Application of linear momentum actuator disc theory to open channel flow

This report presents a step by step extension of the simple one-dimensional linear momentum actuator disc theory (LMADT), which results in the well known Betz-Lanchester limit for wind turbines, to a general cross sectional array of tidal turbines in an open channel tidal flow. Unlike previous models no restriction is placed on the geometry of the turbine array or the Froude number of the flow.One of the key findings from applying LMADT to open channel flow is that the efficiency of an arbitrary array of turbines can be determined relative to the total power extracted from the channel flow, including the effects of downstream mixing. A general form of this dimensionless efficiency may be more important for open channel flow, given the possibility of downstream constraints, than the typical dimensionless power co-efficient used for wind turbines.