The Power Coefficient in the Theory of Energy Extraction from Tidal Channels

Abstract:

The maximum average power available from a fence of turbines deployed in a tidal channel is given by the simple formula, Ρ=γρgaQ_max, where ρga is the amplitude of pressure difference across ends of the channel, Q_max is the maximum volume flux through the channel in the undisturbed state (i.e., before turbines are deployed), and γ is a numerical coefficient. The latter depends only weakly on the underlying dynamical balance of the channel. This is shown to be consequence of quadratic drag and changes to the natural impedance of the channel as deployment of turbines impedes the flow. Additionally, it is shown that the power coefficient γ is relatively insensitive to the form of the turbine drag.