In this article I outline my thoughts on the design challenges and opportunities associated with WECs known as 'Oscillating Wave Surge Converters'. As discussed previously, this term is used to describe seabed-mounted pitching flaps.
Maximising ratio of pitch moment to excitation of remaining 5 DoFs
In a seabed-mounted pitching device, only pitch makes a contribution to power capture. However, excitation will be experienced in all modes of motion. These forces/moments need to be resisted by the seabed attachment, which has an associated cost. Hence one design challenge is to maximise pitch moments (combined excitation and radiation forces) while minimising the forces and moments (excitation only) on the remaining 5 DoFs.
It is not surprising that commercially developed seabed-mounted pitching devices have begun to show signs of design convergence. Design solutions to the challenge of maximising pitch at the expense of other modes are evident in the choice of geometry and shallow water installation:
- Geometry: a large flat flap facing the incoming waves attracts large moments in pitch, but small forces in heave and sway.
- Geometry: there remains the problem that geometry which attracts large pitch moments also attracts large surge forces.
- Shallow water waves: in shallow water, the motion profile is altered in preference of horizontal water particle motions. The heave forces, compared to pitch/surge moments/forces, are smaller than in deeper water.
- Wave directionality: in shallow water, refraction causes waves to change course; they veer in the direction of the beach. Weathervaning of sea-bed reacting devices is not practical. However, in shallow water, the device does not need to align with the waves, as the waves align with the device. Being aligned to the principle wave direction ensures high pitch moments while limiting excitation in sway, roll and yaw.
- Short-crested waves: Refraction concentrates waves in the direction of the beach (less directional spreading). For a 1 DoF concept, it is an advantage to concentrate wave power in the direction best exploited by this DoF, and to minimise the wave power coming from directions that excite non-power capturing modes (sway, roll and yaw).
Note that the term 'excitation' is usually used in the context of a system that has been designed to have a response as a result. Pitching flaps are not designed to respond in modes other than pitch. Nevertheless, the term 'excitation' will be used here to acknowledge that forces and moments will be experienced in modes other than pitch, and will experience (preferably) minute motions as a result.
Another design challenge is ensuring that waves radiated in pitch have the amplitude, phase and direction required to destructively interfere with the incoming wave passing the device.
Achieving the right amplitude of radiated waves
The amplitude of the radiated wave is determined by:
- the amount of motion (pitch amplitude)
- the flap's wave-making ability (radiation damping)
A small flap will not radiate a big wave. This is because the wave-making ability is small, and the amount of motion that would be required for a large wave is not physically possible. Motion is restricted by the presence of end-stops. Furthermore, this concept has inherent load-shedding, because the wave-making ability decreases as the end-stops are approached (less frontal area is exposed to the direction of wave travel).
Another consideration is water depth. If the height of the flap is small, the options are to install it in shallow water, where there are more breaking waves (extreme loads), or fully submerged in deep water, so that much of the wave travels over it. Both these options have drawbacks in terms of loads being too high or too low for cost effective power capture.
During operation, some degree of control can be exerted over the amplitude of pitch motion, and hence amplitude of radiated wave, by the choice of damping coefficient.
Achieving the right phase of radiated waves
The phase of a single body oscillator (with respect to the phase of the exciting wave) is largely determined by the geometry, which fixes the natural period. Generally, a large body is required to attain a natural period that is close to the wave period.
With a single body oscillator, changing the natural period during operation involves changing the mass or the spring by a significant amount. In a large device, neither can be done quickly, but there are options for changing the response over the course of an hour. The mass can be changed by adjusting the ballast. The spring could be adjusted during operation by use of adjustable mechanical springs such as air springs, or by physically adjusting the geometry in a way that buoyancy restoration is altered.
Achieving the right direction of radiated wavesThe direction of radiated waves is usually not given as much emphasis as the amplitude and phase. In earlier posts I've argued the case for direction.
For a shallow-water pitching flap, nominally parallel to the wave front, some of the incident wave may be diffracted by the presence of the flap and travel away from the beach, and some of the incident wave may be transmitted and travel towards the beach.
For a small device, there will be little diffraction. This suggests it would be beneficial to radiate waves principally towards the beach. This could be achieved by an asymmetrical geometry, such as an Edinburgh duck with the pointy 'beak' facing the beach, and the rounded 'back' facing the oncoming waves.
For a large device with a long frontal width, most of the waves incident on the flap will be diffracted away from the beach. This suggests it would be beneficial to radiate principally away from the beach. This could be achieved by an asymmetrical geometry, such as an Edinburgh duck with the pointy 'beak' facing the oncoming waves, and the rounded 'back' facing the beach.
For a medium-sized device, or an array of large devices, there are both waves transmitted towards the beach and reflected away from the beach to be captured. A pitching flap radiates waves in both directions. The ability of this pair of radiated waves to capture the corresponding pair of transmitted/reflected waves depends on the phase difference between the transmitted and reflected waves. I would be very grateful to hear from anyone who could give me more information about this.
'Common sense' vs the mythical CoE function
It is clear that the choice of water-depth, flap height, flap width, and flap symmetry about the pitch axis are important parameters in the (mythical) cost of energy (CoE) function. Were such a function available without the hindsight of operational experience, there exists a likelihood that the parameters required to minimise it would not be those suggested by 'common sense'.
Unfortunately, in the absence of hindsight, all I can offer is my 'common sense'. While the views expressed above are based on some basic physics, they are are basically hunches, and will remain so until appraised with a little academic rigour. I would be very pleased to hear from anyone who is researching this area.
'Yikes' by Badjonni: http://www.flickr.com/photos/badjonni/2000037568/in/set-72157594300378005