Some Aspects of Bifurcation Structure of Laminar Flow in Curved Ducts

A bifurcation study is made of laminar flow in curved ducts. The problem is formulated in a curvilinear coordinate system, and the governing equations, after orthogonal mapping is applied, are solved numerically by an iterative finite-difference method. Many computer runs were made with various duct cross-sections ranging from a circle to a square, to learn the transition of bifurcation structure with this change in cross-section and to reconcile the differences between them. In addition, a simpler technique is proposed to generate symmetric four-cell solutions in a circular pipe and a means is put forward to stabilize four-vortex structures in a complete cross-section.