1. Specialization in Ocean Energy MODELLING OF WAVE ENERGY CONVERSION
António F.O. Falcão
Instituto Superior Técnico,
Universidade de Lisboa
2017

2. MODELLING OF OWC WAVE ENERGY CONVERTERS
PART 4
MODELLING OF OWC WAVE ENERGY CONVERTERS

3. Basic approaches to OWC modelling
will be analized here

4. Basic equations Volume flow rate of air displaced by OWC motion
Decompose into
excitation flow rate
radiation flow rate

5. air compressibility effect
Basic equations
air compressibility effect

6. Thermodynamics of air chamber
Assume compression/decompression process in air chamber to be isentropic (adiabatic + reversible). This implies perfectly efficient air turbine.

7. Thermodynamics of air chamber
Better approximation: real turbine with average efficiency h .
Process is polytropic instead of isentropic,
Replace exponent g by k
Typical values for “good” air turbines: h = 0.6 to 0.7

8. X Aerodynamics of air turbine
Dependence on Mach number Ma in general neglected, because of scarce information from model testing. X

9. Frequency domain analysis
Linear turbine
Linear relationship air density versus pressure
Linearize:
Wells turbine

10. Frequency domain analysis
The system is linear
Decompose
Note: radiation conductance G cannot be negative

11. PICO OWC PLANT, AZORES, PORTUGAL

12. Frequency domain analysis
(deep water)
Axisymmetric body
(deep water)

14. If the inner free surface is approximately flat, then there is a relationship between A, B, G, H, Fe and Qe

15. Frequency domain analysis
Power
Power available to turbine =
pressure head x volume flow rate
Regular waves
Time average

16. Can be rewritten as:
For given OWC and given incident regular waves, Qe and G are fixed.

17. Frequency domain analysis
Power
Turbine power output
Wells turbine

18. Exercise
Consider the Pico OWC plant. Air chamber volume V0 = 1050 m3 .
Compute the average power absorbed from regular waves of period 10 s and amplitude 1.0 m.
Compute approximately D and W for the Wells turbine
Pico plant

19. Pico plant

20. Wells turbine with guide vanes

21. Turbine efficiency

22. Turbine power

23. Turbine flow rate versus pressure head

24. Time-domain analysis of OWCs
The Wells turbine is approximately linear. So frequency-domain analysis is a good approximation.
Other turbines (e.g. impulse turbines) are far from linear. So, time-domain analysis must be used, even in regular waves.
This affects specially the radiation flow rate, with memory effects.
The theoretical approach is similar to time-domain analysis of oscillating bodies.

25. radiation flow rate
memory function

26. MODELLING OF OWC WAVE ENERGY CONVERTERS
END OF PART 4
MODELLING OF OWC WAVE ENERGY CONVERTERS

27. Additional Exercise 5