Abstract
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 language | English |
|---|---|
| Pages (from-to) | 475-490 |
| Number of pages | 16 |
| Journal | Journal of Fluid Mechanics |
| Volume | 119 |
| DOIs | |
| State | Published - 1982 |
| Externally published | Yes |