Numerical simulation of viscoelastic Dean vortices in a curved duct

The purpose of the present study is to proceed to three-dimensional numerical simulations of viscoelastic Dean flows of a modified Phan-Thien–Tanner fluid (S.-C. Xue, N. Phan-Thien, R.I. Tanner, Numerical study of secondary flows of viscoelastic fluid in straight pipes by an implicit finite volume method, J. Non-Newtonian Fluid Mech. 59 (1995) 191–213) through a U-curved channel with a square section. The conservation and constitutive equations written in general orthogonal coordinates are solved on a staggered grid with a finite volume method.Dean flows are explored for the range of Reynolds number 485≤Re≤580485≤Re≤580 (corresponding to Dean number 125≤Dn≤150125≤Dn≤150), for which steady solutions were found. The flow regime considered corresponds to low elasticity number E   in the range 2×10−42×10−4 to 2×10−32×10−3. The presence of two steady Dean cells and the development of two additional vortices are demonstrated. In particular, we examine the influence of elasticity of the extensional parameter of the viscoelastic fluid, and of shear-thinning. We find that these three properties increase the size and intensity of the secondary vortices present in the four-cell structure flows.