A one-dimensional model for tidal array design based on three-scale dynamics

Abstract

In order to make the extraction of tidal current energy economically viable, the power production per turbine must be optimised in each tidal array. Furthermore, the impact of power extraction on the marine flow environment must be understood. These two aims mean that designers must be able to model different configurations of a tidal array in order to create the most efficient, least invasive arrangement. In this paper, an analytical model is developed for array design in idealised rectangular tidal channels with idealised turbines. The model includes the effects of (i) local blockage, (ii) surface deformation and (iii) added drag due to the installation of the array. While these effects have been accounted for individually in past work, the model presented here is the first to include all three such that the interaction between different effects can be understood. Results are presented for optimal local blockage and turbine resistance as functions of inherent channel drag coefficient, channel length and Froude number at various global blockage values. It will be shown that it is necessary to model the effects of local blockage and added drag simultaneously in order to obtain the design parameters of a tidal array (global blockage, local blockage and turbine resistance), which will maximise the power extraction per turbine. Neglecting either effect will lead to an array design with lower power extraction than the optimum, the addition of unnecessary extra turbines and higher lost power from the array.

On the arrangement of tidal turbines in rough and oscillatory channel flow

“…Despite these limitations, however, the present study provides key insights into the effects of channel-scale dynamics on the optimal turbine arrangement and potential for enhanced power capture. Building on the works of Garrett & Cummins (2013), Divett (2014), Creed et al (2017 and Gupta & Young (2017), results from the foregoing analysis demonstrate the importance of incorporating not only local blockage effects but also background roughness and, particularly, oscillatory flow in models of tidal turbines. The greatest power enhancements are shown to require local blockage ratios which would be difficult to achieve in practice, but the present results suggest that, for channels with low ratios of drag to inertial forces, significantly more power can be produced by packing turbines into a small part of the cross-section than can be produced by evenly distributing the turbines across the channel width.…”

“…Divett (2014) later showed the corresponding increase in power production to be ∼41% for an inertia-dominated channel, but did not further investigate the role of the channel's natural dynamic balance in determining the potential power enhancement. Gupta & Young (2017) have since proposed a new theoretical model which extends the two-scale theory to incorporate both free surface deformation and the effects of turbine resistance on the channel flow rate. However, because this extended model is also based on the assumption of quasi-steady flow, it cannot be used to analyse the effects of channel-scale dynamics on the optimal turbine arrangement and potential for enhanced power capture.…”

Performance and wake characteristics of tidal turbines in an infinitely large array

“…Finally, it should be remembered that, in a real tidal array to be built in the future, the cross-sectional average velocity (which was considered as a fixed parameter in the above analysis) would depend on how the flow resistance caused by the entire array alters the natural tidal channel-scale momentum balance (see, e.g. Vennell 2012;Vennell et al 2015;Gupta & Young 2017). As the additional resistance caused by the array would reduce the mass flow rate through the array, the turbine resistance required to maximise the power for a given 'natural' mass flow rate (observed in the 'natural' channel without the array) would be lower than the optimal resistance discussed above.…”

A note on the tuning of tidal turbines in channels

“…Houlsby et al 2008;Vennell 2010;Draper et al 2013Draper et al , 2016 and optimal arrangements for tidal turbines (e.g. Nishino and Willden 2012;Draper and Nishino 2014a, b;Vogel et al 2016;Gupta and Young 2017).…”