article

Abstract

The interaction between the type of the constitutive equation and the degree of mesh refinement is studied in this article for a planar 4:1 contraction and the Finite Element Method. Five constitutive models are used: Phan Thien-Tanner, Johnson-Segalman, White-Metzner, Leonov and Upper Convected Maxwell models. A penalty Galerkin FEM was used to solve the system of the non-linear differential equations. The constitutive equations were fitted to the steady state shear viscosity and normal stress data for a polystyrene melt. In general it was found that the convergence limit based on the Deborah number, De, and the Weissenberg number, We, varied from model to model and from mesh to mesh. From a practical point of view it was observed that the wall shear stress in the downstream region should also be indicated at the point where convergence is lost, since this parameter reflects the throughput conditions. Because of the dependence of convergence on the combination of the mesh size and constitutive equation, predictions of the computations were compared with birefringence data obtained for the polystyrene melt. Refinement of the mesh led to better agreement between the predictions using the PTT model and flow birefringence. The oscillations became worse when the mesh was further refined. The values of the solutions oscillated around the experimental data, even when the numerical algorithm did not converge, while the streamlines remained smoother. Predictions for the existence of vortices, as well as for the entrance pressure loss varied from model to model. The UCM and WM models predicted negative values for the entrance pressure loss.

J.Num.Meth.Fl. 10, 373-400 (1990)

Comparison of Experimental Data with the Numerical Simulation of Planar Entry Flow: Role of the Constitutive Equation