuator Line simulations 119
4.32 Lateral profiles of turbulent kinetic energy within wake for Actuator
Line simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.1 Volume of fluid tow-tank domain for wave simulation . . . . . . . 125
5.2 Vertical profile of streamwise and vertical wave velocity under a
wave trough and crest . . . . . . . . . . . . . . . . . . . . . . . . 126
5.3 Longitudinal variation of streamwise wave velocity at hub-height . 126
5.4 Turbine control . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
5.5 Rotor torque variation with rotational speed (ω) for a range of
inflow velocities (U ) for the University of Manchester rotor . . . . 129
0
5.6 Example of solution for torque-speed control system in steady-state
simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
5.7 Schematic showing arrangement of forced oscillation experiments
in turbulent flow . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
5.8 Time-varying parameters from pulsatile flow test for streamwise
oscilations of frequency f=1.09HZ and Ampitude = 0.0806m/s . . 131
5.9 Schematic showing arrangement of tow tank test with waves (Gal-
loway, 2014) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
5.10 Time varying rotor force and torque from pulsatile flow and VOF
methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
5.11 Time varying blade force and torque from Pulsatile flow and VOF
methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
5.12 Spectrum of force from pulsatile flow pulsatile flow and VOF methods134
5.13 Effect of Actuator Line speed control strategy with comparison to
tow-tank tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
8
List of Figures
5.14 Schematic showing arrangement of flume tests in turbulence flow
with waves (Chapter 3) . . . . . . . . . . . . . . . . . . . . . . . . 136
5.15 Time variation of rotor loads in turbulent flow with waves . . . . 137
5.16 Mean vertical wake profiles for pulsatile flow simulations . . . . . 137
5.17 Wake profiles under wave troughs and peaks for pulsatile flow
simulations at X = 2D . . . . . . . . . . . . . . . . . . . . . . . . 139
5.18 Radial variation of Actuator Line inputs and applied force at the
rotor plane (X = 0) . . . . . . . . . . . . . . . . . . . . . . . . . . 140
5.19 Variation of angle of attack (α) during wave cycle. . . . . . . . . . 141
6.1 Photo of 12 experimental scale turbines installed in a three row array146
6.2 Arraylayoutshowingmeanthrustcoefficientandstandarddeviation
of mean values for each rotor in array of two rows of five rotors . . 147
6.3 Mean thrust coefficient and tip-speed ratio for each turbine within
two row array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
6.4 Mean thrust coefficient of rotors in a single row . . . . . . . . . . 150
6.5 Lateral profiles at X = 2D for a single row of three rotors at
increasing lateral spacings (Y ) . . . . . . . . . . . . . . . . . . . 151
sp
6.6 Lateral profiles downstream of a single row array of five turbines
with a lateral spacingY = 0.5D . . . . . . . . . . . . . . . . . . . 152
sp
6.7 Vertical profiles downstream of central within a single row array of
five turbines with a lateral spacing Y = 0.5D . . . . . . . . . . . 152
sp
6.8 Percentage discrepancy between RANS-BEM and empirical-
superposition relative to experiments for the square of the disk
average velocity U . . . . . . . . . . . . . . . . . . . . . . . . . . 153
D
6.9 Mean thrust and tip-speed ratio for multiple row arrays. . . . . . 154
6.10 Mean thrust and wakes from multiple row arrays. . . . . . . . . . 156
6.11 Torque-speed curve for 1row5 Y 1.5D and 2row55 X 8D arrays159
sp sp
− −
6.12 Mean thrust and tip-speed ratio for turbines within a torque con-
trolled array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
7.1 Single Disk: Vertical profiles of velocity deficit and FKE . . . . . 165
7.2 FiveDisk: VerticalprofilesofvelocitydeficitandFKEforoutermost
disk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165
7.3 Lateral profiles of velocity deficit downstream of five porous disks
at mid-depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
7.4 Experimental measurement of the fractional difference in wave
