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Article: Bifurcation and stability of forced convection in curved ducts of square cross-section

TitleBifurcation and stability of forced convection in curved ducts of square cross-section
Authors
Issue Date2004
PublisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/ijhmt
Citation
International Journal Of Heat And Mass Transfer, 2004, v. 47 n. 14-16, p. 2971-2987 How to Cite?
AbstractA numerical study is made on the fully developed bifurcation structure and stability of the forced convection in a curved duct of square cross-section (Dean problem). In addition to the extension of three known solution branches to the high Dean number region, three new asymmetric solution branches are found from three symmetry-breaking bifurcation points on the isolated symmetric branch. The flows on these new branches are either an asymmetric two-cell state or an asymmetric seven-cell structure. The linear stability of multiple solutions are conclusively determined by solving the eigenvalue system for all eigenvalues. Only two-cell flows on the primary symmetric branch and on the part of isolated symmetric branch are linearly stable. The symmetric six-cell flow is also linearly unstable to asymmetric disturbances although it was ascertained to be stable to symmetric disturbances in the literature. The linear stability is observed to change along some solution branch even without passing any bifurcation or limit points. Furthermore, dynamic responses of the multiple solutions to finite random disturbances are also examined by the direct transient computation. It is found that possible physically realizable fully developed flows evolve, as the Dean number increases, from a stable steady two-cell state at lower Dean number to a temporal periodic oscillation state, another stable steady two-cell state, a temporal intermittent oscillation, and a chaotic temporal oscillation. Among them, three temporal oscillation states have not been reported in the literature. A temporal periodic oscillation between symmetric/asymmetric two-cell flows and symmetric/asymmetric four-cell flows are found in the range where there are no stable steady fully developed solutions. The symmetry-breaking point on the primary solution branch is determined to be a sub-critical Hopf point by the transient computation. © 2004 Elsevier Ltd. All rights reserved.
Persistent Identifierhttp://hdl.handle.net/10722/75806
ISSN
2015 Impact Factor: 2.857
2015 SCImago Journal Rankings: 1.749
ISI Accession Number ID
References

 

DC FieldValueLanguage
dc.contributor.authorWang, Len_HK
dc.contributor.authorYang, Ten_HK
dc.date.accessioned2010-09-06T07:14:44Z-
dc.date.available2010-09-06T07:14:44Z-
dc.date.issued2004en_HK
dc.identifier.citationInternational Journal Of Heat And Mass Transfer, 2004, v. 47 n. 14-16, p. 2971-2987en_HK
dc.identifier.issn0017-9310en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75806-
dc.description.abstractA numerical study is made on the fully developed bifurcation structure and stability of the forced convection in a curved duct of square cross-section (Dean problem). In addition to the extension of three known solution branches to the high Dean number region, three new asymmetric solution branches are found from three symmetry-breaking bifurcation points on the isolated symmetric branch. The flows on these new branches are either an asymmetric two-cell state or an asymmetric seven-cell structure. The linear stability of multiple solutions are conclusively determined by solving the eigenvalue system for all eigenvalues. Only two-cell flows on the primary symmetric branch and on the part of isolated symmetric branch are linearly stable. The symmetric six-cell flow is also linearly unstable to asymmetric disturbances although it was ascertained to be stable to symmetric disturbances in the literature. The linear stability is observed to change along some solution branch even without passing any bifurcation or limit points. Furthermore, dynamic responses of the multiple solutions to finite random disturbances are also examined by the direct transient computation. It is found that possible physically realizable fully developed flows evolve, as the Dean number increases, from a stable steady two-cell state at lower Dean number to a temporal periodic oscillation state, another stable steady two-cell state, a temporal intermittent oscillation, and a chaotic temporal oscillation. Among them, three temporal oscillation states have not been reported in the literature. A temporal periodic oscillation between symmetric/asymmetric two-cell flows and symmetric/asymmetric four-cell flows are found in the range where there are no stable steady fully developed solutions. The symmetry-breaking point on the primary solution branch is determined to be a sub-critical Hopf point by the transient computation. © 2004 Elsevier Ltd. All rights reserved.en_HK
dc.languageengen_HK
dc.publisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/ijhmten_HK
dc.relation.ispartofInternational Journal of Heat and Mass Transferen_HK
dc.titleBifurcation and stability of forced convection in curved ducts of square cross-sectionen_HK
dc.typeArticleen_HK
dc.identifier.openurlhttp://library.hku.hk:4550/resserv?sid=HKU:IR&issn=0017-9310&volume=47&spage=2971&epage=2987&date=2004&atitle=Bifurcation+and+stability+of+forced+convection+in+curved+ducts+of+square+cross-sectionen_HK
dc.identifier.emailWang, L:lqwang@hkucc.hku.hken_HK
dc.identifier.authorityWang, L=rp00184en_HK
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.ijheatmasstransfer.2004.03.002en_HK
dc.identifier.scopuseid_2-s2.0-2442568668en_HK
dc.identifier.hkuros91451en_HK
dc.relation.referenceshttp://www.scopus.com/mlt/select.url?eid=2-s2.0-2442568668&selection=ref&src=s&origin=recordpageen_HK
dc.identifier.volume47en_HK
dc.identifier.issue14-16en_HK
dc.identifier.spage2971en_HK
dc.identifier.epage2987en_HK
dc.identifier.isiWOS:000221630600008-
dc.publisher.placeUnited Kingdomen_HK
dc.identifier.scopusauthoridWang, L=35235288500en_HK
dc.identifier.scopusauthoridYang, T=7404655973en_HK

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