Doctor doctor! I had to tie it down to stop it thrashing about!

Q: We had to tightly moor our device, otherwise its movement would have resulted in waves being radiated away. What could be causing this problem?

First we need to define what we're looking at. We'll dismiss the trivial case of a single body absorber: clearly preventing its motion will give us zero power capture! Hence we must be talking about a floating system with more than one wave activated body. Furthermore, as we talk about tightly mooring the device, it makes sense that one body is a large structure and the other smaller body/ies (e.g. oscillating water columns or flaps) move/s with respect to this main structure.

We've established that wave energy converters work by radiating waves that cancel out the waves being absorbed. Clearly the question is: What sort of radiated waves? In a previous article I showed why the useful radiated waves are not visible during operation, and why the waves that are visible are wasted radiation, or waves that arise from the incident wave, which have not been cancelled. Both are undesirable, as the power they carry away from the system is power that has not been captured.

It won't be possible to completely stop this from happening, because no system is completely linear, the system set-up can only be optimised for one frequency component of the wave spectrum, and some systems are not able to produce the waves in the direction required for complete absorption, even at one frequency component. Nevertheless, by understanding the system, we can keep wasted radiation and un-cancelled incident waves to a minimum for a particular design of device.

How do we minimise wasted radiation and un-cancelled incoming waves?

The wave absorber = wave maker diagrams show us we need to radiate waves of the correct size, phase and direction. In practical terms this means that we need:

• Amplitude: the right level of damping,
• Phase: a system that is close to resonance (or acts close to resonance due to clever control),
• Direction: the correct degrees of freedom of motion to radiate waves in the required directions (see articles on what is required for small, medium and large bodies).

Can tightly mooring a device to prevent wave radiation achieve any of the aims above?

 

Let us return to the example under consideration: power extraction from the relative motion of one large absorber and one or many smaller absorbers. When the main structure is tightly moored (practically no motion), the power take off damps only the motion of the smaller absorber/s (with respect to ground). When the main structure is slackly moored, the power take off damps the relative motion of the large and small absorbers.

The amplitude, phase, and direction conditions refer to the combined wave radiated by the large and small absorbers. It is likely that the larger absorber will make a bigger contribution to this combined wave for the following reasons:

• the size of the radiated wave depends on the size of the body and the amplitude of motion. It is possible for small bodies to radiate waves bigger than those radiated by large bodies, but to do so they need larger amplitude motions. 
• large amplitude motions are limited by stroke: smaller bodies tend to have lower maximum stroke lengths by virtue of their geometry.
• large amplitude motions occur when a system is excited close to its natural period. In general, larger bodies have higher natural periods; bodies that are small compared to the wavelength tend to have natural periods much lower than the wave period.  

We cannot say with certainty that the larger body has a higher natural period than the smaller body/ies because we do not know enough about the geometry or modes of motion, which also influence the natural period. However, it is fair to say that the most likely scenario is that the larger absorber will have a larger amplitude response, and a higher natural period. This means that the relative motion, and the wave radiated by the device as a whole, will be dominated by the motion of the large body.

If this is indeed the case, then tightly mooring our device will not bring us closer to achieving the desired amplitude and phase of radiated wave: indeed this action would result in lower natural periods than previously, resulting in a system further away from resonance at the frequency of interest, and thus a radiated wave further away from the required phase at the frequency of interest.

The waves radiated also need to be in the right direction. This depends on the size and shape of the device: if the incident width is small then radiated waves are required in the same direction as the transmitted waves; if it is large enough to reflect some of the incident waves, then radiated waves are also required in the directions of those reflected waves.

Only knowledge of the geometry and modes of motion would be able to tell us whether the large or smaller bodies were more successful at radiating waves in the right direction. 

Doctor's advice:

If tests showed that performance did indeed improve by tightly mooring the large body, one possible explanation is that the large body had not been designed to radiate waves in the correct direction. Examples of such cases are waves being radiated out to the side, a body with small incident width that radiated towards the incident waves, or a body with a large incident width that did not radiate towards the incident waves.

Another explanation is that the geometry had been chosen so that the natural periods of the large and small bodies were close together. This would leave very little phase difference between their responses. As power is captured from the relative motion of the large and small bodies, it can be seen that a large phase difference is beneficial.   

In conclusion, it is possible to improve the performance of a multi-body device by mooring the largest body, if the large body had been designed to radiate waves in the wrong direction, or if the small body/ies had been designed to move in phase with the large body. Surely it would be better to design the large body so that it pays for its keep by playing an active role in wave absorption?

Image credits:

'Tied down' by Nicole Braun http://www.flickr.com/photos/nicolesphotos/2354062172/

'Splishy splashy explored' by Rachel Carter http://www.flickr.com/photos/raggle/3163752268/

Other articles in the Doctor doctor! series:

Doctor doctor! I see waves before my eyes!

Doctor doctor! Surely radiation can't be good for me?