Wave energy:   Appendix 1 [ main text | hovedtekst ]

Principles of energy absorption 100% absorption A crucial principle in wave energy absorption is that one cannot destroy a wave without creating a wave, and vice versa. A) An incoming wave. No oscillating body is present. B) A body oscillating in heave (vertically) creates a symmetric wave. No incoming wave is present. C) A body oscillating in surge or pitch (horizontally) creates an anti-symmetric wave. No incoming wave is present. D) The sum of A, B and C implies 100% energy absorption, as the waves cancel each other downstream of the body. The above figures show that if a body oscillates with the appropriate amplitudes and phases, it will generate a wave which exactly cancels the incoming wave at the downstream side of the body. This implies that all the energy contained in the incoming wave is absorbed by the oscillating body. Hence, we point out the following important facts: One has to create a wave in order to destroy a wave. One cannot absorb the energy in a wave without creating another wave. The amount of energy absorbed from a wave by an oscillating body depends on the amplitudes and phases of the oscillatory motion. Provided the optimum amplitudes and phases, an oscillating body can theoretically absorb all the energy in the incoming wave. The conditions determining the appropriate amplitude and phase of the oscillation is called the optimum amplitude condition and the optimum phase condition, respectively. In order to satisfy these conditions, one has to restrain the oscillations in exactly the right way. The conditions are explained briefly in the following: The optimum phase condition A system which oscillates freely (i.e., in the absence of any external time-varying force), will do so with its natural frequency. This frequency is determined by the system's stiffness, mass and damping. If the oscillations are forced (driven by some external time-varying force), the oscillation amplitude will be maximum if the frequency of the force coincides with the natural frequency of the system. When this happens, we say that the system oscillates in resonance. In the case of a wave energy converter, the resonance situation arises when the frequency of the incoming wave equals the natural frequency of the converter. We say that the optimum phase condition is satisfied, and the absorbed energy is maximum. If the wavelength (and hence, the frequency) of the incoming wave is constant, we may ensure resonance by choosing a converter with the appropriate parameters. Unfortunately, the wavelength varies somewhat in all wave climates. The converter will therefore be out of resonance at least some of the time. We may however obtain a sort of artificial resonance when the frequency of the wave is lower than the converter's resonance frequency. This technique, called phase control, is carried out by adjusting the parameters of the converter while it oscillates. Obviously, the mass of a system cannot easily be changed during operation, at least not quickly. The stiffness and damping, however, can. We only mention the simplest and crudest method here, namely the technique of latching the system at appropriate intervals of the oscillation period. In this way we can ensure that the oscillating part of the device attains the optimum phase relative to the wave. Phase control is especially interesting in the case of small converters. Having a high resonance frequency, they may be controlled to near optimum phase at any wave frequency of practical interest. The optimum amplitude condition We have now briefly discussed the problem of achieving the optimum phase of the oscillating device. In order to maximize the power output we also have to satisfy the optimum amplitude condition. This condition specifies the oscillation amplitude of the system ensuring maximum power output (provided that the phase is optimum, too). Let's consider a light body oscillating freely on the water surface. It is obvious that no energy can be extracted from such a free oscillation, since the introduction of any power take-off mechanism would impose a restriction on the motion, and the oscillation would no longer be free. Consider, on the other hand, the case that the body is restrained from oscillating at all (e.g. by means of some latching mechanism). It is equally obvious that no power can be exctracted in this case either, since the body is not moving. We conclude from this that the power output will have to be maximum for some intermediate damping of the system. Arne Brendmo Latest rev. 2007-03-01