Optimization of the power output from ducted turbines

For many years there has been interest in the possibility of enhancing the performance of wind turbines by encasing them in a duct or 'shroud', but practical considerations have prevented commercial realization. While this possibility is not ruled out, more beneficial schemes for shrouding may well arise for water turbines in tidal streams. In this paper, the performance of a shrouded turbine has been analysed using one-dimensional theory by treating the ducts upstream and downstream of the turbine as contractions or expansions having specified diffusion efficiencies. It is shown that, for given diffuser efficiencies, there is an optimum turbine resistance for generating maximum power, because the swallowing capacity of the duct is increased as the resistance decreases. Simple experiments with static resistance elements in the duct have confirmed this theory for the swallowing capacity and shown that there is little to be gained by controlled diffusion at inlet. However, efficient controlled diffusion at outlet can lead to power enhancements of more than 30 per cent over an optimized turbine of the same area in the freestream. To achieve this, a more lightly loaded turbine must be utilized. Claims in the literature of much greater enhancements than this are sometimes made in relation to non-optimized conditions for the freestream case. The alternative requirement, that maximum power should be extracted from a given inlet area, is also analysed and shown to require a highly loaded turbine.