Doctor doctor! I see waves before my eyes!

Q: If I can see waves being radiated, that's good ... right?

Fig 1: Duck radiating a wave

We've established that wave energy converters need a radiated wave to cancel out the wave being absorbed.

Question is, if you are watching a device operating in a wave tank or a sea trial, and you can see a wave being radiated, does this prove that the device is doing a good job of power capture?

A quick recap of linear mass-spring-damper models

In the spirit of not frightening away readers with equations, I shall refer to the Wikipedia (1) (2) and wave in the general direction of Wolfram (1) (2) (3). A user-guide follows:

• If we know how a linear system moves in response to an excitation by a single frequency (a sinusoid) we can use superposition to find the response to an excitation composed of many frequencies; so let's make things simple and consider single frequency excitation.
• The response to such an excitation is the sum of a transient which dies away, and an underlying steady state response: a sinusoid with the same frequency as the excitation, but a different amplitude and phase.
• Both the amplitude and phase of the steady-state response depend on the forcing frequency. They can be plotted against excitation frequency (Fig 1).

Fig 1: Universal resonance curve

Does Falnes's wave maker diagram apply to all WECs ?

Fig 1: Falnes's wave absorber = wave maker diagram

Falnes's assertion that 'a good wave absorber must be a good wavemaker', and his diagram depicting the amplitude and phase conditions for optimum absorption have been around since the early days of wave energy theory. I'd always thought that the wave absorber = wave maker diagram (Fig 1) was general, and applied to all wave energy converters. Would you be surprised if I told you that it applied to point absorbers only? (by point absorber I mean a body that is at least an order of magnitude smaller than the wavelength of the incident waves)

Botticelli's Venus: nice goddess, pity about the waves.

You know you've reached the room that houses Botticelli’s Venus by the crowds of people obscuring the view of the painting. It is certainly stunning from up close though.

Like a beauty spot, this painting is all the more beautiful for it's flaws. Consider the half-shell.

Wrong turns on the way through the 96% capture maze

The photo below (Fig 1) was used to show that 96% of the energy in the wave coming from the right had been absorbed by the duck. In a previous post I showed how we can draw this conclusion from the photo alone. Like navigating through a maze, my first attempts at solving this problem took me up several dead ends. It is worth discussing these, as I'm sure I'm not the only one to have made these mistakes?

How to design a device that absorbs no wave power

1. Do not provide a point of reaction for the PTO. e.g the PTO opposes surge motion between two floating vertical plates, one behind the other; ensure one of these plates is light and porous so it offers little resistance to the PTO force; ensure they are close together to minimise excitation phase difference.
   
   
2. Avoid restoring forces in the degree of freedom (DoF) where power is extracted. There is no buoyancy restoration in surge, sway or yaw, so extract power from these DoF, ensuring that extra spring is not inadvertently applied. Moorings provide spring in these DoF, so just let the device drift where it wants.
   
   
3. Avoid useful wave radiation. Ensure that when the power take off (PTO) system is run in reverse (motoring), the waves generated are as small as possible. Better still, generate large waves that travel in the opposite direction, or have a similar phase, to the waves you're trying to cancel out. The next three points describe pragmatic methods for achieving this goal. 
    
4. Get the level of damping wrong. Light as a feather or heavy as a brick.
   
   
5. Mismatch natural period and wave period. Design the device so that the natural (resonant) period is as far as possible from the energy period of the waves you want to capture. 
   
   
6. Make it really really small. This will make the bandwidth of the capture curve really narrow; combined with a mismatch between natural period and wave period this will ensure very little energy is captured indeed.
   
   
7. Pump up those losses. Induce turbulent flow by lining exterior surfaces with mesh beaches similar to those used in wave tanks. Use a leaky transmission system. Design the bit just above the water-line so that small motions induce slap and slam loads. Install the biggest generator possible to ensure you stay at  the low end of the generator efficiency curve during normal operation.
   

Ai Weiwei's wave

 

Ai Weiwei is an engineer's artist: he makes towers out of bicycles, polygons out of wood, and surveillance cameras out of marble. His work comments on the impact of industrialisation on culture and the environment; he uses electronic communication as part of his art. 

Seven key principles for converting wave energy

1.  Provide a point of reaction. Power is captured when wave induced motion is damped. The force resisting the motion results in an equal force in the opposite direction. This has to be opposed by something; no sky hooks allowed.
    
2. The DoF where power is extracted must have a restoring force. There must be a way to restore the change in position due to wave induced motion. Gravity is the simplest method; buoyancy does the job for heave, pitch and roll motion. If power is captured from surge, sway or yaw motions, a restoring force must be supplied by mechanical springs, or by coupling to a motion that has buoyancy. 
    
3. Radiated waves capture waves. When the power take off (PTO) system is run in reverse (motoring), the waves generated indicate the potential for capturing ocean waves. Good performance results from radiation of waves that have the same direction of travel, the same amplitude, and the opposite phase, as the waves you want to capture. These are the waves that the incoming wave splits into once it reaches the device: the waves reflected and/or transmitted by the wave energy converter.
    
4. Get the level of damping just right. Like baby bear’s porridge.
    
5. Match natural period to wave period. Radiating a wave which is out of phase with the waves you want to capture is important. At resonance the phase takes care of itself. The options are to design for a natural period that equals the design wave peiod, to have a range of operating modes with different natural periods, or to use the PTO force to trick the system into behaviour with the desired natural period.
    
6. Size matters. The smaller the device, the narrower the bandwidth of the capture curve, and the lower the natural period. These disadvantages trade off against cost, so clearly size is an important cost of energy consideration.
    
7. Manage losses. Reduce losses (PTO, overheads) in low energy seas; shed loads and power in high energy seas.