Monday, 5 August 2013

Design challenges - Oscillating Wave Surge Converters





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:
  1. the amount of motion (pitch amplitude)
  2. the flap's wave-making ability (radiation damping)
The geometry of the flap determines its wave-making ability. Design parameters such as water depth and frontal width determine the amplitude and width of radiated wave per degree of pitch.

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 waves

The 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.



Image credit:

'Yikes' by Badjonni: http://www.flickr.com/photos/badjonni/2000037568/in/set-72157594300378005



5 comments:

  1. Ally, I don't think you are far off in your "common sense" thinking. But you have missed a couple of the more important aspects of OWSC selection, design and siting.

    For proprietary reasons there are limits on how forthcoming I can be here, but there are fundamental reasons why OWSCs are destined to become the dominant WEC for most situations.

    Wave power tends to diminish over distance and even more so due to friction and breaking waves caused by shoaling water. However, in most conditions the energy flux per meter of depth is vastly increased as waves approach the beach. Equally important is fact that in shallow water it becomes practical to intercept most of the energy flux as compared to WEC technologies positioned at the surface in deep water. These two facts combine to allow OWSCs to attain exceptionally high wave-energy conversion efficiencies compared to other WEC types.

    You are right that the particle paths associated with waves in shallow water become elongated in the surge direction. They are ellipses at the surface and collapse to pure horizontal reciprocal motion at the seabed. The geometry and constrained motion of a hinged flap is nicely poised to exploit these kinetics.

    I sense you over estimate the importance of resonance in these highly damped devices. I also think the availability of rotary motion at the flap hinge needs to be recognized as a feature that allows attractive PTO options that are missing in other designs.

    Why do you see cost of energy being mythical?

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    1. Hi Cliff – thanks for sharing your thoughts – it's always good to hear from someone who has first-hand experience of specific technologies.

      Good point about damping of translations vs rotations. I had wondered whether this was another advantage of pitch over surge for OSWCs? I'd felt that perhaps sliders (allowing surge) would be larger and less robust than joints (allowing pitch), but I couldn't put my finger on the engineering specifics – was this your line of thought?

      My reason for referring to CoE as mythical is that, like capacity factor, it can only be known with any certainty in retrospect. Yet CoE estimations for wave power are usually not presented in a way that makes this uncertainty apparent. I caught myself doing exactly this in the first draft, so added 'mythical' as a note-to-self.

      You are correct about my overemphasis of resonance – I have over-simplified the matter by focussing on the idea of 'natural period'. I used this term to refer to one period at which all system mass and spring (including added mass, slow tuning, and reactive PTO terms) cancel. I'm not sure the terms 'natural period' or 'resonance' are even strictly correct in the context of control parameters which tune dynamic response. Perhaps something like 'induced natural period' would be better?

      My meaning would have been clearer if I'd said that the requirement for achieving the correct phase of radiated wave at a given frequency was cancellation of all system mass and spring at that frequency. The phase is independent of system damping. In general, larger structures are closer to this requirement at frequencies of interest: as their natural periods are higher, less mucking about is required to achieve a favourable 'induced natural period'.

      The question of course is whether the correct phase is a worthy goal. While correct phase will ensure maximum power capture for a given amplitude of motion (and wave radiated), it is but one factor that determines the potential for a competitive CoE. This is one example of how the 'true' CoE function could overturn 'common sense': we might find there are some design issues that dominate CoE. Solutions to such issues could result in the lowest CoE, despite not optimising power to weight ratio, or achieving 'good' performance in terms of radiating waves of favourable amplitude, phase or direction.

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  2. Yes, one can agonize themselves silly over the virtue of translation vs. rotation. Not that it matters, but at some depths and at some wave lengths, the exponential decay of the horizontal particle displacements match nicely the motions of a bottom hinged paddle.

    Unless we chose to actively intervene in an OWSC's flap motions, the amplitude and phase of the response are purely dependent on PTO damping levels. It is not difficult to understand that excessive damping resulting in zero rotation will yield zero power. Similarly, zero PTO damping and unfettered flap motion will also yield zero power. Hopefully obvious is the fact that somewhere between those extremes lies an optimum.

    I'm still not buying your "mythical." These phenomena and OWSC performance in general are as predictable as any hydrodynamic process and once tested in the ocean they can be quantified accurately. I'd agree that costs of manufacture and installation are difficult to nail down at these early stages, but these sorts of projections must be made if there is any hope of financing further development.

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    1. The good match between the horizontal displacements of a pitching flap and water particles in deep water waves suggest this would be an efficient wave maker. In shallow water however, the particle motions might be better matched by a surging plate (or better still by a pitching/surging plate). As far as I'm aware, all shallow water OWSCs use pitch rather than surge. I was wondering whether engineering advantages of pivots over sliders were a consideration?

      The phase of the response can be controlled using non-linear damping (such as latching). I had linear theory in mind when I said that the phase depends on reactive terms (mass and spring) rather than damping.

      Ok, I see you'll need some convincing about the uncertain nature of CoE! Several seriously smart people have put together cost of energy models for wave power arrays. If they'd converged on similar CoE functions, one would expect some consensus about favourable design features. Yet the only consensus appears to be within polarized camps. Pelamis and Carbon Trust insist on deep water sites. Anyone with a shallow-water concept would beg to differ, as I'm sure you will confirm! Similar polarisations exist for whether high average power sites hold the most economical potential, and what the optimal unit size for an individual device should be. Not only is the CoE function a hot topic of debate, many of its inputs are uncertain (such as discount rate, social/environmental value) or are only known retrospectively (installation costs, maintenance costs, plant availability, component degradation, resource variability, future value of renewable generation, and plant lifetime).

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  3. More discussions on the Linked-In 'Wave Energy Group': http://www.linkedin.com/groups/Design-priorities-pitching-flaps-147831.S.263404171?qid=f9daa1a2-9d1d-46fd-804a-369e13bc4091&trk=group_most_recent_rich-0-b-ttl&goback=.gde_147831_member_263404171.gmr_147831

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