Numerical study of Dean vortices in developing Newtonian and viscoelastic flows through a curved duct of square cross-section

This study is devoted to the three-dimensional numerical simulation of developing secondary flows of Newtonian and viscoelastic fluids through a curved duct of square cross-section. The Phan-Thien–Tanner (PTT) model is used to represent viscoelastic effects. The numerical method uses a finite volume discretization with a staggered grid, and the equations are written in general orthogonal coordinates. The numerical simulations produced for 3 different Dean numbers (125, 137 and 150) show clearly the presence of two steady Dean cells and the upstream development of a four-cell pattern when the centrifugal forces become significant. The comparison between Newtonian and PTT flows shows that the transition from twin-cells to four-cells is anticipated for the viscoelastic fluid.