3D simulation of the hierarchical multi-mode molecular stress function constitutive model in an abrupt contraction flow

A recent development of the Molecular Stress Function constitutive model, the Hierarchical Multi-Mode Molecular Stress Function (HMMSF) model has been shown to fit a large range of rheometrical data with accuracy, for a large range of polymer melts. We develop a 3D simulation of the HMMSF model and compare it to experimental data for the flow of Lupolen 1840H LDPE through an abrupt 3D contraction flow. We believe this to be the first finite element implementation of the HMMSF model. It is shown that the model gives a striking agreement with experimental vortex opening angles, with very good agreement to full-field birefringence measurements, over a wide range of flow rates. A method to give fully-developed inlet boundary conditions is implemented (in place of using parabolic inlet boundary conditions), which gives a significantly improved match to birefringence measurements in the inlet area, and in low stress areas downstream from the inlet. Alternative constitutive model parameters are assessed following the principle that extensional rheometer data actually provides a 'lower bound' for peak extensional viscosity. It is shown that the model robustly maintains an accurate fit to vortex opening angle and full-field birefringence data, provided that both adjustable parameters are kept such that both shear and extensional data are well fitted.

Automated summary

This study develops a 3D simulation to compare the Hierarchical Multi-Mode Molecular Stress Function (HMMSF) model with experimental data, showing a good agreement between the model and the data. An improved boundary condition method is proposed to enhance the match with experimental results. In addition, the parameter setting of the constitutive model is assessed.