height (∆H) with and without the disks installed . . . . . . . . . 168
7.5 Directional and frequency spectra for the generation of regular
waves at boundary of SWAN simulation . . . . . . . . . . . . . . 170
7.6 Schematic of SWAN model . . . . . . . . . . . . . . . . . . . . . . 170
7.7 Two-dimensional depth average velocity (U ) for five disks obtained
x
from empirical-superposition wake model . . . . . . . . . . . . . . 171
7.8 Lateral profiles of depth averaged velocity (U ) for five disks ob-
x
tained from empirical-superposition wake method and RANS-BEM 172
7.9 Variation of wave height (H/H ) from SWAN simulation using
0
a velocity field defined from empirical-superposition wake model
compared to experimental measurement . . . . . . . . . . . . . . 173
7.10 Lateral profiles of fractional difference in wave height . . . . . . . 174
9
List of Figures
7.11 Wave direction (Θ) from SWAN simulation . . . . . . . . . . . . . 174
7.12 Variation of wave height (as Figure 7.9), calculated without refraction.175
7.13 Influence of the location of the downstream wave generating bound-
ary on the SWAN wave field . . . . . . . . . . . . . . . . . . . . . 176
7.14 Wave height over five turbine array . . . . . . . . . . . . . . . . . 177
7.15 Wave propagation direction over five turbine array . . . . . . . . . 177
7.16 Wave height in the centre of the domain (y = 0) . . . . . . . . . . 177
7.17 Effect of relative wave current direction on propagating wave field.
Contour of fractional change in wave height . . . . . . . . . . . . 178
B.1 Probe arrangement for measurment of near be velocity profile . . 198
B.2 Phase averaging methods used for obtaining near bed friction velocity199
B.3 Phase averaged near bed vertical velocity profile for kd = 1 wave . 199
B.4 Wake generation for scaled rotor in turbulent flow for two operating
points . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200
C.1 Geometry of UoM Rotor. Göttingen 804 foil . . . . . . . . . . . . 202
C.2 Lift and Drag Coefficients of Göttingen 804 foil . . . . . . . . . . 202
C.3 Mean power and load prediction for UoM rotor with two areofoil
data sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
C.4 Geometry of Galloway (2014) Rotor. NACA 48XX foil . . . . . . 203
C.5 Lift and Drag Coefficients of NACA 48XX foil . . . . . . . . . . . 203
C.6 Geometry of Galloway (2014) Rotor. NACA 48XX foil . . . . . . 204
C.7 Lift and Drag Coefficients of NACA 48XX foil . . . . . . . . . . . 204
C.8 Effect of smoothing length (r ) on an Actuator Line simulation . 205
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C.9 Effect of cell size on power and thrust coefficient for a range of
tip-speed ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
C.10 Vertical wake profiles for wake mesh refinement study . . . . . . . 208
D.1 Mean loads for specified tip-speed ratio and speed control to give
target torque . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
D.2 Effect of relaxation factor (K ) on the calcuated rotaitonal speed
R
for the Actuator Line methods . . . . . . . . . . . . . . . . . . . . 210
D.3 Proccessing of data for forced oscillation experiments . . . . . . . 210
D.4 Pulsatile flow test for waves of frequency 0.5127 and Amplitude =
0.1078m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
E.1 Wake profile for single row of three rotors . . . . . . . . . . . . . . 213
E.2 Wake profile at X = 2D for single row of two rotors at increasing
lateral spacings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
E.3 Interpolationmethodforobtaineddiskaveragedvelocitiesofturbine
located on second row. Example shown 4 diameters downstream . 214
E.4 Methods used for obtaining disk averaged velocities . . . . . . . . 215
E.5 Percentage difference of thrust coefficient C for RANS-BEM pre-
T
dictions compared to experimental measurements . . . . . . . . . 216
F.1 Longitudinal profile showing comparison of wake generated by a
single scaled rotor and porous disk . . . . . . . . . . . . . . . . . 217
F.2 Lateral profiles of fractional difference in wave height for SWAN
with mesh refinement . . . . . . . . . . . . . . . . . . . . . . . . . 219
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