TY - JOUR

T1 - Asymptotic Representation of Vorticity and Dissipation Energy in the Flux Problem for the Navier–Stokes Equations in Curved Pipes

AU - Chupakhin, Alexander

AU - Mamontov, Alexander

AU - Vasyutkin, Sergey

N1 - This research was funded by the Ministry of Education of the Russian Federation through project 14.W03.31.0002 (mathematical formulation and conclusion) and by the Russian Science Foundation through project No 20-71-10034.

PY - 2024/2/2

Y1 - 2024/2/2

N2 - 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.

AB - 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.

UR - https://www.webofscience.com/wos/woscc/full-record/WOS:001149059500001

UR - https://www.mendeley.com/catalogue/f4fc87c4-1da8-3198-b8a4-aee5afe63f05/

U2 - 10.3390/axioms13010065

DO - 10.3390/axioms13010065

M3 - Article

VL - 13

SP - 65

JO - Axioms

JF - Axioms

SN - 2075-1680

IS - 1

ER -