Lloyd’s Register services to the energy industry A simplified model for oscillating water column motion Rebecca Sykes Mechanical Engineer Technical Directorate May 23, 2012
A simplified model for oscillating water column motion
Jun 14, 2015
Rebecca Sykes (Mechanical Engineer) discusses different modelling techniques for understanding the physical process within a floating OWC. Using a simplified OWC model, Rebecca explores ways to get around the limitations of the commonly used "Boundary Element Model".
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Lloyd’s Register services to the energy industry
A simplified model for oscillating water column motionRebecca SykesMechanical EngineerTechnical DirectorateMay 23, 2012
Lloyd’s Register services to the energy industry
Oscillating water column
• Conventional OWC have been shoreline devices
• LIMPET, Scotland
• Pico, Azores
• Sanze, Japan…
• Wave shoaling reduces energy to shoreline
Power is extracted from the wave induced vertical motion of the water free surface compressing airin a volume above. This can be used to drive an air turbine, such as the Wells turbine, which is designed for reciprocating flows.
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Oscillating water column
Jacket
Gravity based
TLP
Floating OWC
• Conventional OWC have been shoreline devices
• LIMPET, Scotland
• Pico, Azores
• Sanze, Japan…
• Wave shoaling reduces energy to shoreline
• Potential for greater energy extraction offshore
• Options – fixed, semi-fixed or floating
Majority of proposed/prototype offshore OWC have been floating but there is potential to combine
with other technologies and so use their support structure
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Objective
To present a model that furthers our understanding of the physical processes within a floating Oscillating Water Column
The diffraction and radiation problem which existed for the fixed OWC must be extended
when floating to include radiation from the device motion
Floating – cheaper CAPEX option (?)…
…but more complex to simulate
THEREFORE: Increased complexity in predicting the energy capture
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OWC modelling
Physical modelling
High time and cost
Scaling
Increased potential for error at small scale
Analytical modelling
Device/geometry specific
Specialist mathematical skills
Need for verification and validation
Numerical modelling
Computational time/ accuracy trade-off
Need for verification and validation
Application of OWC boundary condition not always easily available
Three previously used modelling techniques
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Simplified OWC model
• A simple geometrical model was used to highlight the fundamental physics avoiding proprietary device specific particularities
• An OWC is a highly resonant device when undamped, and is hydrodynamically narrow banded in frequency
• Vertical oscillation -power producing oscillationGeometry examined
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Mathematical model
OWCOWCOWCOWC SPSgLS
...3
32
210
and
...3
32
210
tPtPtPPtOWCP
ttttOWC
SPSgLS1110
Time domain piston model from [1]:
ηOWC and POWC can be expanded as series in powers of the small parameter
Substituting into (1) and taking those terms up to first order
(1)
Assuming 1 and P1 are harmonic such that
Which gives the frequency domain equation
OWC
POWC
(2)
11102 ˆˆ pgL
ti e
1ˆRe
1
tipP e
1Re
1Considered internal
volume of water
Initially considering a fixed OWC to examine the diffraction pressure
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Mathematical model prediction
Pressure magnitude Pressure phase
-0.1-0.05
00.05
0.1
-0.1
-0.05
0
0.05
0.1-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
x (m)y (m)
z (m
)
5
10
15
20
25
30
35
40
45
-0.1-0.05
00.05
0.1
-0.1
-0.05
0
0.05
0.1-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
x (m)y (m)
z (m
)0
0.5
1
1.5
2
2.5
3
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Structure for validation – fixed model to validate diffraction solution
AI
h
d
x
b
a
z
Wave probe
pz = -144mm
pz = -201mm
pz = -270mm
ηOWC
• Vertical cylinder:
o b = 50.5mm
o a = 47.0mm
o d = 300mm
o h = 1m
• Tank: 2.65m x 23.27m
• Regular waves
• Measurements:
o Free surface elevation
o Pressure at three depths
Schematic of model used in wave flume experimental testing
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Validation
Comparison of diffraction pressure (normalised by incident wave amplitude) in the frequency domain
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Mathematical model for floating OWC
a
d
a
g nnn
1121 tanh
ArttP sincos211
where κ1n = 1.8412, 5.3314, 8.5363, 11.706, 14.8636,…, κ1n = κ1(n –1) + .
Sloshing modes natural frequencies for fluid in a cylindrical tank:
Pressure due to acceleration and sloshing in surge:
Pressure due to acceleration and sloshing in pitch:
d
a
ArzttP sincos255
When the water column is defined by a floating structure, radiation effects must also be considered; for a structurethat is axisymmetric about a vertical axis in unidirectional waves, the dominant lateral modes are surge and pitch.
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Mathematical model for floating OWC
1 51 3 4 5' ' 'Tp p p p gz g y x
5p1
p
Piston model
Due to surge
Due to pitch Hydrostatic
where and are the complex amplitudes of the acceleration and sloshing pressures and (x', y', z') are the body fixed coordinates of a general position on the wall.
Total dynamic pressure on the internal surface of a floating OWC:
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Floating structure for validation – floating model
AIx
z
PTI5
PTI4
PTI3
PTI2
PTI1
h
ba
d
Ballast
Wave probeReflective marker
PTO2
PTO1
PTO5
PTO4
PTO3
Spacing material
• Model dimensions:
• 2b =315mm
• 2 a = 104mm
• d = 300mm
• h = 1m
• Tank: 2.65m x 23.27m
• Regular waves
• Measurements:
• Model displacement
• Free surface elevation
• Pressure at three depths
Schematic of model used in wave flume experimental testing
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Validation
Wavedirection
Comparison of dynamic pressure (normalised by incident wave amplitude) in the frequency domain
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Validation
Wavedirection
Comparison of dynamic pressure (normalised by incident wave amplitude) in the frequency domainWhere model has been rotated with respect to wave direction to assess lateral pressures
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What to take away from this…
• Simple model can be used to effectively relate the pressure and free surface elevation for the piston mode of an OWC under certain conditions
• Majority of losses must occur around or outside the column mouth to explain observed losses between Boundary Element Method model and physical testing
• Model can be used to identify areas which can be modeled using simpler inviscid theory such that computational resources can be focused on areas with viscous phenomena
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Any questions?
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Lloyd’s Register services to the energy industry
Services are provided by members of the Lloyd's Register Group. For further information visit www.lr.org/entities
For more information, please contact:
Rebecca SykesMechanical Engineer – Renewable Energy, Technology Directorate
Lloyd’s Register Group ServicesDenburn House, 25 Union TerraceAberdeen, AB10 1NN
T +44 (0)1224 267694E [email protected] www.lr.org/energy
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