locally-resonant wave energy converter · wave energy farms capacity of individual wecs currently...
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![Page 1: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/1.jpg)
Locally-resonant wave energy converter
Fabien Montiel & Ben Wilks
Department of Mathematics & Statistics, University of Otago
OERC Symposium 2018
F. Montiel
![Page 2: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/2.jpg)
What is wave energy?
A form of marine renewable energy (MRE)
Converts ocean wave mechanical energy to electrical energy, e.g. with a turbine.
A device extracting wave energy is called a wave energy converter (WEC).
F. Montiel
![Page 3: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/3.jpg)
What is wave energy?
A form of marine renewable energy (MRE)
Converts ocean wave mechanical energy to electrical energy, e.g. with a turbine.
A device extracting wave energy is called a wave energy converter (WEC).
F. Montiel
![Page 4: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/4.jpg)
What is wave energy?
A form of marine renewable energy (MRE)
Converts ocean wave mechanical energy to electrical energy, e.g. with a turbine.
A device extracting wave energy is called a wave energy converter (WEC).
F. Montiel
![Page 5: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/5.jpg)
WEC technology
Point absorber
Attenuator
Wave surge converter
Oscillating water column (OWC)
and more ...
F. Montiel
![Page 6: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/6.jpg)
WEC technology
Point absorber
Attenuator
Wave surge converter
Oscillating water column (OWC)
and more ...
F. Montiel
![Page 7: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/7.jpg)
WEC technology
Point absorber
Attenuator
Wave surge converter
Oscillating water column (OWC)
and more ...
F. Montiel
![Page 8: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/8.jpg)
WEC technology
Point absorber
Attenuator
Wave surge converter
Oscillating water column (OWC)
and more ...
F. Montiel
![Page 9: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/9.jpg)
WEC technology
Point absorber
Attenuator
Wave surge converter
Oscillating water column (OWC)
and more ...F. Montiel
![Page 10: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/10.jpg)
Wave energy resources
text
International
∼20,000 TW h/yr on world’s coastline1.
Intensification of winds is expected tofurther increase available wave power,especially in the Southern Ocean.
NZ
25 kW per metre of coastline2.
1Reguero et al., 2015, Applied Energy.2Stevens et al., 2005, Water & Atmosphere.
F. Montiel
![Page 11: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/11.jpg)
Wave energy resources
text
International
∼20,000 TW h/yr on world’s coastline1.
Intensification of winds is expected tofurther increase available wave power,especially in the Southern Ocean.
NZ
25 kW per metre of coastline2.
1Reguero et al., 2015, Applied Energy.2Stevens et al., 2005, Water & Atmosphere.
F. Montiel
![Page 12: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/12.jpg)
Wave energy resources
text
International
∼20,000 TW h/yr on world’s coastline1.
Intensification of winds is expected tofurther increase available wave power,especially in the Southern Ocean.
NZ
25 kW per metre of coastline2.
1Reguero et al., 2015, Applied Energy.2Stevens et al., 2005, Water & Atmosphere.
F. Montiel
![Page 13: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/13.jpg)
Wave energy farms
Capacity of individual WECs currently limited(∼O(100–1000) kW).
Commercial developments looking at large scalefarms (100–1000 MW) composed of hundreds ofWECs.
Goal: Maximise power absorption through waveinterference (park effect3
) with q > 1).
qfactor(ω) =Parray(ω)
N × Psingle(ω).
3Babarit, 2013, Renewable Energy.F. Montiel
![Page 14: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/14.jpg)
Wave energy farms
Capacity of individual WECs currently limited(∼O(100–1000) kW).
Commercial developments looking at large scalefarms (100–1000 MW) composed of hundreds ofWECs.
Goal: Maximise power absorption through waveinterference (park effect3)
with q > 1).
qfactor(ω) =Parray(ω)
N × Psingle(ω).
3Babarit, 2013, Renewable Energy.F. Montiel
![Page 15: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/15.jpg)
Wave energy farms
Capacity of individual WECs currently limited(∼O(100–1000) kW).
Commercial developments looking at large scalefarms (100–1000 MW) composed of hundreds ofWECs.
Goal: Maximise power absorption through waveinterference (park effect3)
with q > 1).
qfactor(ω) =Parray(ω)
N × Psingle(ω).
3Babarit, 2013, Renewable Energy.F. Montiel
![Page 16: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/16.jpg)
Wave energy farms
Capacity of individual WECs currently limited(∼O(100–1000) kW).
Commercial developments looking at large scalefarms (100–1000 MW) composed of hundreds ofWECs.
Goal: Maximise power absorption through waveinterference (park effect3
)
with q > 1).
qfactor(ω) =Parray(ω)
N × Psingle(ω).
