1. 03 June 2016
Study for the Hull Shape of a
Wave Energy Converter-Point Absorber
Filippos Kalofotias
Design Optimization & Modeling Improvement

2. Contents
 Background
 Problem Definition
 Research Objectives and Questions
 Model Description
 Design Optimization
 Modeling Improvement
 Model Validation
 Conclusions & Recommendations
 Questions?
03 June 2016Filippos Kalofotias 2

3. Background
03 June 2016Filippos Kalofotias 3
‘’Deciphering the title’’
Wave Energy = Energy transfer from wind waves
Converters = Devices transforming wave
energy to electrical
Point Absorber

4. Background
03 June 2016Filippos Kalofotias 4
Point Absorber

5. Problem Definition
03 June 2016Filippos Kalofotias 5
P. Wellens (2004) / S. Kao (2014)
Studied :
 Maximization of power extraction under irregular
waves
 Optimum Spring and Damper Configuration
 During sea state (Wellens)
 During smaller intervals of the sea state (Kao)
Did not study :
 Optimum dimensions of the buoy for the
studied wave climate
 Other shapes for the buoy than Cylinder
 Viscous Effects
 Wave force estimation with large motions
Control
Strategy
Design
Optimization
+
Physical
Modeling

6. Research Objectives & Questions
03 June 2016Filippos Kalofotias 6
Research Objectives
 Derive an efficient design for the
buoy (hull) of the Point Absorber
Shape
+
Dimensions
 Improve physical modeling of
the Point Absorber’s response to
waves
Viscous
+
Wave Force

7. Research Objectives & Questions
03 June 2016Filippos Kalofotias 7
Research Questions
What is the most efficient design?
 Influence of shape to efficiency?
 Influence of dimensions to efficiency?
 Efficiency comparison of different designs?
How to improve Point Absorber’s modeling?
 Viscous effects estimation?
 Wave force including large buoy’s motion?
 Influence of additions to the previous model?

8. Model Description
03 June 2016Filippos Kalofotias 8
Linear Mass-Spring-Damper System
Newton’s 2nd Law
Force Analysis
Restricted to up and down motion
Equation
Solution?
Coefficients?
Excitation Force?
Nonlinear Viscous
Effects?

9. Model Description
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Solution
Frequency Domain
Time Domain
 Irregular waves – JONSWAP
 Superposition of component
regular waves - RAO
 Linearity is a must
 Fast and valuable for statistics
 Time step solution of buoy’s
position and velocity
 Phase shifts needed
 Instantaneous power and
average over time
 Nonlinear effects such viscous
forces can be included

10. Model Description
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Coefficients
3D – Diffraction Theory / NEMOH
Spring, ksp and damper, β
 Radiation Damping, b(ω)
 Added Mass, a(ω)
 Predetermined and adjustable
 Resonance at peak frequency
 Optimum damper coefficient
Restoring, c
 Determined by waterline area
 Radius dependent

11. Model Description
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Excitation Force
3D – Diffraction Theory / NEMOH
 Force amplitude per frequency
 Per meter wave amplitude
 Doubling the wave amplitude
doubles the wave force
 Equilibrium position estimation
 Superposition principle
 For time dependent, Fexc (t)
phase shift is needed
NEMOH neglects viscous effects
Nonlinear Viscous
Effects?

12. Model Description
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Nonlinear Viscous Effects
Computational Fluid Dynamics / ComFLOW3
 Fully viscous numerical solution of
Navier-Stokes equations
 Numerical tank
 Boundary conditions
 Turbulence modeling
 Grid size
 Free surface
 Computationally expensive
 ComFLOW3 provides viscous
information for the Time Domain
model

13. Design Optimization
03 June 2016Filippos Kalofotias 13
Wave Climate
Scatter Diagram
Evaluation Criterion
 Hs ≤ 4.5m (95% of annual)
 Hs > 4.5m non operational
Efficiency
 Proportion of extracted power to
available
 Available depends on radius

14. Design Optimization
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Geometry
3 Shapes
Dimensions
 Max R=10m
 Max TD=15m

15. Design Optimization
Dimensioning
Frequency Domain Results
03 June 2016Filippos Kalofotias 15

16. Design Optimization
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Shape Evaluation
 3 Final designs, Cyl8, Bul6, Con6
 Similar efficiencies
 Viscous assessment is needed
How do we include viscous effects in
the Time Domain model?
Drag Force (Morison type)
Oscillating body in calm water
Oscillating body in waves / stagnation pressure
How do we find Cd?

