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 N-2, 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 N-2, the gradient of N-2 and cross-sectional geometry theta (i.e., generation term E-Omega). Moreover, helicity density was considered as an excellent indicator of secondary flow pattern. Effects of material properties (including anisotropic parameter alpha, solvent viscosity ratio beta and relaxation time lambda) and flow passage geometrical configuration (aspect ratio of cross sections gamma, the number of polygon sides n) on secondary flow strength and pattern were investigated with E-Omega. Finally, a universal variable sigma(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. (C) 2017 Elsevier Ltd. All rights reserved.