Bifurcation and stability analysis of laminar flow in curved ducts

The development of viscous flow in a curved duct under variation of the axial pressure gradient q is studied. We confine ourselves to two‐dimensional solutions of the Dean problem. Bifurcation diagrams are calculated for rectangular and elliptic cross sections of the duct. We detect a new branch of asymmetric solutions for the case of a rectangular cross section. Furthermore we compute paths of quadratic turning points and symmetry breaking bifurcation points under variation of the aspect ratio γ (γ=0.8…1.5). The computed diagrams extend the results presented by other authors. We succeed in finding two origins of the Hopf bifurcation. Making use of the Cayley transformation, we determine the stability of stationary laminar solutions in the case of a quadratic cross section. All the calculations were performed on a parallel computer with 32×32 processors. Copyright © 2009 John Wiley & Sons, Ltd.