Three-dimensional finite element analysis of viscoelastic flow

Abstract

<p>3-D numerical analysis of a viscoelastic flow is a necessity for better understanding of viscoelastic fluids and viscoelastic flow. It is important both from the scientific and technological points of view. Analysis of viscoelastic flow is a difficult task as it is associated with the problems arising from intrinsic complexity of the fluid. Progress in the area of 3-D analysis of viscoelastic flow has been further hindered by the increase in the size of the problem and number of variables. The outlet boundary condition for 3-D flow of a viscoelastic fluid is another problem. Segregated methods were used to solve the creeping flow formulation of the duct flow to save computer time and memory. A pressure correction method was selected and compared with the fully coupled method. A 3-D and 2.5-D segregated algorithm were proposed using the modified Phan-Thien Tanner constitutive equation and the EVSS method to decouple the calculation of stresses from the flow kinematics. Results from the 2.5-D algorithm were verified by comparison with the reported results from literature. Results for cases of high Wi were obtained and it was shown that for MPTT fluid, the intensity of the secondary flows becomes independent of Wi at high Wi. The effects of Re on the secondary flows were also studied and new patterns of secondary flows involving up to eight vortices in each quarter were reported. Results from the 2.5-D analysis were compared with the results of a 3-D algorithm in the analysis of the viscoelastic flow in straight ducts. Different cases of boundary conditions were studied and observations are reported. It is reported for the first time that a deviation from a fully developed solution occurs near the outlet. The problem of the destruction of the vortex pattern and the consequent increase in the primary flow velocity component were then analysed. It was established that the fully developed flow solution is a valid solution for the 3-D formulation of the problem and the problem arises from a combination of the decoupling of the stresses and imposing outlet boundary conditions. The 3-D algorithm was further evaluated for the cases of flow in complex geometries, using two test cases from the literature. One of the cases involved a converging duct and the other involved a 4:1 abrupt contraction. Results from 3-D and 2-D planar analysis were compared with the reported experimental results.</p>