Secondary flow structures in developing viscoelastic fluid flow through curved ducts with square cross section

The present paper numerically investigates viscoelastic fluid flow in the developing flow regime through both straight and 90-degree curve ducts. The aim is to investigate the effects of the first and second normal-stress differences (N1 and N2) as well as the curvature ratio (κ=D/R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\kappa = D/R$$\end{document}, where R and D are the curvature radius and channel side, respectively) and Reynolds number on the secondary flow patterns. Simulations were carried out in developing flow conditions in curved ducts using the finite volume method. The Reynolds numbers were 10, 20, 30, 40, 50, and 100, and the curvature ratios were 0.05, 0.066, 0.1, and 0.2. The Giesekus constitutive equation was utilized to model the non-linear rheological behavior of a 5.0 wt.% solution of polyisobutylene (PIB) in tetradecane (C14H30). The results reveal that a secondary flow with eight corner vortices is generated in a fully developed flow of viscoelastic fluid through a straight duct. This behavior is attributed to the difference in the second normal stress in the flow field. The results of the current study confirm that the second normal stress difference and change in the sign of N2 around the cross section’s corners trigger these corner vortices. Furthermore, the effects of the curvature ratio on the distributions of first and second normal-stress differences in the developing Dean flow were studied for the first time. The vorticity vector method was used for mixing-enhancement assessment. The results show that the intensity of secondary flows was significantly higher in viscoelastic fluid at all curvature ratios and at all considered Reynolds numbers than in Newtonian fluid flow.