Numerical study on secondary flows of viscoelastic fluids in straight ducts: Origin analysis and parametric effects

Numerical simulations were conducted on viscoelastic fluid flows in straight ducts with different cross sections, for which the origin of secondary flows and influences of material parameters and flow passage geometrical configuration were numerically investigated. The Giesekus constitutive model was chosen to describe the viscoelastic fluid with the second normal stress difference N₂, and solved by embedding UDF (User-defined Function) into the CFD (computational fluid dynamics) code FLUENT. The origin of such kind of secondary flow was theoretically studied from the perspective of the budget of vorticity energy for the first time. Sufficient and necessary condition for the existence of secondary flow was then developed in terms of N₂, the gradient of N₂ and cross-sectional geometry ϑ (i.e., generation term E_Ω). Moreover, helicity density was considered as an excellent indicator of secondary flow pattern. Effects of material properties (including anisotropic parameterα, solvent viscosity ratio β and relaxation time λ) and flow passage geometrical configuration (aspect ratio of cross sectionsr, the number of polygon sides n) on secondary flow strength and pattern were investigated with E_Ω. Finally, a universal variable σ_s was proposed to describe non-circularity of cross section, based on which the results for ducts with different cross sections can be normalized together.