Viscoelastic flow in a curved duct with rectangular cross section over a wide range of Dean number

Abstract

The incompressible flow of a Maxwell fluid through a curved duct with a rectangular cross section is numerically investigated over a wide range of the Dean number and curvature of the duct. Unsteady solutions, such as periodic, multi-periodic, and chaotic solutions, are obtained by using the spectral method. The combined effects of the large Dean number, Deborah number, and curvature on fluid flow behaviors are discussed in detail. It is found that increasing the Deborah number accelerates the occurrence of the four-cell structure of secondary flow no matter what the Dean number is. Periodic solutions are found to appear for the case of a smaller Dean number due to the presence of elasticity. The periodic solution turns to a chaotic solution if the Dean number is further increased. The chaotic solution is weak for a smaller Deborah number, while it becomes strong for a larger Deborah number. In addition, time evolution calculations at Dn = 300 show that the flow state changes significantly if the curvature δ is increased to be the critical value of the curvature δc = 0.26, while it remains almost unchanged for δ > δc or δ < δc.