Wave energy conversion based on multi-mode line absorbing systems

176 Pages·2015·5.84 MB·English

Wave energy conversion based on multi-mode line
absorbing systems

A thesis submitted to The University of Manchester for the degree of
Doctor of Philosophy
in the Faculty of Engineering and Physical Sciences

2015

Efrain Carpintero Moreno

School of Mechanical, Aerospace and Civil Engineering
Contents
Contents ..................................................................................................................................................... 2
List of figures............................................................................................................................................... 6
List of tables .............................................................................................................................................. 10
Nomenclature ........................................................................................................................................... 12
Abstract .................................................................................................................................................... 14
Declaration ............................................................................................................................................... 15
Copyright Statement ................................................................................................................................. 16
Dedication................................................................................................................................................. 17
Acknowledgement .................................................................................................................................... 17
The Author ................................................................................................................................................ 18
Chapter I Introduction ...................................................................................................................... 19
1.1. Global status of renewable energy ............................................................................................... 19
1.2. Renewable energy in UK................................................................................................................ 22
Wave energy resource in UK seas........................................................................................................... 23
1.3. Renewable energy in Mexico......................................................................................................... 24
Wave energy resource in Mexican seas ................................................................................................. 25
1.4. Research objectives ....................................................................................................................... 27
Specific Objectives .................................................................................................................................. 27
1.5. Summary ....................................................................................................................................... 27
Chapter II Literature review ................................................................................................................ 29
2.1. Current devices classified by converter type ................................................................................. 29
2.2. Modelling techniques .................................................................................................................... 37
Linear wave diffraction theory ............................................................................................................... 37
CFD models ............................................................................................................................................. 38
Spectral wave modelling ......................................................................................................................... 38
2.3. Performance evaluation of WECs – experimental modelling ........................................................ 39
2.4. Response in extreme conditions .................................................................................................... 40
2.5. Ocean energy research at the University of Manchester .............................................................. 41
2
The Manchester Bobber ......................................................................................................................... 41
2.6. Summary ....................................................................................................................................... 43
Chapter III Linear modelling of multi-body wave energy converter ..................................................... 44
3.1. Linear wave theory ........................................................................................................................ 44
3.2. Modelling of a single wave energy converter ............................................................................... 49
Application to a wave energy converter ................................................................................................. 49
3.3. Numerical modelling in heave for a two-float WEC ...................................................................... 51
Two-body converter configuration work principle ................................................................................. 51
Discretization of the heave equations for the converter floats – coupled system ................................. 54
Obtaining vertical floats velocities for the couple floats system ............................................................ 55
Obtaining body forces with WAMIT ....................................................................................................... 56
3.4. Converter optimization for the two-body configuration ............................................................... 59
Optimization criteria ............................................................................................................................... 59
Optimization for two-float array with a 1/40th geometrical scale .......................................................... 60
Hydrodynamic and excitation forces – Case 4b ................................................................................. 61
Prediction of the power output – Case 4b ......................................................................................... 64
Results for different float configurations ............................................................................................... 65
3.5. Optimization of the mechanical force applied to the system. ....................................................... 66
3.6. Summary ....................................................................................................................................... 67
Chapter IV Experimental method ......................................................................................................... 69
4.1 Description of the experiments .............................................................................................................. 69
4.2. Wave definition ............................................................................................................................. 70
Irregular waves - JONSWAP spectrum .................................................................................................... 70
Wave power formulation ....................................................................................................................... 72
4.3. Froude scaling law ......................................................................................................................... 72
4.4. Facilities ......................................................................................................................................... 74
Manchester facilities .............................................................................................................................. 74
Plymouth facilities .................................................................................................................................. 75
4.5. Wave system models ..................................................................................................................... 76
Operation system for the three-float converter ..................................................................................... 76
4.6. Experimental procedure ................................................................................................................ 78
3
Wave definition for testing at the University of Manchester ................................................................. 78
Wave definition for testing at Plymouth University ............................................................................... 78
Wave field evaluation ............................................................................................................................. 79
Experimental procedure for testing with the converter in place ........................................................... 82
Data post processing to obtain the power output ............................................................................. 84
Obtaining the rod velocity for 1/40 scale model .......................................................................... 84
Obtaining the rod velocity for 1/8 scale model ............................................................................ 86
4.7. Summary ....................................................................................................................................... 87
Chapter V Experimental investigation of multi-body WEC .................................................................. 88
5.1. M4 wave energy converter – “the converter evolution” ............................................................... 88
5.2. Development of the two-float system ........................................................................................... 91
Two-float system parameter investigation ............................................................................................. 94
5.3. Development of three-float system ............................................................................................... 98
5.4. Summary ..................................................................................................................................... 106
Chapter VI Evaluation of a three-float wave energy system at two scales ......................................... 107
6.1. Scaled laboratory models ............................................................................................................ 107
1/40th scale models ............................................................................................................................... 107
1/8th scale models ................................................................................................................................. 109
6.2. Experiments with a 1/40th laboratory scale model ..................................................................... 111
Experimental results in regular waves .................................................................................................. 111
Experiment results in irregular waves .................................................................................................. 114
6.3 Experiments with a 1/8th laboratory scale model ....................................................................... 119
Regular waves ....................................................................................................................................... 120
Irregular waves ..................................................................................................................................... 122
6.4. Results comparison across scales ................................................................................................ 128
6.5. Summary ..................................................................................................................................... 131
Chapter VII Power projection for full-scale prototypes ....................................................................... 133
7.1. Power projection method ............................................................................................................ 134
7.2 Wave energy resource - Scatter plots.......................................................................................... 135
7.3 Defining the action range of a tuned device at each site ............................................................ 139
7.4 Power projection for deployment sites........................................................................................ 140
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Results for a converter with 𝝀𝒔=𝟒𝟎 .................................................................................................. 141
Results for a converter with 𝝀𝒔=𝟖𝟏 .................................................................................................. 142
7.5. Predicted power variation with the length scale factor .............................................................. 143
7.6 Summary ..................................................................................................................................... 147
Chapter VIII Discussion and Conclusions.......................................................................................... 148
8.1. Overview ..................................................................................................................................... 148
8.2. Discussion .................................................................................................................................... 148
Systematic methodology for converter design ..................................................................................... 150
Power projection finding ...................................................................................................................... 151
8.3. Conclusions .................................................................................................................................. 151
8.4. Contribution of this research ....................................................................................................... 152
8.5. Future work ................................................................................................................................. 153
Mooring system design......................................................................................................................... 153
Survivability study ................................................................................................................................. 153
Feasibility study at the specific selected place ..................................................................................... 154
Investigation of the political and environmental regulations of suitable sites for positioning a full-scale
prototype .............................................................................................................................................. 154
Appendix A ............................................................................................................................................. 155
Appendix B .............................................................................................................................................. 160
References .............................................................................................................................................. 170

