A control volume approach for integral viscoelastic models and its application to contraction flow of polymer melts

Abstract

A numerical scheme based on the control volume discretization is developed for integral-type viscoelastic models. The strain history tracking can be done more efficiently using finite volumes with staggered grids than using finite elements. The Semi-Implicit Method for Pressure Linked Equations (SIMPLE) with alternating direction implicit (ADI) iterations is employed to solve the momentum equations on staggered grids, with the non-Newtonian stress contribution integrated upstream along stream-lines and treated as a source term in each control volume. The new method gave better computing stability and solution smoothness than its finite element counterpart. The new scheme is used to simulate the 5.75:1 abrupt circular contraction flow of a low-density polyethylene (LDPE) melt with KBKZ model, for which experimental data on recirculation vortex growth with elasticity are available in the literature. A comparison of the numerical results with experimental data on the opening angle of vortex shows good agreement and some improvement over previous finite element computations. A mesh refinement study with three meshes demonstrated good mesh convergence. The present control volume scheme is found to be more than twice as fast as its finite element counterpart in dealing with integral viscoelastic models, at least in simple geometries.