Semi analytical method for calculating Dean's vortex in Torus of elliptical cross section
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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.
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1985 ◽
Vol 40
(8)
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pp. 789-799
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2003 ◽
Vol 54
(6)
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pp. 1094-1100
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2019 ◽
Vol 234
(2)
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pp. 165-172
1998 ◽
Vol 08
(03)
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pp. 431-444
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