Envelope boundary conditions for the upper surface of two-dimensional canopy interacting with fluid flow

Akita, Shota; Okabayashi, Kie; Takeuchi, Shintaro

doi:https://doi.org/10.1007/s10404-024-02779-z

Envelope boundary conditions for the upper surface of two-dimensional canopy interacting with fluid flow

Akita, Shota; Okabayashi, Kie; Takeuchi, Shintaro

Microfluidics and Nanofluidics, 2025, 29(7)

Number of Access:279（2025-08-15 06:45 Counts）

Identifier to cite or link to this item: https://hdl.handle.net/11094/99612

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Title	Envelope boundary conditions for the upper surface of two-dimensional canopy interacting with fluid flow
Creator	CreatorName Akita, Shota
	NRID 1000040774162 1000040774162 researchmap permalink okakie okakie Scopus Author ID 35320309200 35320309200 ORCID 0000-0001-9682-647X 0000-0001-9682-647X CreatorName Okabayashi, Kie
	NRID 1000050372628 1000050372628 ORCID 0000-0003-0091-4542 0000-0003-0091-4542 researchmap permalink 50372628 50372628 Scopus Author ID 35474283000 35474283000 CreatorName Takeuchi, Shintaro
Subject	Canopy-tip boundary condition
	Coarse graining
	Envelope model
	Fluid structure interaction
Description	This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s10404-024-02779-z.
Abstract	Boundary conditions at the surface of a layer of flexible fibers (i.e. the canopy envelope) subjected to fluid flow are proposed for uniform and non-uniform motions of the fibers, where the fibers exhibit identical and individual motions, respectively, to understand the mechanisms of the swaying motion of the canopy. By assuming small deflections, the fibers are treated as rigid rods hinged to a flat wall and the effects of the hydrodynamic force on the fibers are expressed with the moment of fluid forces by averaging the Navier–Stokes equations. For the uniformly moving case, displacement of the envelope is represented by a mass-spring-damper system driven by the hydrodynamic force. As the non-uniformity of the canopy behavior enhances, the effects of the diffusion of fiber velocities and fluid inertia along the fiber stems play a more important role in the envelope displacement equation. Numerical simulations of fluid flow are conducted with the envelope displacement models as the boundary conditions at the canopy surface. The validity of the present models is assessed by comparison with the results of fluid–structure interaction (FSI) simulation, which directly solves the interaction between individual fibers and fluid by an immersed boundary method. With the envelope model for non-uniform displacement, the grid convergence of the numerical result is about a first order rate. The comparison of the terms in the envelope model for non-uniform displacement shows that diffusion of fiber velocities dominates the motion of fibers. The applicability of the model is assessed by varying the number density of the fibers.
Publisher	Springer Science and Business Media Deutschland GmbH
Source Title	Microfluidics and Nanofluidics
Volume (Issue)	29(7)
Date of Issued	2025-02-01
Language	English
Handle URL	https://hdl.handle.net/11094/99612
PISSN	16134982
eISSN	16134990
Relation.isVersionOf	DOI (Publisher Version) https://doi.org/10.1007/s10404-024-02779-z
Access Rights	embargoed access
CopyRight	© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.
CopyRight	The full-text file will be made open to the public on 1 February 2026 in accordance with the publisher's policy.
oaire:version	Accepted Manuscript
Category	学術雑誌論文 Journal Article

Resource Type	journal article
Local Type	Journal Article
DCTERMS.bibliographicCitation	Microfluidics and Nanofluidics. 2025, 29(7)
DC.title	Envelope boundary conditions for the upper surface of two-dimensional canopy interacting with fluid flow
DC.creator	Akita, Shota
	Okabayashi, Kie
	Takeuchi, Shintaro
DC.publisher	Springer Science and Business Media Deutschland GmbH
DC.language' scheme='DCTERMS.RFC1766	English
DCTERMS.issued' scheme='DCTERMS.W3CDTF	2025-02-01
DC.identifier	https://doi.org/10.1007/s10404-024-02779-z
DC.subject	Canopy-tip boundary condition
	Coarse graining
	Envelope model
	Fluid structure interaction
DC.description	This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s10404-024-02779-z.
DCTERMS.abstract	Boundary conditions at the surface of a layer of flexible fibers (i.e. the canopy envelope) subjected to fluid flow are proposed for uniform and non-uniform motions of the fibers, where the fibers exhibit identical and individual motions, respectively, to understand the mechanisms of the swaying motion of the canopy. By assuming small deflections, the fibers are treated as rigid rods hinged to a flat wall and the effects of the hydrodynamic force on the fibers are expressed with the moment of fluid forces by averaging the Navier–Stokes equations. For the uniformly moving case, displacement of the envelope is represented by a mass-spring-damper system driven by the hydrodynamic force. As the non-uniformity of the canopy behavior enhances, the effects of the diffusion of fiber velocities and fluid inertia along the fiber stems play a more important role in the envelope displacement equation. Numerical simulations of fluid flow are conducted with the envelope displacement models as the boundary conditions at the canopy surface. The validity of the present models is assessed by comparison with the results of fluid–structure interaction (FSI) simulation, which directly solves the interaction between individual fibers and fluid by an immersed boundary method. With the envelope model for non-uniform displacement, the grid convergence of the numerical result is about a first order rate. The comparison of the terms in the envelope model for non-uniform displacement shows that diffusion of fiber velocities dominates the motion of fibers. The applicability of the model is assessed by varying the number density of the fibers.
DC.rights	© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2024.
DC.rights	The full-text file will be made open to the public on 1 February 2026 in accordance with the publisher's policy.
DC.format	99612
citation_title	Envelope boundary conditions for the upper surface of two-dimensional canopy interacting with fluid flow
citation_author	Akita, Shota
	Okabayashi, Kie
	Takeuchi, Shintaro
citation_publisher	Springer Science and Business Media Deutschland GmbH
citation_language	English
citation_date	2025-02-01
citation_journal_title	Microfluidics and Nanofluidics
citation_volume	29
citation_issue	7
citation_doi	https://doi.org/10.1007/s10404-024-02779-z
citation_public_url	https://hdl.handle.net/11094/99612

Envelope boundary conditions for the upper surface of two-dimensional canopy interacting with fluid flow

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