Some effects of flow expansion on the aerodynamics of horizontal-axis wind turbines

<p>The flow upwind of an energy-extracting horizontal-axis wind turbine expands as it approaches the rotor, and the expansion continues in the vorticity-bearing wake behind the rotor. The upwind expansion has long been known to influence the axial momentum equation through the axial component...

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Autores principales:	D. H. Wood, E. J. Limacher
Formato:	article
Lenguaje:	EN
Publicado:	Copernicus Publications 2021
Materias:	Renewable energy sources TJ807-830
Acceso en línea:	https://doaj.org/article/d683d1ec9b5246b1ae196df609c2efe4
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id	oai:doaj.org-article:d683d1ec9b5246b1ae196df609c2efe4
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spelling	oai:doaj.org-article:d683d1ec9b5246b1ae196df609c2efe42021-11-09T06:39:05ZSome effects of flow expansion on the aerodynamics of horizontal-axis wind turbines10.5194/wes-6-1413-20212366-74432366-7451https://doaj.org/article/d683d1ec9b5246b1ae196df609c2efe42021-11-01T00:00:00Zhttps://wes.copernicus.org/articles/6/1413/2021/wes-6-1413-2021.pdfhttps://doaj.org/toc/2366-7443https://doaj.org/toc/2366-7451<p>The flow upwind of an energy-extracting horizontal-axis wind turbine expands as it approaches the rotor, and the expansion continues in the vorticity-bearing wake behind the rotor. The upwind expansion has long been known to influence the axial momentum equation through the axial component of the pressure, although the extent of the influence has not been quantified. Starting with the impulse analysis of <span class="cit" id="xref_text.1"><a href="#bib1.bibx12">Limacher and Wood</a> (<a href="#bib1.bibx12">2020</a>)</span>, but making no further use of impulse techniques, we derive its exact expression when the rotor is a circumferentially uniform disc. This expression, which depends on the radial velocity and the axial induction factor, is added to the thrust equation containing the pressure on the back of the disc. Removing the pressure to obtain a practically useful equation shows the axial induction in the far wake is twice the value at the rotor only at high tip speed ratio and only if the relationship between vortex pitch and axial induction in non-expanding flow carries over to the expanding case. At high tip speed ratio, we assume that the expanding wake approaches the Joukowsky model of a hub vortex on the axis of rotation and tip vortices originating from each blade. The additional assumption that the helical tip vortices have constant pitch allows a semi-analytic treatment of their effect on the rotor flow. Expansion modifies the relation between the pitch and induced axial velocity so that the far-wake area and induction are significantly less than twice the values at the rotor. There is a moderate decrease – about 6 % – in the power production, and a similar size error occurs in the familiar axial momentum equation involving the axial velocity.</p>D. H. WoodE. J. LimacherCopernicus PublicationsarticleRenewable energy sourcesTJ807-830ENWind Energy Science, Vol 6, Pp 1413-1425 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Renewable energy sources TJ807-830
spellingShingle	Renewable energy sources TJ807-830 D. H. Wood E. J. Limacher Some effects of flow expansion on the aerodynamics of horizontal-axis wind turbines
description	<p>The flow upwind of an energy-extracting horizontal-axis wind turbine expands as it approaches the rotor, and the expansion continues in the vorticity-bearing wake behind the rotor. The upwind expansion has long been known to influence the axial momentum equation through the axial component of the pressure, although the extent of the influence has not been quantified. Starting with the impulse analysis of <span class="cit" id="xref_text.1"><a href="#bib1.bibx12">Limacher and Wood</a> (<a href="#bib1.bibx12">2020</a>)</span>, but making no further use of impulse techniques, we derive its exact expression when the rotor is a circumferentially uniform disc. This expression, which depends on the radial velocity and the axial induction factor, is added to the thrust equation containing the pressure on the back of the disc. Removing the pressure to obtain a practically useful equation shows the axial induction in the far wake is twice the value at the rotor only at high tip speed ratio and only if the relationship between vortex pitch and axial induction in non-expanding flow carries over to the expanding case. At high tip speed ratio, we assume that the expanding wake approaches the Joukowsky model of a hub vortex on the axis of rotation and tip vortices originating from each blade. The additional assumption that the helical tip vortices have constant pitch allows a semi-analytic treatment of their effect on the rotor flow. Expansion modifies the relation between the pitch and induced axial velocity so that the far-wake area and induction are significantly less than twice the values at the rotor. There is a moderate decrease – about 6 % – in the power production, and a similar size error occurs in the familiar axial momentum equation involving the axial velocity.</p>
format	article
author	D. H. Wood E. J. Limacher
author_facet	D. H. Wood E. J. Limacher
author_sort	D. H. Wood
title	Some effects of flow expansion on the aerodynamics of horizontal-axis wind turbines
title_short	Some effects of flow expansion on the aerodynamics of horizontal-axis wind turbines
title_full	Some effects of flow expansion on the aerodynamics of horizontal-axis wind turbines
title_fullStr	Some effects of flow expansion on the aerodynamics of horizontal-axis wind turbines
title_full_unstemmed	Some effects of flow expansion on the aerodynamics of horizontal-axis wind turbines
title_sort	some effects of flow expansion on the aerodynamics of horizontal-axis wind turbines
publisher	Copernicus Publications
publishDate	2021
url	https://doaj.org/article/d683d1ec9b5246b1ae196df609c2efe4
work_keys_str_mv	AT dhwood someeffectsofflowexpansionontheaerodynamicsofhorizontalaxiswindturbines AT ejlimacher someeffectsofflowexpansionontheaerodynamicsofhorizontalaxiswindturbines
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Some effects of flow expansion on the aerodynamics of horizontal-axis wind turbines

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