Word count 47,574

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List of figures
Figure 1.1: Global electricity energy production on 2014, [1]. ........................................................................ 21
Figure 1.2: Global energy resources, wave power per meter of wave front [kW/m], [2]. ............................... 21
Figure 1.3: Annual average wave height [m] and power [kW/m] for UK seas [12]. ......................................... 23
Figure 1.4: Wave period occurrence at UK seas............................................................................................... 24
Figure 1.5: Annual average wave energy density in Mexican seas [kW/m], (www.sener.gob.mx) ................. 26
Figure 1.6: Annual average wave height, 𝑯𝒎𝒆𝒂𝒏, in Mexican seas [m], (www.sener.gob.mx) ..................... 26
Figure 1.7: Annual average zero-crossing wave period, 𝑻𝒛, in Mexico seas [s], (www.sener.gob.mx) ........... 26
Figure 2.1: Point absorbers, current technology. ............................................................................................. 31
Figure 2.2: Attenuators, current technology. ................................................................................................... 33
Figure 2.3: Terminators, current technology. .................................................................................................. 34
Figure 2.4: Oscillating water columns, current technology. ............................................................................ 35
Figure 2.5: Overtopping devices, current technology. ..................................................................................... 36
Figure2.6: Schematic approach at still position of Manchester Bobber (courtesy of Prof Stansby). ............... 42
Figure 3.1 Boundary values for linear waves, adapted from Dean & Dalrymple [93]. ..................................... 47
Figure 3.2: Wave energy differential mass approach. [68]. ............................................................................. 48
Figure 3.3: Schematic representation of the work principle for the two-body converter configuration. ....... 52
Figure 3.4: Freedom degrees for a simple floating body [94]. ......................................................................... 53
Figure 3.5: Sensitivity analysis of the different methodology for body representation in WAMIT runs. ........ 58
Figure 3.6: a) WAMIT floats array, b) Body representation by an a finite number of panels. ......................... 61
Figure 3.7: Hydrostatic coefficients, a) added mass, b) radiation damping. .................................................... 63
Figure 3.8: Excitation force on converter floats due to heave mode of motion. ............................................. 63
Figure 3.9: Power output for the two-float array (Case 4b); without (solid line) and with (dotted line) drag
effects. .............................................................................................................................................................. 64
Figure 3.10: Power output at different float arrays configurations; case 1a (black line), case 2a (green line),
case 3a (red line), case 4b (blue line), and case 5a (purple line). ..................................................................... 65
Figure 3.11: Power output (left), vertical float response (centre and right for float 1 and 2, respectively) at
different mechanical applied forces for a wave amplitude of 0.01 m, 𝑩𝟗𝟗,𝒎𝒂𝒙=𝟐𝟒.𝟔 [(N-s)/m]. .......... 66
Figure 3.12: Power contours as function of mechanical force, 𝑹𝒎𝒆𝒄𝒉, and angular wave frequencies, w. 67
6
Figure 4.1: Manchester wave flume. ................................................................................................................ 74
Figure 4.2: Wave basin at the Marine Institute at Plymouth University. ......................................................... 75
Figure 4.3: Working principle for the three-float array model. ....................................................................... 77
