Misled by Betz and unsteady flow
A turbine array is an adjustable flow resistance R placed in a tidal channel. Ideally, it is designed and operated to maximise energy yield. Garrett & Cummins (2005), using optimal control theory applied to the RCelement channel (R) and basin (C), showed: the energy extraction from the flow PT...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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European Wave and Tidal Energy Conference
2022-12-01
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| Series: | International Marine Energy Journal |
| Subjects: | |
| Online Access: | https://marineenergyjournal.org/imej/article/view/103 |
| _version_ | 1797976815593062400 |
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| author | Peter F. Pelz Jan Lemmer Christian B. Schmitz |
| author_facet | Peter F. Pelz Jan Lemmer Christian B. Schmitz |
| author_sort | Peter F. Pelz |
| collection | DOAJ |
| description |
A turbine array is an adjustable flow resistance
R placed in a tidal channel. Ideally, it is designed
and operated to maximise energy yield. Garrett & Cummins
(2005), using optimal control theory applied to the RCelement
channel (R) and basin (C), showed: the energy
extraction from the flow PT + PD is maximised when the
flow rate is slowed down by a factor of 1/√3. This result
is independent of the ratio of the extracted mechanical
power PT to the total power extraction including the power
loss PD due to the mixing of the bypass flows within the
turbine field. The optimisation task for turbine arrays is
maximising PT. This objective raises two questions: ”What
is the maximum power PT that can be extracted, and what is
the optimal design (size, topology) and operation to achieve
this output?” When addressing them, the literature still
uses the Betz ‘limit’ as a reference. The work presented
highlights two major problems. First, the Betz ’limit’ is
not a constant upper bound for open channel flow. This
problem has been discussed and solved by the first author
(2011, 2020). Second and more importantly, the presented
paper points out the misconception under which several
research studies referred to array topologies as ‘optimal’
with regard to design and operation. Hereby, the presented
paper contributes to the advancement of tidal power on an
axiomatic basis. The misleading by Betz and overvaluing
of transient effects is made transparent in a scientific
discourse.
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| first_indexed | 2024-04-11T04:56:58Z |
| format | Article |
| id | doaj.art-d7bececc46484406ab76eaefad1b3b51 |
| institution | Directory Open Access Journal |
| issn | 2631-5548 |
| language | English |
| last_indexed | 2024-04-11T04:56:58Z |
| publishDate | 2022-12-01 |
| publisher | European Wave and Tidal Energy Conference |
| record_format | Article |
| series | International Marine Energy Journal |
| spelling | doaj.art-d7bececc46484406ab76eaefad1b3b512022-12-26T13:05:15ZengEuropean Wave and Tidal Energy ConferenceInternational Marine Energy Journal2631-55482022-12-015310.36688/imej.5.239-247Misled by Betz and unsteady flowPeter F. Pelz0Jan Lemmer1Christian B. Schmitz2Chair of Fluid Systems, Technische Universität DarmstadtChair of Fluid Systems, Technische Universität DarmstadtIndustrial Science GmbH, Darmstadt A turbine array is an adjustable flow resistance R placed in a tidal channel. Ideally, it is designed and operated to maximise energy yield. Garrett & Cummins (2005), using optimal control theory applied to the RCelement channel (R) and basin (C), showed: the energy extraction from the flow PT + PD is maximised when the flow rate is slowed down by a factor of 1/√3. This result is independent of the ratio of the extracted mechanical power PT to the total power extraction including the power loss PD due to the mixing of the bypass flows within the turbine field. The optimisation task for turbine arrays is maximising PT. This objective raises two questions: ”What is the maximum power PT that can be extracted, and what is the optimal design (size, topology) and operation to achieve this output?” When addressing them, the literature still uses the Betz ‘limit’ as a reference. The work presented highlights two major problems. First, the Betz ’limit’ is not a constant upper bound for open channel flow. This problem has been discussed and solved by the first author (2011, 2020). Second and more importantly, the presented paper points out the misconception under which several research studies referred to array topologies as ‘optimal’ with regard to design and operation. Hereby, the presented paper contributes to the advancement of tidal power on an axiomatic basis. The misleading by Betz and overvaluing of transient effects is made transparent in a scientific discourse. https://marineenergyjournal.org/imej/article/view/103Betz limitblockagecoefficient of performanceoptimisationquasi-steady flowtidal array |
| spellingShingle | Peter F. Pelz Jan Lemmer Christian B. Schmitz Misled by Betz and unsteady flow International Marine Energy Journal Betz limit blockage coefficient of performance optimisation quasi-steady flow tidal array |
| title | Misled by Betz and unsteady flow |
| title_full | Misled by Betz and unsteady flow |
| title_fullStr | Misled by Betz and unsteady flow |
| title_full_unstemmed | Misled by Betz and unsteady flow |
| title_short | Misled by Betz and unsteady flow |
| title_sort | misled by betz and unsteady flow |
| topic | Betz limit blockage coefficient of performance optimisation quasi-steady flow tidal array |
| url | https://marineenergyjournal.org/imej/article/view/103 |
| work_keys_str_mv | AT peterfpelz misledbybetzandunsteadyflow AT janlemmer misledbybetzandunsteadyflow AT christianbschmitz misledbybetzandunsteadyflow |