3Babarit, 2013, Renewable Energy.F. Montiel
![Page 17: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/17.jpg)
Motivation: sonic crystals
Hard cylinders Split-ring resonators
Goal: manipulate incident wave field passively to achieve e.g. band gaps, trapping, cloaking, ...F. Montiel
![Page 18: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/18.jpg)
Motivation: band gaps
Simulation parameters4
5 × 51 array
radius 0.2m
angle 45◦
spacing 0.6m
frequency sweep: f = 10–450Hz
Band gaps
Gap 1: Helmholtz resonator frequency (split-ring geometry)
Gap 2: Bragg resonance (periodic arrangement)
4Montiel, Chung, Karimi & Kessissoglou, 2017, Wave Motion.F. Montiel
![Page 19: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/19.jpg)
Motivation: band gaps
Simulation parameters4
5 × 51 array
radius 0.2m
angle 45◦
spacing 0.6m
frequency sweep: f = 10–450Hz
Band gaps
Gap 1: Helmholtz resonance (split-ring geometry)
Gap 2: Bragg resonance (periodic arrangement)
4Montiel, Chung, Karimi & Kessissoglou, 2017, Wave Motion.F. Montiel
![Page 20: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/20.jpg)
A new concept of OWC
Features
Fixed, rigid cylindrical shell
Bottom-mounted and surface-piercing structure
Opening connecting interior and exterior domains
Pressurised internal chamber
Low-frequency resonance (Helmholtz)
Wave interaction problem can be solved usingsemi-analytical mathematical techniques!
F. Montiel
![Page 21: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/21.jpg)
A new concept of OWC
Features
Fixed, rigid cylindrical shell
Bottom-mounted and surface-piercing structure
Opening connecting interior and exterior domains
Pressurised internal chamber
Low-frequency resonance (Helmholtz)
Wave interaction problem can be solved usingsemi-analytical mathematical techniques!
F. Montiel
![Page 22: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/22.jpg)
A new concept of OWC
Features
Fixed, rigid cylindrical shell
Bottom-mounted and surface-piercing structure
Opening connecting interior and exterior domains
Pressurised internal chamber
Low-frequency resonance (Helmholtz)
Wave interaction problem can be solved usingsemi-analytical mathematical techniques!
F. Montiel
![Page 23: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/23.jpg)
A new concept of OWC
Features
Fixed, rigid cylindrical shell
Bottom-mounted and surface-piercing structure
Opening connecting interior and exterior domains
Pressurised internal chamber
Low-frequency resonance (Helmholtz)
Wave interaction problem can be solved usingsemi-analytical mathematical techniques!
F. Montiel
![Page 24: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/24.jpg)
Oscillating water column (OWC) models
Uniform pressure model
Internal surface condition: free surface
Power take-off (PTO): through turbinemotion
Tuning: air pressure in chamber
F. Montiel
![Page 25: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/25.jpg)
Simulation — example without PTO
Parameters
h = 10 m, a = 1 m,d = 5 m, α = π/8
f = 0.38 Hz (λ ≈ 10 m)
Link to animation
F. Montiel
![Page 26: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/26.jpg)
Simulation — example without PTO
Parameters
h = 10 m, a = 1 m,d = 5 m, α = π/8
f = 0.38 Hz (λ ≈ 10 m)
Link to animation
F. Montiel
![Page 27: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/27.jpg)
Simulation — example without PTO
Parameters
h = 10 m, a = 1 m,d = 5 m, α = π/8
f = 0.38 Hz (λ ≈ 10 m)
Link to animation
F. Montiel
![Page 28: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/28.jpg)
Our WEC — d = 5m (no PTO)
Parameters
h = 10 m, a = 1 m, d = 5 m
α varies
f = 0.01–1 Hz
Output
Scattering cross-section σ measuresmagnitude of resonance.
text
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
5
10
15
F. Montiel
![Page 29: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/29.jpg)
Our WEC — d = 5m (no PTO)
Parameters
h = 10 m, a = 1 m, d = 5 m
α varies
f = 0.01–1 Hz
Output
Scattering cross-section σ measuresmagnitude of resonance.
text
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
5
10
15
F. Montiel
![Page 30: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/30.jpg)
Our WEC — d = 3m (no PTO)
Parameters
h = 10 m, a = 1 m, d = 3 m
α varies
f = 0.01–1 Hz
Output
Scattering cross-section σ measuresmagnitude of resonance.
text
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
5
10
15
F. Montiel
![Page 31: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/31.jpg)
Our WEC — d = 1m (no PTO)
Parameters
h = 10 m, a = 1 m, d = 1 m
α varies
f = 0.01–1 Hz
Output
Scattering cross-section σ measuresmagnitude of resonance.
text
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
5
10
15
F. Montiel
![Page 32: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/32.jpg)
Our WEC — d = 0.5m (no PTO)
Parameters
h = 10 m, a = 1 m, d = 0.5 m
α varies
f = 0.01–1 Hz
Output
Scattering cross-section σ measuresmagnitude of resonance.
text
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
5
10
15
F. Montiel
![Page 33: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/33.jpg)
Wrap-up
Future research
Resonance analysis
Couple to PTO
WEC farms
More realistic geometry/fluid
Experiments in wave basin
THANK YOU!
F. Montiel
![Page 34: Locally-resonant wave energy converter · Wave energy farms Capacity of individual WECs currently limited (˘O(100{1000) kW). Commercial developments looking at large scale farms](https://reader033.vdocuments.us/reader033/viewer/2022060216/5f061c827e708231d41658be/html5/thumbnails/34.jpg)
Wrap-up
Future research
Resonance analysis
Couple to PTO
WEC farms
More realistic geometry/fluid
Experiments in wave basin
THANK YOU!
F. Montiel