The Viscoelastic Swirled Flow in the Confusor

A two-dimensional mathematical model for a steady viscoelastic laminar flow in a confusor was developed under the condition of swirled flow imposed at the inlet. Low density polyethylene was considered as a working fluid. Its behavior was described by a two-mode Giesekus model. The proposed mathematical model was tested by comparing it with some special cases presented in the literature. Additionally, we propose a system of equations to find the nonlinear parameters of the multimode Giesekus model (mobility factor) based on experimental measurement. The obtained numerical results showed that in a confusor with the contraction rate of 4:1, an increase in the swirl intensity at Wi < 5.1 affects only the circumferential velocity, while the axial and radial velocities remain constant. The distribution pattern of the first normal stress difference in the confusor is qualitatively similar to the one in a channel with abrupt contraction, i.e., as the viscoelastic fluid flows in the confusor, the value of N1 increases and reaches a maximum at the end of the confusor. Dimensionless damping coefficients of swirl are used to estimate the swirl intensity. The results show that the swirl intensity decreases exponentially.