Figure 4.4: Wave gauges array at the University of Manchester. .................................................................... 80
Figure 4.5: Wave gauges array at Plymouth University. .................................................................................. 81
Figure 4.6: Calibration curve for the three wave gauges used at the University of Manchester flume’s. ....... 81
Figure 4.7: Strain gauge calibration, schematic configuration (left side), calibration curve (right side). ........ 83
Figure 4.8: Wave energy converter location at the University of Manchester flume. ..................................... 84
Figure 4.9: PTO system for 1/40 scale model. .................................................................................................. 85
Figure 4.10: PTO system for 1/8 scale model. .................................................................................................. 86
Figure 4.11: Geometrical analysis to obtain 𝑴𝒅.............................................................................................. 87
Figure 5.1: Two-float configurations for experimental testing. ....................................................................... 89
Figure 5.2: Power variation with wave period for Cfg1 (Table 5.2) for five different wave heights. ............... 92
Figure 5.3: Power variation with wave period for Cfg2 (Table 5.2) for five different wave heights. ............... 93
Figure 5.4:Comparison of the average power output with wave period for Cfg3 and Cfg4 at 𝑯=𝟎.𝟎𝟐 m. . 96
Figure 5.5: Comparison of the average power output with wave period for Cfg4 and Cfg5, 𝑯=𝟎.𝟎𝟐 m. ... 96
Figure 5.6: Comparison of the average power output with wave period for Cfg4 and Cfg6, 𝑯=𝟎.𝟎𝟐 m .... 98
Figure 5.7: Schematic wave energy converter diagram with the three-float array. ........................................ 99
Figure 5.8: Average power with wave period for the two-float and three-float array, and H=0.02 m. ......... 100
Figure 5.9: Average power output with wave period for different floats spacing, 𝑺𝟏, and H=0.02 m. ......... 101
Figure 5.10: Average power output with wave period for five different float 3 drafts, 𝒅𝟑, and 𝑯=𝟎.𝟎𝟐 m.
........................................................................................................................................................................ 102
Figure 5.11: Average power output with wave period for different floats spacing, 𝑺𝟐, and 𝑯=𝟎.𝟎𝟐 m. . 103
Figure 5.12: Average power output with wave period for different pivot point, h, heights and 𝑯=𝟎.𝟎𝟐 m.
........................................................................................................................................................................ 104
Figure 5.13: Average power output with wave period for configurations with different 𝒅𝟏 and 𝑯=𝟎.𝟎𝟐 m.
........................................................................................................................................................................ 104
Figure 5.14: Average power output with wave period for different wave height. ........................................ 105
Figure 6.1: Manchester device - Sketch of configuration with flat bases, dimensions [m]. .......................... 108
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Figure 6.2: Manchester device - Sketch of configuration with rounded bases, dimensions [m]. .................. 109
Figure 6.3: Plymouth device - Sketch of configuration for large scale, dimensions [m]. ............................... 110
Figure 6.4: Power output comparison with wave period for converter with flat and rounded base floats. . 112
Figure 6.5: Power output comparison with wave period for different wave hiehgts. ................................... 112
Figure 6.6: Variation of water surface elevation, 𝜼, moment, 𝑴𝒅, angle, 𝜽, and power output with time for
regular waves of 𝑯≈𝟎.𝟎𝟐𝟑 m and 𝑻≈𝟏.𝟎𝟓 s. Converter with rounded base floats. .............................. 114