17. Design Optimization
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Forced Oscillation Tests in ComFLOW3

18. Design Optimization
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Efficiency Comparison
 Cylinder has the largest drag
coefficients
 Bullet has smaller drag
coefficient for fast oscillations
than the Cone
 Drag force becomes important
at high velocities
 Drag coefficients vary according
to the flow conditions
 So, not steady during simulation
Drag coefficients, Cd results

19. Design Optimization
03 June 2016Filippos Kalofotias 19
Efficiency Comparison
Time Domain Results
with steady drag coefficients
Frequency Domain Results
no viscous forces
Spring coefficients per sea
state for Bullet and Cone

20. Design Optimization
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Final Design Selection
 Resonates further in the
scatter diagram
 Highest efficiency at the
most energetic sea states
 Less drag forces for fast
oscillations
 PTO damper optimization
can increase efficiency

21. Modeling Improvement
03 June 2016Filippos Kalofotias 21
Final Model 1
Parameterization of Cd
 Detailed inclusion of viscous effects
 Adjustment of Cd at every time step
Reynolds number
Keulegan-Carpenter number
Forced Oscillation Tests

22. Modeling Improvement
03 June 2016Filippos Kalofotias 22
Final Model 1
Assumption : Re and KC refer to the maximum velocity
Vm. In Time Domain model the maximum velocity is not
known before hand. The actual is used.
Results
What about PTO damping
coefficient optimization?
PTO damping coefficient selective optimization

23. Modeling Improvement
03 June 2016Filippos Kalofotias 23
Final Model 2
 Inclusion of the buoy’s motion in
excitation force estimation
 Calculation of Froude-Krylov force
at every time step
 NEMOH runs at 11 different
positions for the Diffraction force
 Estimation of Diffraction force at
every time step with interpolation
Results
Excitation force comparison

24. Model Validation
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Frequency vs Time Domain
Δω = 0.01 rad/s Δω = 0.001 rad/s

25. Model Validation
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Final Model 1 vs ComFLOW3
Forced Oscillation Test
Forced Oscillation Test
With waves

26. Conclusions & Recommendations
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Conclusions
What is the most efficient design?
 Within the 21 evaluated designs, Bul6 was qualified as the most efficient
 No guarantee that Bul6 is the optimum design
Influence of shape and dimensions?
 Coupled optimization problem
 Different shape leads to different optimum dimensions
 Resonance properties
 Excitation force
Efficiency comparison of different designs?
 Optimum dimensions per shape
 Viscous effects assessment
 Inclusion of viscous damping in PTO damper optimum configuration

27. Conclusions & Recommendations
03 June 2016Filippos Kalofotias 27
Conclusions
How to improve Point Absorber’s modeling?
 Final Model 1 increased the physical accuracy of the model.
 Final Model 2 proved to be computationally expensive without adding
significant physical information to the model
Viscous effects estimation?
 Stagnation pressure method for drag force
 Forced Oscillation Tests
 Drag coefficient parameterization
 Time step adjustment
Wave force including large buoy’s motion?
 It appear that for large buoys the assumption of estimating the excitation
force at equilibrium position is valid
 Linear wave theory and linear diffraction theory cannot add anymore
physical accuracy in the model

28. Conclusions & Recommendations
03 June 2016Filippos Kalofotias 28
Conclusions
Influence of additions to the previous model?
 More than 10% decrease in power extraction because of drag force
 Optimum PTO damper configuration shift as a result of the extra
damping
 Important for control strategies
Recommendations
 Nonlinear excitation force assessment
 Nonlinear restoring and radiation forces
 PTO modeling
 Point Absorber farms

29. 03 June 2016Filippos Kalofotias 29
Questions?