On the relationship between turbine thrust and near-wake velocity and vorticity
Vortical impulse theory is used to investigate the relationship between turbine thrust and the near-wake velocity and vorticity fields. Three different hypotheses regarding the near-wake structure allow the derivation of novel expressions for the thrust on a steadily rotating wind turbine, and these...
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Veröffentlicht in: | Journal of fluid mechanics 2022-10, Vol.949, Article A24 |
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description | Vortical impulse theory is used to investigate the relationship between turbine thrust and the near-wake velocity and vorticity fields. Three different hypotheses regarding the near-wake structure allow the derivation of novel expressions for the thrust on a steadily rotating wind turbine, and these are tested using stereoscopic particle-image velocimetry (PIV) data acquired just behind a rotor in a water channel. When one assumes that vortex lines and streamlines are aligned in a rotor-fixed frame of reference, one obtains a PIV-based thrust estimate that fails even to capture the trend of the directly measured thrust, and this failure is attributed to an implicit assumption that most of the generated thrust does useful work. When one neglects the axial gradients of radial velocity, the PIV-based thrust estimate captures the measured thrust trend, but underpredicts its magnitude by approximately $33\,\%$. The third and most promising physical proposition treats the trailing vortices as purely ‘rolling’ structures that exhibit zero-strain rate in their cores, with the corresponding thrust estimates in close agreement with direct thrust measurements. This best-performing expression appears as a correction to the classical thrust expression from momentum theory, possessing additional squared-velocity terms that can account for the high-thrust regime of turbine operation that is typically addressed empirically. |
doi_str_mv | 10.1017/jfm.2022.722 |
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Three different hypotheses regarding the near-wake structure allow the derivation of novel expressions for the thrust on a steadily rotating wind turbine, and these are tested using stereoscopic particle-image velocimetry (PIV) data acquired just behind a rotor in a water channel. When one assumes that vortex lines and streamlines are aligned in a rotor-fixed frame of reference, one obtains a PIV-based thrust estimate that fails even to capture the trend of the directly measured thrust, and this failure is attributed to an implicit assumption that most of the generated thrust does useful work. When one neglects the axial gradients of radial velocity, the PIV-based thrust estimate captures the measured thrust trend, but underpredicts its magnitude by approximately $33\,\%$. The third and most promising physical proposition treats the trailing vortices as purely ‘rolling’ structures that exhibit zero-strain rate in their cores, with the corresponding thrust estimates in close agreement with direct thrust measurements. This best-performing expression appears as a correction to the classical thrust expression from momentum theory, possessing additional squared-velocity terms that can account for the high-thrust regime of turbine operation that is typically addressed empirically.</description><identifier>ISSN: 0022-1120</identifier><identifier>EISSN: 1469-7645</identifier><identifier>DOI: 10.1017/jfm.2022.722</identifier><language>eng</language><publisher>Cambridge, UK: Cambridge University Press</publisher><subject>Aerodynamics ; Data acquisition ; Image acquisition ; JFM Papers ; Momentum ; Momentum theory ; Particle image velocimetry ; Radial velocity ; Rotors ; Strain rate ; Streamlines ; Thrust ; Trailing vortices ; Turbine engines ; Turbines ; Velocity ; Vorticity ; Wind power ; Wind turbines</subject><ispartof>Journal of fluid mechanics, 2022-10, Vol.949, Article A24</ispartof><rights>The Author(s), 2022. 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Fluid Mech</addtitle><description>Vortical impulse theory is used to investigate the relationship between turbine thrust and the near-wake velocity and vorticity fields. Three different hypotheses regarding the near-wake structure allow the derivation of novel expressions for the thrust on a steadily rotating wind turbine, and these are tested using stereoscopic particle-image velocimetry (PIV) data acquired just behind a rotor in a water channel. When one assumes that vortex lines and streamlines are aligned in a rotor-fixed frame of reference, one obtains a PIV-based thrust estimate that fails even to capture the trend of the directly measured thrust, and this failure is attributed to an implicit assumption that most of the generated thrust does useful work. When one neglects the axial gradients of radial velocity, the PIV-based thrust estimate captures the measured thrust trend, but underpredicts its magnitude by approximately $33\,\%$. The third and most promising physical proposition treats the trailing vortices as purely ‘rolling’ structures that exhibit zero-strain rate in their cores, with the corresponding thrust estimates in close agreement with direct thrust measurements. 