Asymptotic Representation of Vorticity and Dissipation Energy in the Flux Problem for the Navier–Stokes Equations in Curved Pipes

Asymptotic Representation of Vorticity and Dissipation Energy in the Flux Problem for the Navier–Stokes Equations in Curved Pipes Full article

Journal

Axioms
ISSN: 2075-1680

Output data

Year: 2024, Volume: 13, Number: 1, Article number : 65, Pages count : 18 DOI: 10.3390/axioms13010065

Tags

curved tube; vorticity; energy dissipation; curvature; torsion; viscous fluid

Authors

Chupakhin Alexander ^1,2 , Mamontov Alexander ^3,2 , Vasyutkin Sergey ²

Affiliations

1	Department of Mathematics and Mechanics, Novosibirsk State University, Pirogova Str. 2, Novosibirsk 630090, Russia
2	Lavrentyev Institute of Hydrodynamics SB RAS, Lavrentyev Pr. 15, Novosibirsk 630090, Russia
3	Basic Studies Department, Siberian State University of Telecommunications and Information Science, Kirova Str. 86, Novosibirsk 630102, Russia

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.

Chupakhin A. , Mamontov A. , Vasyutkin S.
Asymptotic Representation of Vorticity and Dissipation Energy in the Flux Problem for the Navier–Stokes Equations in Curved Pipes
Axioms. 2024. V.13. N1. 65 :1-18. DOI: 10.3390/axioms13010065 WOS РИНЦ OpenAlex

Submitted:	Dec 1, 2023
Accepted:	Jan 16, 2024
Published print:	Jan 19, 2024

Web of science:	WOS:001149059500001
Elibrary:	60425363
OpenAlex:	W4391035195

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