Bifurcation in steady laminar flow through curved tubes

K. Nandakumar, Jacob H. Masliyah

Research output: Contribution to journalArticlepeer-review

107 Scopus citations


The occurrence of dual solutions in curved ducts is investigated through a numerical solution of the Navier-Stokes equations in a bipolar-toroidal co-ordinate system. With the shape of duct being the region formed by the natural co-ordinate surfaces, it was possible to alter the duct geometry gradually and preserve the prevailing form of the velocity field, in a manner suggested by Benjamin (1978). In addition to the Dean number Dn = Re/R½c, a geometrical parameter that defines the shape of the duct was also varied systematically to study the bifurcation of a two-vortex solution into a two- and four-vortex solution. Dual solutions have been found for all geometrical shapes investigated here. Of particular interest are the shapes of a full circle and a semicircle with a curved outer wall.

Original languageEnglish
Pages (from-to)475-490
Number of pages16
JournalJournal of Fluid Mechanics
StatePublished - 1982
Externally publishedYes


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