A family of vortex rings and a variational application to potential flows around three-dimensional bodies
Autor(a) principal: | |
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Data de Publicação: | 2008 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online) |
Texto Completo: | http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1678-58782008000200004 |
Resumo: | A variational formulation and solution of general three-dimensional potential flows gave rise to the construction of a special family of trial functions. This family is composed by circular-sector vortex rings, here named α-rings, i.e., rings that are positioned on the border of a circular sector with aperture angle α. An explicit formula for the velocity potential describing the α-rings family is here derived. A particular case is the well-known circular vortex-ring. The formula is given in terms of a uniformly valid series involving trigonometric and Hypergeometric functions. Results concerning the complete circular ring are compared to the well-known solution given, in closed form, in terms of Bessel functions, validating the present formula. Convergence is discussed. Graphical examples are shown for various rings of different sector angles. As an elementary application, the steady potential flow around three-dimensional bodies in unbounded fluid is formulated and solved under the variational approach. The variational method is fully validated through the sphere problem and for a family of spheroids. Examples concerning either translatory or rotatory motion around a transversal axis are presented for the spheroid family. |
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Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online) |
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A family of vortex rings and a variational application to potential flows around three-dimensional bodiespotential flowsector vortex-ringsvariational methodthree-dimensional bodiesA variational formulation and solution of general three-dimensional potential flows gave rise to the construction of a special family of trial functions. This family is composed by circular-sector vortex rings, here named α-rings, i.e., rings that are positioned on the border of a circular sector with aperture angle α. An explicit formula for the velocity potential describing the α-rings family is here derived. A particular case is the well-known circular vortex-ring. The formula is given in terms of a uniformly valid series involving trigonometric and Hypergeometric functions. Results concerning the complete circular ring are compared to the well-known solution given, in closed form, in terms of Bessel functions, validating the present formula. Convergence is discussed. Graphical examples are shown for various rings of different sector angles. As an elementary application, the steady potential flow around three-dimensional bodies in unbounded fluid is formulated and solved under the variational approach. The variational method is fully validated through the sphere problem and for a family of spheroids. Examples concerning either translatory or rotatory motion around a transversal axis are presented for the spheroid family.Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM2008-06-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S1678-58782008000200004Journal of the Brazilian Society of Mechanical Sciences and Engineering v.30 n.2 2008reponame:Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online)instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)instacron:ABCM10.1590/S1678-58782008000200004info:eu-repo/semantics/openAccessPesce,Celso P.Simos,Alexandre N.eng2008-07-10T00:00:00Zoai:scielo:S1678-58782008000200004Revistahttps://www.scielo.br/j/jbsmse/https://old.scielo.br/oai/scielo-oai.php||abcm@abcm.org.br1806-36911678-5878opendoar:2008-07-10T00:00Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM)false |
dc.title.none.fl_str_mv |
A family of vortex rings and a variational application to potential flows around three-dimensional bodies |
title |
A family of vortex rings and a variational application to potential flows around three-dimensional bodies |
spellingShingle |
A family of vortex rings and a variational application to potential flows around three-dimensional bodies Pesce,Celso P. potential flow sector vortex-rings variational method three-dimensional bodies |
title_short |
A family of vortex rings and a variational application to potential flows around three-dimensional bodies |
title_full |
A family of vortex rings and a variational application to potential flows around three-dimensional bodies |
title_fullStr |
A family of vortex rings and a variational application to potential flows around three-dimensional bodies |
title_full_unstemmed |
A family of vortex rings and a variational application to potential flows around three-dimensional bodies |
title_sort |
A family of vortex rings and a variational application to potential flows around three-dimensional bodies |
author |
Pesce,Celso P. |
author_facet |
Pesce,Celso P. Simos,Alexandre N. |
author_role |
author |
author2 |
Simos,Alexandre N. |
author2_role |
author |
dc.contributor.author.fl_str_mv |
Pesce,Celso P. Simos,Alexandre N. |
dc.subject.por.fl_str_mv |
potential flow sector vortex-rings variational method three-dimensional bodies |
topic |
potential flow sector vortex-rings variational method three-dimensional bodies |
description |
A variational formulation and solution of general three-dimensional potential flows gave rise to the construction of a special family of trial functions. This family is composed by circular-sector vortex rings, here named α-rings, i.e., rings that are positioned on the border of a circular sector with aperture angle α. An explicit formula for the velocity potential describing the α-rings family is here derived. A particular case is the well-known circular vortex-ring. The formula is given in terms of a uniformly valid series involving trigonometric and Hypergeometric functions. Results concerning the complete circular ring are compared to the well-known solution given, in closed form, in terms of Bessel functions, validating the present formula. Convergence is discussed. Graphical examples are shown for various rings of different sector angles. As an elementary application, the steady potential flow around three-dimensional bodies in unbounded fluid is formulated and solved under the variational approach. The variational method is fully validated through the sphere problem and for a family of spheroids. Examples concerning either translatory or rotatory motion around a transversal axis are presented for the spheroid family. |
publishDate |
2008 |
dc.date.none.fl_str_mv |
2008-06-01 |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1678-58782008000200004 |
url |
http://old.scielo.br/scielo.php?script=sci_arttext&pid=S1678-58782008000200004 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
10.1590/S1678-58782008000200004 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
text/html |
dc.publisher.none.fl_str_mv |
Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM |
publisher.none.fl_str_mv |
Associação Brasileira de Engenharia e Ciências Mecânicas - ABCM |
dc.source.none.fl_str_mv |
Journal of the Brazilian Society of Mechanical Sciences and Engineering v.30 n.2 2008 reponame:Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online) instname:Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM) instacron:ABCM |
instname_str |
Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM) |
instacron_str |
ABCM |
institution |
ABCM |
reponame_str |
Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online) |
collection |
Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online) |
repository.name.fl_str_mv |
Journal of the Brazilian Society of Mechanical Sciences and Engineering (Online) - Associação Brasileira de Engenharia e Ciências Mecânicas (ABCM) |
repository.mail.fl_str_mv |
||abcm@abcm.org.br |
_version_ |
1754734681017810944 |