Figure 6.7: Variation of capture width ratio (based on 𝑻𝒆) with ratio of peak period to 𝑻𝒑 to resonant heave
period for float 3, 𝑻𝒓𝟑 (from WAMIT model) for uni-directional irregular waves and 𝜸=𝟑.𝟑. .................. 115
Figure 6.8: Variation of water surface elevation, 𝜼, moment, 𝑴𝒅, angle, 𝜽, and power output with time for
uni-directional irregular waves of 𝑯𝒔≈𝟎.𝟎𝟒𝟑 m, 𝑻𝒑≈𝟏.𝟏𝟏 s and 𝜸=𝟑.𝟑. .......................................... 116
Figure 6.9: Variation of capture width ratio (based on 𝑻𝒆) with ratio of peak period, 𝑻𝒑, to resonant heave
period for float 3, 𝑻𝒓𝟑 (from WAMIT model) for uni-directional irregular waves with 𝜸=𝟏,𝟑.𝟑. ............. 117
Figure 6.10: Variation of capture width ratio (based on 𝑻𝒆) with ratio of peak period, 𝑻𝒑, to resonant heave
period for float 3, 𝑻𝒓𝟑 (from WAMIT model) with 𝜸=𝟑.𝟑 and 𝒔=∞,𝟑𝟎,𝟓, rounded-base floats. ......... 118
Figure 6.11: Variation of capture width ratio (based on 𝑻𝒆) with ratio of peak period to 𝑻𝒑 to resonant
heave period for float 3, 𝑻𝒓𝟑 (from WAMIT model) with 𝜸=𝟏.𝟎 and 𝒔=∞,𝟑𝟎,𝟓, rounded-base floats.
........................................................................................................................................................................ 119
Figure 6.12: Variation of average power output with real wave height for different wave periods. ............ 120
Figure 6.13: Variation of average power output with wave height square for different wave periods. ....... 121
Figure 6.14: Variation of water surface elevation, 𝜼, moment, 𝑴𝒅, angle, 𝜽, and power output with time for
regular waves of 𝑯≈𝟎.𝟎𝟏𝟗 m and 𝑻≈𝟐.𝟓 s. Large scale model. ............................................................. 122
Figure 6.15: Variation of average power output with real wave height for different peak wave periods. ... 123
Figure 6.16: Variation of average power output with real wave height for different peak wave periods. ... 123
Figure 6.17: Variation of water surface elevation, 𝜼, moment, 𝑴𝒅, angle, 𝜽, and power output with time for
uni-directional regular waves of 𝑯𝒔≈𝟎.𝟐𝟑𝟖 m and 𝑻𝒑≈𝟐.𝟔 s. Large scale model. ................................ 124
Figure 6.18: Converter performance for different ranges of mechanical damping. ...................................... 125
Figure 6.19: Variation of capture width ratio (based on 𝑻𝒆) with ratio of peak period to 𝑻𝒑 to resonant
heave period for float 3, 𝑻𝒓𝟑 (from WAMIT model) irregular waves with 𝜸=𝟑.𝟑 and 𝒔=∞,𝟑𝟎 and 5. . 126
Figure 6.20: Variation of capture width ratio (based on 𝑻𝒆) with ratio of peak period to 𝑻𝒑 to resonant
heave period for float 3, 𝑻𝒓𝟑 (from WAMIT model) irregular waves with 𝜸=𝟑.𝟑 and 𝜸=𝟏.𝟎. .............. 127
Figure 6.21: Variation of power output with ratio of peak period to 𝑻𝒑 to resonant heave period for float 3,
𝑻𝒓𝟑 (from WAMIT model) irregular waves at significant wave height target of 𝑯𝒔 = 𝟎.𝟐 m. .................. 128
8
Figure 6.22: Comparison of the Capture width ratio between different laboratory scale models for
unidirectional irregular waves with 𝜸=𝟑.𝟑 and different significant wave heights. ................................. 129
Figure 6.23: Capture width ratio comparison between different laboratory scale models for spreading
(𝒔=𝟑𝟎) irregular waves with 𝜸=𝟑.𝟑 and different significant wave heights. ......................................... 130
Figure 6.24: Capture width ratio comparison between different laboratory scale models for spreading
(𝒔=𝟓) irregular waves with 𝜸=𝟑.𝟑 and different significant wave heights. ............................................ 131
Figure 7.1: Specific locations for power capture projections with M4 wave energy converter. ................... 134
Figure 7.2: Wave energy occurrence and capture width for the selected places. ......................................... 140
Figure 7.3: Variation of the average power output (left hand side) and power/mass ratio (right hand side)
with the device length/predominant wave length ratio for the economics analysis. ................................... 146

