Exact and limiting solutions of fluid flow for axially oscillating cylindrical pipe and annulus

The Navier–Stokes equations have been solved to derive the expressions of the velocity distributions for two cases: (1) oscillatory flows inside and outside of an axially oscillating cylindrical pipe, and (2) oscillatory flow inside an axially oscillating cylindrical annulus. In both the cases, in a...

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Bibliographic Details
Published in:SN applied sciences 2021-03, Vol.3 (3), p.339, Article 339
Main Authors: Sarkar, U. K., Biswas, Nirmalendu
Format: Article
Language:English
Subjects:
Annuli
Applied and Technical Physics
Chemistry/Food Science
Earth Sciences
Engineering
Engineering: Recent Problems in Fluid Mechanics
Environment
Fluid flow
Materials Science
Non-Newtonian fluids
Oscillating flow
Partial differential equations
Pipes
Research Article
Velocity
Velocity distribution
Viscosity
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Summary:The Navier–Stokes equations have been solved to derive the expressions of the velocity distributions for two cases: (1) oscillatory flows inside and outside of an axially oscillating cylindrical pipe, and (2) oscillatory flow inside an axially oscillating cylindrical annulus. In both the cases, in addition to the exact expressions for the velocity profiles, particular emphasis has been given for the determination of approximate velocity distributions for the high frequency and low frequency or quasi-static limits. It is shown that, for sufficiently large value of an appropriate frequency parameter, the velocity distribution inside the axially or longitudinally oscillating cylindrical annulus can be approximated as a superposition of the velocity distribution inside an axially oscillating cylindrical pipe of radius R ¯ o and the velocity distribution outside an axially oscillating cylindrical pipe of radius R ¯ i , where R ¯ i and R ¯ o are the inner and outer radii of the axially oscillating annulus, respectively.
ISSN:2523-3963
2523-3971
DOI:10.1007/s42452-021-04192-5