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The performance of a wave energy converter in shallow water

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**1. **The performance of a wave energy converter in shallow water Matt Folley Trevor Whittaker Alan Henry

**2. **A surging point absorber in shallow water

**3. **An ideal point absorber Power capture = Pi . ? / p
Typical sea
T = 10 secs, Pi = 50 kW/m
Power capture ˜ 2.5 MW
2.5 MW » power capture of any projected point absorber

**4. **Effect of motion constraints Power capture, P = Pmax(2r-r2)
r = X / X0
X0 = F / 2?B
Pmax = F2 / 8B
F = wave force, B = hydrodynamic damping
P = 0.5 F?X (1 – r/2)
Power capture proportional to wave force for highly constrained motion

**5. **Effect of viscous losses Power capture, P = F2 / 8(B + Bv)
Bv = viscous damping coefficient
Power capture proportional to wave force squared as B / Bv ? 0

**6. **Long wave approximation of surge wave force Wave force proportional to horizontal water particle acceleration
Horizontal acceleration increases with reduction in water depth
x = horizontal water particle amplitude,
y0 = deep water particle amplitude,
kh = non-dimensional water depth

**7. **Surge wave force ratio

**8. **Effect of water depth on incident wave power Reduction in incident wave power due to seabed friction and wave breaking
Department of Energy nearshore wave energy resource study (1992) indicates that the reduction in incident wave power for commonly occurring sea-states from a water depth of 40 metres to 10 metres is typically about 10%
The larger difference in average annual incident wave power is due to a greater reduction in rarely occurring, highly energetic sea-states that contribute disproportionately to the average annual incident wave power

**9. **Comparative performance of a surging point absorber in deep and shallow water Flap-type wave energy converter
Flap width = 12.0 metres Flap draft = 10.5 metres Flap thickness = 1.0 metres Flap natural period = 12.0 seconds
Shallow water depth = 12.0 metres
Deep water depth = 50.0 metres
Reduction in wave power = 20%
Quadratic viscous drag coefficient = 388 kNs2/m2

**10. **Equations of motion

**11. **Power capture with linear damper

**12. **Power capture with complex conjugate control

**13. **Power capture with reduced viscous losses, CD = 100 kNs2/m2

**14. **Power capture with shallow water incident wave power reduction of 50%

**15. **Conclusions Power capture depends on incident wave force for small surging WEC’s
Surge wave force is larger in shallow water due to increased horizontal water particle motion
Incident wave power of commonly occurring sea-states not dramatically reduced by water depth
Small surging WEC’s typically have a higher power capture in shallow water

**16. **Further work Improved modelling of the reduction in incident wave power reduction with water depth
Wave-tank modelling of WEC power capture in deep and shallow water

**17. **Power per unit volume (CCC)

**18. **Capture factor (CCC)