Oscillating Water Column Hydrodynamic Efficiency [1]
OWCs are point absorber wave energy converting devices so their hydrodynamic efficiency is usually defined in terms of 'capture width' ratio. The time-averaged rate of energy input into the system per unit wave crest width is:
where Pw, is time averaged energy flux incident waves which linear wave theory defines as
Where A, ρ, g and vg nd are wave amplitude, water density, gravitational acceleration and group velocity respectively. Group velocity is defined as vg=dω/dk.
The dispersion relation, K=ktanhkh, where K=ω2/g, relates wave frequency ω and wave number k. For plane progressive waves of small amplitudes, the energy flux rate can also be described as:
The dispersion relation, K=ktanhkh, where K=ω2/g, relates wave frequency ω and wave number k. For plane progressive waves of small amplitudes, the energy flux rate can also be described as:
where h is water depth. the time-averaged energy flux transferred across the interior free-surface of the chamber is given by:
where Si is the cross-sectional area of the free-surface, p is the applied hydrodynamic pressure and Vn the normal velocity of the interior free surface. The capture width ratio is useful in wave tank experiments because the tank's finite width, l, can be multiplied by the incident waves' energy flux (J/s/m) to find J/s or the 'rate of energy'. From the hydrodynamic efficiency of an OWC can be found using:
the maximum and minimum values of which are zero and one. When the efficiency, η, is 1, this means all the energy of the wave has been captured and the interior free surface is in a resonant mode. The device can only stay at optimal efficiency if the rate of energy extraction is equal to the rate of energy input from incident waves so that the interior free-surface remains in resonance. This tells us that oscillating water columns must be scaled and built so that on-average, the interior free-surface is in resonance.