Effective flow of a viscous liquid through a helical pipe

Eduard Marušić-Paloka; Igor Pažanin

doi:10.1016/j.crme.2004.09.005

Effective flow of a viscous liquid through a helical pipe
[Ecoulement effectif d'un liquide visqueux dans un tube hélicoïdal.]

Présenté par : Évariste Sanchez-Palencia

Eduard Marušić-Paloka ¹ ; Igor Pažanin ¹

¹ Department of Applied Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia

Comptes Rendus. Mécanique, Volume 332 (2004) no. 12, pp. 973-978.

Résumé
Abstract

On considère un écoulement dans un tube de section circulaire et de forme hélicoïdale paramétré par $r_{ɛ} (x_{1}) = (x_{1}, a \cos \frac{x_{1}}{ɛ}, a \sin \frac{x_{1}}{ɛ})$ , où ɛ est la distance entre deux tours de la spirale. Le rayon de la section du tube est lui aussi supposé égal à ɛ. A partir de l'écoulement microscopique décrit par le système de Navier–Stokes et en utilisant l'analyse asymptotique par rapport à ce petit paramètre ɛ on obtient l'écoulemment effectif décrit par une formule explicite de type Poiseuille associée à une petite déviation due à la géometrie du tube.

We study the flow of a viscous fluid through a pipe with helical shape parameterized with $r_{ɛ} (x_{1}) = (x_{1}, a \cos \frac{x_{1}}{ɛ}, a \sin \frac{x_{1}}{ɛ})$ , where the small parameter ɛ stands for the distance between two coils of the helix. The pipe has small cross-section of size ɛ. Using the asymptotic analysis of the microscopic flow described by the Navier–Stokes system, with respect to the small parameter ɛ that tends to zero, we find the effective fluid flow described by an explicit formula of the Poisseuile type including a small distorsion due to the particular geometry of the pipe.

Reçu le : 2004-07-21
Accepté le : 2004-09-21
Publié le : 2004-11-02

DOI : 10.1016/j.crme.2004.09.005

Keywords: Fluid mechanics, Helical pipe, Navier–Stokes equations
Mots-clés : Mécanique des fluides, Tube hélicoïdale, Équations de Navier–Stokes

Affiliations des auteurs :

Eduard Marušić-Paloka ¹ ; Igor Pažanin ¹

¹ Department of Applied Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia

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Eduard Marušić-Paloka; Igor Pažanin. Effective flow of a viscous liquid through a helical pipe. Comptes Rendus. Mécanique, Volume 332 (2004) no. 12, pp. 973-978. doi : 10.1016/j.crme.2004.09.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.09.005/

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Eduard Marušić-Paloka; Igor Pažanin Modelling of the porous medium flow with pressure-dependent viscosity and drag coefficient, Zeitschrift für Naturforschung A, Volume 78 (2023) no. 9, p. 823 | DOI:10.1515/zna-2023-0109
Eduard Marušić-Paloka; Igor Pažanin Effects of boundary roughness and inertia on the fluid flow through a corrugated pipe and the formula for the Darcy–Weisbach friction coefficient, International Journal of Engineering Science, Volume 152 (2020), p. 103293 | DOI:10.1016/j.ijengsci.2020.103293
Elena Miroshnikova Pressure-driven flow in a thin pipe with rough boundary, Zeitschrift für angewandte Mathematik und Physik, Volume 71 (2020) no. 4 | DOI:10.1007/s00033-020-01355-z
Eduard Marušić-Paloka; Igor Pažanin On the Viscous Flow Through a Long Pipe With Non-Constant Pressure Boundary Condition, Zeitschrift für Naturforschung A, Volume 73 (2018) no. 7, p. 639 | DOI:10.1515/zna-2018-0129
Eduard Marušić-Paloka; Igor Pažanin Non-isothermal fluid flow through a thin pipe with cooling, Applicable Analysis, Volume 88 (2009) no. 4, p. 495 | DOI:10.1080/00036810902889542
Igor Pažanin; Mehrdad Massoudi On the Solvability of a Problem of Stationary Fluid Flow in a Helical Pipe, Mathematical Problems in Engineering, Volume 2009 (2009) no. 1 | DOI:10.1155/2009/957061
Eduard Marušić-Paloka; Igor Pažanin Modelling of heat transfer in a laminar flow through a helical pipe, Mathematical and Computer Modelling, Volume 50 (2009) no. 11-12, p. 1571 | DOI:10.1016/j.mcm.2009.09.006
Subhashini Vashisth; Vimal Kumar; Krishna D. P. Nigam A Review on the Potential Applications of Curved Geometries in Process Industry, Industrial Engineering Chemistry Research, Volume 47 (2008) no. 10, p. 3291 | DOI:10.1021/ie701760h

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