Asymptotic Representation of Vorticity and Dissipation Energy in the Flux Problem for the Navier–Stokes Equations in Curved Pipes
This study explores the problem of describing viscous fluid motion for Navier–Stokes equations in curved channels, which is important in applications like hemodynamics and pipeline transport. Channel curvature leads to vortex flows and closed vortex zones. Asymptotic models of the flux problem are u...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Online Access: | https://www.mdpi.com/2075-1680/13/1/65 |
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| author | Alexander Chupakhin Alexander Mamontov Sergey Vasyutkin |
| author_facet | Alexander Chupakhin Alexander Mamontov Sergey Vasyutkin |
| author_sort | Alexander Chupakhin |
| collection | DOAJ |
| description | This study explores the problem of describing viscous fluid motion for Navier–Stokes equations in curved channels, which is important in applications like hemodynamics and pipeline transport. Channel curvature leads to vortex flows and closed vortex zones. Asymptotic models of the flux problem are useful for describing viscous fluid motion in long pipes, thus considering geometric parameters like pipe diameter and characteristic length. This study provides a representation for the vorticity vector and energy dissipation in the flow problem for a curved channel, thereby determining the magnitude of vorticity and energy dissipation depending on the channel’s central line curvature and torsion. The accuracy of the asymptotic formulas are estimated in terms of small parameter powers. Numerical calculations for helical tubes demonstrate the effectiveness of the asymptotic formulas. |
| first_indexed | 2024-03-08T11:05:13Z |
| format | Article |
| id | doaj.art-5392d1cc692e4c33a65f6b16bd4a0d00 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-08T11:05:13Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-5392d1cc692e4c33a65f6b16bd4a0d002024-01-26T15:04:08ZengMDPI AGAxioms2075-16802024-01-011316510.3390/axioms13010065Asymptotic Representation of Vorticity and Dissipation Energy in the Flux Problem for the Navier–Stokes Equations in Curved PipesAlexander Chupakhin0Alexander Mamontov1Sergey Vasyutkin2Department of Mathematics and Mechanics, Novosibirsk State University, Pirogova Str. 2, Novosibirsk 630090, RussiaLavrentyev Institute of Hydrodynamics SB RAS, Lavrentyev Pr. 15, Novosibirsk 630090, RussiaLavrentyev Institute of Hydrodynamics SB RAS, Lavrentyev Pr. 15, Novosibirsk 630090, RussiaThis study explores the problem of describing viscous fluid motion for Navier–Stokes equations in curved channels, which is important in applications like hemodynamics and pipeline transport. Channel curvature leads to vortex flows and closed vortex zones. Asymptotic models of the flux problem are useful for describing viscous fluid motion in long pipes, thus considering geometric parameters like pipe diameter and characteristic length. This study provides a representation for the vorticity vector and energy dissipation in the flow problem for a curved channel, thereby determining the magnitude of vorticity and energy dissipation depending on the channel’s central line curvature and torsion. The accuracy of the asymptotic formulas are estimated in terms of small parameter powers. Numerical calculations for helical tubes demonstrate the effectiveness of the asymptotic formulas.https://www.mdpi.com/2075-1680/13/1/65curved tubevorticityenergy dissipationcurvaturetorsionviscous fluid |
| spellingShingle | Alexander Chupakhin Alexander Mamontov Sergey Vasyutkin Asymptotic Representation of Vorticity and Dissipation Energy in the Flux Problem for the Navier–Stokes Equations in Curved Pipes Axioms curved tube vorticity energy dissipation curvature torsion viscous fluid |
| title | Asymptotic Representation of Vorticity and Dissipation Energy in the Flux Problem for the Navier–Stokes Equations in Curved Pipes |
| title_full | Asymptotic Representation of Vorticity and Dissipation Energy in the Flux Problem for the Navier–Stokes Equations in Curved Pipes |
| title_fullStr | Asymptotic Representation of Vorticity and Dissipation Energy in the Flux Problem for the Navier–Stokes Equations in Curved Pipes |
| title_full_unstemmed | Asymptotic Representation of Vorticity and Dissipation Energy in the Flux Problem for the Navier–Stokes Equations in Curved Pipes |
| title_short | Asymptotic Representation of Vorticity and Dissipation Energy in the Flux Problem for the Navier–Stokes Equations in Curved Pipes |
| title_sort | asymptotic representation of vorticity and dissipation energy in the flux problem for the navier stokes equations in curved pipes |
| topic | curved tube vorticity energy dissipation curvature torsion viscous fluid |
| url | https://www.mdpi.com/2075-1680/13/1/65 |
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