Effect of contraction ratio upon viscoelastic flow in contractions: The axisymmetric case

A comprehensive numerical study of the effects of the contraction ratio upon viscoelastic flow through axisymmetric contractions was carried out. Six contraction ratios were examined (CR = 2, 4, 10, 20, 40 and 100) using the Oldroyd-B and Phan-Thien-Tanner (PTT) constitutive equations, under creeping-flow conditions and for a wide range of Deborah numbers (De). The results enabled the construction of vortex pattern maps, with CR and De as independent parameters, elucidating the role of these dimensionless groups in controlling vortex growth, vortex type (lip or corner vortices), and pressure-drop characteristics. The extensional parameter of the PTT model was also varied (ɛ = 0-0.5) and it was found that for small values of ɛ the Couette correction is a monotonic decreasing function of De, while for high ɛ values it is a monotonic increasing function.