@article{Pelz_Lemmer_Schmitz_2022, title={Misled by Betz and unsteady flow: Review on turbine arrays falsely deemed ‘optimal’}, volume={5}, url={https://marineenergyjournal.org/imej/article/view/103}, DOI={10.36688/imej.5.239-247}, abstractNote={<p>A turbine array is an adjustable flow resistance<br />R placed in a tidal channel. Ideally, it is designed<br />and operated to maximise energy yield. Garrett &amp; Cummins<br />(2005), using optimal control theory applied to the RCelement<br />channel (R) and basin (C), showed: the energy<br />extraction from the flow PT + PD is maximised when the<br />flow rate is slowed down by a factor of 1/√3. This result<br />is independent of the ratio of the extracted mechanical<br />power PT to the total power extraction including the power<br />loss PD due to the mixing of the bypass flows within the<br />turbine field. The optimisation task for turbine arrays is<br />maximising PT. This objective raises two questions: ”What<br />is the maximum power PT that can be extracted, and what is<br />the optimal design (size, topology) and operation to achieve<br />this output?” When addressing them, the literature still<br />uses the Betz ‘limit’ as a reference. The work presented<br />highlights two major problems. First, the Betz ’limit’ is<br />not a constant upper bound for open channel flow. This<br />problem has been discussed and solved by the first author<br />(2011, 2020). Second and more importantly, the presented<br />paper points out the misconception under which several<br />research studies referred to array topologies as ‘optimal’<br />with regard to design and operation. Hereby, the presented<br />paper contributes to the advancement of tidal power on an<br />axiomatic basis. The misleading by Betz and overvaluing<br />of transient effects is made transparent in a scientific<br />discourse.</p>}, number={3}, journal={International Marine Energy Journal}, author={Pelz, Peter F. and Lemmer, Jan and Schmitz, Christian B.}, year={2022}, month={Dec.}, pages={239–247} }