Elsevier

Renewable Energy

Volume 32, Issue 11, September 2007, Pages 1961-1966
Renewable Energy

Technical Note
How much energy can be extracted from moving water with a free surface: A question of importance in the field of tidal current energy?

https://doi.org/10.1016/j.renene.2006.11.006Get rights and content

Abstract

This short technical note addresses the extraction of energy from a simplified channel in which flow is driven by a head difference between inlet and outlet. This model is used to indicate that there is a maximum rate at which energy can be artificially extracted from the flowing water and that this rate is related to the kinetic energy flux in the unexploited channel but with a multiplying factor which is related to the channel physical properties. Counter intuitively, this multiplier can exceed unity in some circumstances. The simple channel has some similarities to tidal channels but is here presented as an abstraction to allow appreciation of the relationships between energy extraction, flow speed and channel properties.

Introduction

Tidal and other marine currents are increasingly being considered as potential sources of renewable energy. Large prototype systems have now been installed in the UK [1] and Norway [2] and it is likely that other systems will be tested shortly. The available resource, however, is not well understood, although there has been work published relating to the nature, if not the magnitude, of the available extractable resource [3], [4], [5]. In the UK an estimate of the extractable resource has been published by the Carbon Trust [6], which appears to suggest a somewhat disappointing tidal current resource of 18 TW h/a, which equates to approximately 6 GW of installed capacity, assuming a capacity factor of 35%. This estimate was based on the extraction of 20% of the kinetic energy flux at a range of selected sites, which is defined in the report as the significant impact factor (SIF). The justification for the SIF is that it represents that proportion of the kinetic flux which can be extracted without causing major flow disruption. No attempt is made in the report to justify how this figure is determined and some members of the marine renewable community have expressed concern that the flux-SIF approach to resource assessment may be flawed. In this short note, a very simple flow model is used to, at least partially, support the flux-SIF approach but also to suggest that, if higher levels of flow alteration is considered acceptable, then substantially more energy might be available than suggested by the Carbon Trust report.

Section snippets

Determining the relationship between flow speed, driving head and power extraction

The approach is based upon a simple model of a flat bottomed, constant width, channel in which the flow is driven by a head difference between the inlet and outlet. Dynamic effects are ignored. It is recognised that this limits the model's applicability in the case of tidal currents, which should be considered part of a complex shallow water wave form but as, in coastal waters, tides are driven almost entirely by oceanic tides rather than by direct astronomic forcing [7], the approach should be

Conclusions

There is nothing inherently wrong with the flux-SIF approach to resource assessment; indeed Eq. (13) supports the use of the undisturbed kinetic flux density as a useful indicator of achievable resource. The simple channel based analysis does, however, suggest that achievable power extractions might be considerably higher that those suggested if flow speed reductions of up to 1/3 are considered acceptable. Indeed the true limits to resource extraction could be substantially higher than

Acknowledgements

The authors wish to thank the Engineering and Physical Sciences Research Council for their support of the Supergen (Marine) research consortium and Professor Stephen Salter of the University of Edinburgh for asking the pertinent questions which resulted in the authors writing this short document.

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