Bifurcation structure of a fluid flow in a helical square duct

The incompressible viscous fully developed steady now through a helical duct of square crosssection under various flow conditions has been studied numerically. The now structure for helical duct is examined, which depends on various Dean number Dn=√2k'a3/μvG, dimensionless curvature Κ' , dimensionless torsion τ and aspect ratio γ=b/a , where a is the half width and b is the half height of the cross-section, μ lhe viscosity, v the kinematic viscosity and G the constant pressure gradient along the axial direction. Attention-grabbing flow behaviors have been observed in this investigation. One of the most important characteristics of the flow is the bifurcation structure. Many bifurcation areas have been found in the solution curve in case of curved duct and only one bifurcation area has been found in case of helical duct Multiple pair of vortices have been found in the bifurcation areas. The axial flow is shifted more quickly towards the outer wall of the crosssection for high Dean numbers. Spectral method is used as a main tool for numerical calculations, where the Chebyshev polynomial, the collocation methods, the Arc-length methods and the Newton-Raphson method are also used as secondary tools.