A head-driven model of turbine fence performance

Abstract

This paper presents an analytic model for the analysis of co-planar turbine fences that partially span the width of a channel in which the flow is driven by a sinusoidally oscillating driving head. The thrust presented by the turbines reduces the flow rate through the channel leading to a solution for overall power that is dependent upon turbine resistance and flow blockage as well as on channel characteristics. We introduce a return parameter, in terms of power per turbine area, to assess optimum turbine fence deployment for a given channel. We find that the optimal deployment rests on a universal curve independent of the channel characteristics, and that these characteristics – namely the integrated channel bed friction and a modified channel Froude number – move the optimum along this curve. We find that blockage considerations play a large role in the performance of a tidal farm – its achievable power, optimal return, channel flow rate reduction and device thrust – and that the scales of blockage must be considered even when designing relatively unblocked farms. The impact of the channel characteristics on the optimal arrangement, alongside environmental constraints that may limit permissible flow blockage, are quantified and discussed.