Bifurcation Phenomena of Secondary Flows in Curved Duct of Square Cross-Section

Abstract

Based on the flow model and its mathematical description in curvilinear coordinates, the steady and fully developed laminar flow in the curved pipe of square cross-section was simulated by the Galerkin method. The results show that the eye points of the secondary flow vortex at low Reynolds numbers almost locate at the position of 0.457 on the vertical axis, the axial velocity maximum shifts inward or outward when the pipe curvature parameter and flow conditions change. Furthermore the bifurcation flow is studied to draw the bifurcation state diagram, and the Reynolds number corresponding to the bifurcation point of the four-vortex solution is accurately equal to 300.1.