Wednesday, 24 June 2015

Renewable UK W&T 2015 - Engineering requirements for cost effectiveness

How can we engineer cost effective wave power? This was the subject of two talks at this year's Renewable UK wave & tidal conference: Stephen Salter presented 'A thought experiment to identify the ideal wave energy system', while Peter Fraenkel presented 'Scaling up to reduce costs'. Peter's talk gave the design philosophy behind his latest design of tidal turbine; the principles are applicable to wave power.

How to capture waves efficiently

Prof Salter used the example of wavemakers to demonstrate what is required for good wave absorption. He offered the following thought experiment (quote from private communication 2014): 

“Let us imagine a wide test tank with a large number of separate, narrow, dry-back wavemakers along one wall. Opposite the row of wave makers is a rigid wall which will act as a perfect reflector of all incoming waves. A single wave maker at the centre of the row generates a wave group which radiates out as concentric semi-circles according to the Huygens principle. Figure 1 shows the group about to arrive at the reflecting wall. The single wave maker would have been putting power into the water which could be exactly measured from its force and velocity or torque and angular velocity. The reflections from the vertical will be like waves from the mirror image of the source behind the reflection wall and are shown in figure 2.

Suppose now that the rigid reflecting wall is replaced by a second bank of dry-back wave makers which are driven so as to produce wave fronts that are the inverse of the reflections and so would exactly cancel all the reflections at every point in the tank. If energy has been put in by the first single wave maker but is no longer anywhere in the water it must have been absorbed by the second bank of wave makers. We could measure the amount of energy from the force and velocity signals from each of them. The second row of wave makers has to move so as to radiate the inverse replica of what the rigid cliff would have reflected.

What is true of a short wave group from the original single wavemaker will also be true of a second wave maker and indeed of all the wave makers making a continuous sea state from a large number of separate wave fronts at various angles and wave lengths. We could either calculate the command signals to the second bank with a computer fed with information from the first bank or we could measure the forces exerted on them by the waves and set up a control loop to maintain a relationship between forces and velocities. This would allow waves from any other objects in the tank to be absorbed as well as ones from the wave makers. This form of force control is now common in a large fraction of the world’s test tanks and gives very much greater stability for long wave tests and faster recovery between tests.”

How to capture waves economically

The next topic Prof Salter addressed was a list of requirements for economic wave capture. The ideas were along the lines of maximising structural efficiency in small seas while reducing the loads that drive system costs. For structural efficiency in small waves he noted the following requirements:
  • High force x velocity product: to radiate waves as big as those being captured. For most shapes, surge attracts higher forces than heave, especially in shallow water. A combination of heave and surge (at a 45 deg slope) attracts the highest forces.
  • Directionality: the thought experiment shows the advantage of only radiating waves on one side. To generate waves on one side only requires either asymmetry, e.g. air-bags, sliding wedges on a solid back wall, ducks on a spine; or capture in a combination of surge and heave.
  • Array operation: the thought experiment also shows the importance of minimising the gaps in a line of absorbers, and of having individual power take off for each absorber.
  • Phase coherence: the applied forces over the whole body should be in phase. Hence the length of the absorber (in the direction of wave travel) should be a small fraction of wavelength, and the width should be a small fraction of the crest-length.
  • Avoiding losses from vortex shedding: the radius of curvature should be no smaller than the economic wave amplitude.

To reduce cost incurring loads on the system he noted the following requirements:
  • Move ‘freely’ through big waves: low freeboard
  • A design that avoids end-stops is advantageous. Hence rotations are better than translations.
  • Transmit surplus energy to the beach:  Theory [Longuet-Higgins and Stewart] tells us the mooring force depends on the amplitudes of the incident, reflected and transmitted waves: \( F_{moor} = ¼ \rho g (a_{in}^2 + a_{ref}^2\: –a_{trans}^2) \). Hence to reduce mooring forces (in big seas) we should seek to reduce reflected waves and increase transmitted waves.

How to build a marine energy array economically

Prof Salter’s list of requirements suggest to me a line of many closely spaced, medium sized, absorbers. So it was interesting to see a similar conclusion being expressed for tidal arrays. Peter Fraenkel approached the problem from an economic perspective. He demonstrated the main economic drivers using estimations of the cost breakdowns for arrays of ten turbines, of various sizes, assuming a ‘typical’ turbine design: each turbine on a pile-driven support. These are shown in the diagram below (reproduced from his presentation). This illustrates two trends:
  1. Turbine unit costs increase with scale: power capture is proportional to the rotor diameter squared, whereas loads are proportional to the diameter cubed. Hence the cost per kW of the blades, hub and nacelle increase with the rotor diameter.
  2. Balance of plant unit costs decrease with scale: any cost with a high proportion of overheads, such as installation, will favour larger unit sizes. There are more kW to spread these fixed costs over.

