| Issue |
MATEC Web Conf.
Volume 286, 2019
14th Congress of Mechanics (CMM2019)
|
|
|---|---|---|
| Article Number | 07004 | |
| Number of page(s) | 3 | |
| Section | Fluid Mechanics, Rheology, Modeling, Instabilities and Transition | |
| DOI | https://doi.org/10.1051/matecconf/201928607004 | |
| Published online | 14 August 2019 | |
Semi analytical method for calculating Dean's vortex in Torus of elliptical cross section
Laboratory of Mechanics, Faculty of Sciences Aïn Chock, B.P. 5366, Maarif, Hassan II University, Casablanca 20100, Morocco
* Corresponding authors : E-mail : s.ajgoun@outlook.fr
Based on the work of Dean (1927 and 1928) [1-2] and Cuming (1952) [3], the stationary flow of an incompressible Newtonian fluid through a curved pipe of uniform curvature and with elliptic cross section is studied. The Navier-Stokes equations are expressed in toroïdal coordinates system (s,r,θ). Following Dean’s approach, the governing equations for the fluid motion through a curved elliptical channel are solved by using an original semi analytical method for the resolution of a biharmonic equation. The main interest in this study is to test and validate in the case of an elliptical cross section the proposed semi-analytical method. The latter can then be used for other geometries for which explicit solutions are not available.
Key words: Toroïdal coordinates / Curvature / Curved pipes / Centrifugal force / Dean vortex.
© The Authors, published by EDP Sciences, 2019
This is an open access article distributed under the terms of the Creative Commons Attribution License 4.0 (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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