1. Specialization in Ocean Energy MODELLING OF WAVE ENERGY CONVERSION António F.O. Falcão Instituto Superior Técnico, Universidade de Lisboa 2014

2. 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. Basic equations

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

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

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

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

10. PICO OWC PLANT, AZORES, PORTUGAL

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

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

14. Frequency domain analysis Power Turbine power output Wells turbine

15. Exercise Compute the turbine power ouput of the Pico OWC plant, for regular waves of period 10 s and amplitude 1.0 m. The diameter of the turbine rotor is 2.3 m. The maximum alowable rotational speed is about 1500 rpm.

16. Wells turbine of Pico plant

17. Frequency domain analysis Dimensional analysis

18. Model testing: similarity laws for air chamber and air turbine Correct dynamic similarity requires all terms in equation to take equal values in similar conditions at model size 1 and full size 2. air chamber 1 2

19. The two turbines are geometrically similar Turbine dimensionless parameters (representing the turbine aerodynamic performance) take equal values for similar conditions of the air pressure cycle in the chamber of the model and the full-sized converter. We take such conditions as those of maximum air pressure. Turbine size Turbine rotational speed

20. 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.

21. radiation flow rate memory function

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