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Ding, Liuyang ; Piqué, Alexander ; Smits, Alexander J. ; Hultmark, Marcus</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c302t-55bdc9aee8a7cf4011b164565529bee55700fb9b1e4528ce0a0c632cc77949c53</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Aerodynamics</topic><topic>Data acquisition</topic><topic>Image acquisition</topic><topic>JFM Papers</topic><topic>Momentum</topic><topic>Momentum theory</topic><topic>Particle image velocimetry</topic><topic>Radial velocity</topic><topic>Rotors</topic><topic>Strain rate</topic><topic>Streamlines</topic><topic>Thrust</topic><topic>Trailing vortices</topic><topic>Turbine engines</topic><topic>Turbines</topic><topic>Velocity</topic><topic>Vorticity</topic><topic>Wind power</topic><topic>Wind turbines</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Limacher, Eric J.</creatorcontrib><creatorcontrib>Ding, Liuyang</creatorcontrib><creatorcontrib>Piqué, Alexander</creatorcontrib><creatorcontrib>Smits, Alexander J.</creatorcontrib><creatorcontrib>Hultmark, Marcus</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Central (Corporate)</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Water Resources Abstracts</collection><collection>ProQuest Central (purchase pre-March 2016)</collection><collection>Science Database (Alumni Edition)</collection><collection>Technology Research Database</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni) (purchase pre-March 2016)</collection><collection>Research Library (Alumni Edition)</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>Natural Science Collection</collection><collection>Earth, Atmospheric & Aquatic Science Collection</collection><collection>Environmental Sciences and Pollution Management</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>ASFA: Aquatic Sciences and Fisheries Abstracts</collection><collection>Engineering Research Database</collection><collection>ProQuest Central Student</collection><collection>Research Library Prep</collection><collection>Aerospace Database</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) 2: Ocean Technology, Policy & Non-Living Resources</collection><collection>SciTech Premium Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Aquatic Science & Fisheries Abstracts (ASFA) Professional</collection><collection>ProQuest Engineering Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Research Library</collection><collection>Science Database</collection><collection>Engineering Database</collection><collection>Research Library (Corporate)</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Earth, Atmospheric & Aquatic Science Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering Collection</collection><collection>ProQuest Central Basic</collection><collection>DELNET Engineering & Technology Collection</collection><jtitle>Journal of fluid mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Limacher, Eric J.</au><au>Ding, Liuyang</au><au>Piqué, Alexander</au><au>Smits, Alexander J.</au><au>Hultmark, Marcus</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>On the relationship between turbine thrust and near-wake velocity and vorticity</atitle><jtitle>Journal of fluid mechanics</jtitle><addtitle>J. Fluid Mech</addtitle><date>2022-10-25</date><risdate>2022</risdate><volume>949</volume><artnum>A24</artnum><issn>0022-1120</issn><eissn>1469-7645</eissn><abstract>Vortical impulse theory is used to investigate the relationship between turbine thrust and the near-wake velocity and vorticity fields. Three different hypotheses regarding the near-wake structure allow the derivation of novel expressions for the thrust on a steadily rotating wind turbine, and these are tested using stereoscopic particle-image velocimetry (PIV) data acquired just behind a rotor in a water channel. When one assumes that vortex lines and streamlines are aligned in a rotor-fixed frame of reference, one obtains a PIV-based thrust estimate that fails even to capture the trend of the directly measured thrust, and this failure is attributed to an implicit assumption that most of the generated thrust does useful work. When one neglects the axial gradients of radial velocity, the PIV-based thrust estimate captures the measured thrust trend, but underpredicts its magnitude by approximately $33\,\%$. The third and most promising physical proposition treats the trailing vortices as purely ‘rolling’ structures that exhibit zero-strain rate in their cores, with the corresponding thrust estimates in close agreement with direct thrust measurements. This best-performing expression appears as a correction to the classical thrust expression from momentum theory, possessing additional squared-velocity terms that can account for the high-thrust regime of turbine operation that is typically addressed empirically.</abstract><cop>Cambridge, UK</cop><pub>Cambridge University Press</pub><doi>10.1017/jfm.2022.722</doi><tpages>28</tpages><orcidid>https://orcid.org/0000-0003-4282-3198</orcidid><orcidid>https://orcid.org/0000-0002-1391-6208</orcidid><orcidid>https://orcid.org/0000-0002-3883-8648</orcidid><orcidid>https://orcid.org/0000-0002-3046-2551</orcidid></addata></record> |
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subjects | Aerodynamics Data acquisition Image acquisition JFM Papers Momentum Momentum theory Particle image velocimetry Radial velocity Rotors Strain rate Streamlines Thrust Trailing vortices Turbine engines Turbines Velocity Vorticity Wind power Wind turbines |
title | On the relationship between turbine thrust and near-wake velocity and vorticity |
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