While these two design constraints may appear in conflict, note that costs increase with rotor diameter, but decrease with rating of the installed unit. This suggests the necessity of a multi-MW unit with multiple rotors. Peter noted other requirements for an economic array as:
  • Unit can be easily removed from and returned to site
  • Maintenance can be done on site
  • A cheaper method of providing seabed reaction than driven piles is required

Peter described how these design requirements had informed the new Fraenkel-Wright design: SuperTideGen. This is a floating catamaran supporting four 1MW turbines (each the size of SeaGen’s rotors). The rotors can be individually lifted for on-site maintenance (see below), and the blades can be pitched to capture efficiently in both directions.

Longuet-Higgins and Stewart 1962. Radiation stress in water waves. Deep-Sea Research, 1964, Vol. II, pp. 529 to 562: Pergamon

Image credits:
'Rubber Ducky' by Sean Kenney:
Wavemakers diagram courtesy of Steven Salter
Representative cost breakdowns, courtesy of Peter Fraenkel, see pg 2 of All Energy presentation
SuperTideGen, courtesy of Peter Fraenkel, see pg 16 of All Energy presentation 


I would like to thank Renewable UK for the complementary ticket that enabled me to attend and write up the highlights. I am also grateful to Stephen Salter and Peter Fraenkel for discussions that helped me to accurately convey their contributions.


  1. Having a low freeboard may reduce the effect of some cost incurring loads (see Salter's suggestions on reducing cost incuring loads) but I am not sure that this is the whole story.

    For instance:

    1. the 1st and 2nd order wave forces (which generally don't include a contribution from wave pressures on the freeboard of a vessel) often drive mooring loads.

    2. It is feasible that the submerged part of a low freeboard device could come out of water in some wave conditions and then be abruptly re-immersed (from any direction) resulting in a slamming load on the hull.

    There are almost certainly other cost incurring loads which occur irrespective of whether you have a low freeboard or not.

    Be careful too not to correlate the greatest cost with either biggest expected waves or big expected wave induced vessel loads. There isn't necessarily a direct correlation with either one - particularly where impulsive load effects (e.g. slamming or snatch loads) are an issue.

    What is actually important for cost would seem to be how the system (moorings and device structure) responds to loads.

    For example for some big hydrodynamic loads it is possible that the response of the structure/moorings is relatively benign as the part of the response spectrum which is excited by the loading is small.

    Equally smaller (and more frequently occuring) hydrodynamic loads may excite a more energetic part of structure/mooring response spectrum causing for example progressive damage to a system (e.g. structural fatigue).

    So perhaps giving wider thought to what type of loads effect the dynamic response of both the structure and moorings (and the occurence of these loads) is what is required to design a system with manageable cost incurring loads.

    1. Thanks for this deeper look at mooring loads.

      Are you saying that we can limit mooring loads by designing for a low response at the periods associated with storm seas?

      It sounds like you are suggesting that the damaging loads could occur in the frequently occurring (smaller) seastates jsut because they happen more often? In these seastates, would it be possible to reduce mooring loads without reducing power capture? e.g.. designing for low response at these peroids might well reducing mooring loads but would also reduce power capture!

  2. Reply from Stephen Salter:

    It is important to distinguish the short term, wave-by-wave alternating forces from the long term unidirectional forces which the Edinburgh group called the mooring force. The long-spine duck system could reduce the short-term forces by allowing the spine joints to yield at bending moments bigger than some chosen value. The big anxiety then was the joint angle needed for safety. Tank tests showed that the extreme wave aimed at the most sensitive point on the spine needed 4 degrees for the spine to be safe. The 1981 design allowed for a joint angle of 12 degrees. Richard Yemm and his Pelamis team designed joints for even bigger angles. The results for various values of joints stiffness in a wide range of sea states can be downloaded from Browse to /Wave energy/Old reports/Longspine bending 1984. Videos of the projects can be seen in Youtube by entering 'Jamie Taylor Power for Change'.

    The long term drift forces are set by the amplitudes of incident, reflected and transmitted waves. Chris Retzler did a long series of comparisons of different appendages. Low freeboards were a great help and we found some long spine shapes that would drift gracefully out to sea. The Retzler results can be seen in /Longspine with appendages. Figure 4.4 shows the reduction with rising wave amplitude for some shapes.

    Jamie Taylor also did a series of extreme wave impact tests with the impact point at a range of distances from the model. His results are in /Slamming test 4 year 1978. We could measure forces on fixed and yielding mountings and link the force records to photographs of the wave surface. There were plenty of surprises like the maximum force happening in the second trough following the nominal peak shown on page 27.

    The very low values for mooring force are shown in the /Long spine mooring 1986 report. This also measured, Figure 4.5, the amount of flexing that would be needed for the electrical cables and a very satisfactory fatigue life based on the cable flexing tests carried out by Jim McConnell at Pirelli in their report 8526P. They showed that the selected cable would fail after 1 to 10 million bending cycles at 40,000 microstrain. In the South Uist wave climate the 10 million cycle strain would be less than 100 microstrain. We could claim a factor of safety of 400.

  3. Thank you for all these details, Stephen.

    Stephen asked me to put up the correct link to the reports; it should be