9
List of tables
Table 1.1: Electricity trend [1] [MToe]. ............................................................................................................ 20
Table 1.2: Carbon budgets for the period 2008-2027 [8, 9]............................................................................. 22
Table 1.3: Trend of total energy production coming from green energies [1]. ............................................... 22
Table 1.4: Trend of total electricity production coming from green energies [1]. ........................................... 22
Table 1.5: Renewables energies contribution to electricity production in UK [11]. ........................................ 23
Table 1.6: Trend of total electricity production coming from green energies [1]. ........................................... 25
Table 1.7: Renewables energies contribution to electricity production in Mexico [11]. ................................. 25
Table 2.1: Key points of the point absorbers devices. ..................................................................................... 31
Table 2.2: Key points of the point absorbers devices. ..................................................................................... 33
Table 2.3: The Salter’s Duck characteristics. .................................................................................................... 34
Table 2.4: Oscillating water columns – technical aspects. ............................................................................... 35
Table 2.5: Overtopping devices. ....................................................................................................................... 36
Table 3.1: Different sizing floats configuration. ............................................................................................... 61
Table 4.1: Scaling factors [68]. ......................................................................................................................... 73
Table 4.2: Wave parameters at full-scale prototype. ....................................................................................... 79
Table 5.1: Versions of the two float 1/40th scale model for experimental testing. ........................................ 90
Table 5.2: Floats and wave Parameters for experimental phase 1. ................................................................. 91
Table 5.3: Floats and wave Parameters for experimental phase 2. ................................................................. 95
Table 5.4: Geometrical parameters for some configuration using a the three-float array. ............................. 99
Table 5.5: Distance variation of spacing between float 2 and float 3. ........................................................... 103
Table 5.6: Optimal converter configuration by the experimental phase. ...................................................... 106
Table 6.1: Mass distribution and inertias for flat base configuration with origin at hinge point. .................. 108
Table 6.2: Heave natural periods for flat base floats based on WAMIT......................................................... 108
Table 6.3: Mass distribution and inertias for rounded base configuration with origin at hinge. .................. 109
Table 6.4: Heave natural periods for rounded base floats based on WAMIT. ............................................... 109
Table 6.5: Mass distribution and inertias the for 1/8th scale with origin at hinge. ....................................... 110
Table 6.6: Heave natural periods for rounded base floats based on WAMIT. ............................................... 110
10