A revisitation of White-Metzner viscoelastic fluids

The famous White-Metzner (WM) constitutive equation expresses a relatively simple nonlinear viscoelastic fluid of polymer melts. However, such a differential stress model, substantial with strong hyperbolic and singular problems, has hitherto always obtained unsatisfactory simulations of corner vortex in a typical contraction flow, especially for high Weissenberg numbers. A modified WM model useful for viscoelastic fluid computations is, therefore, proposed herein. As a validation, this model primarily fits the first normal stress difference for characterizing a fluid's elasticity, as well as shear viscosity and extensional viscosity. It is significant to discuss the vortex formation and growth, with the predicted vortex sizes in good agreement with the experimental data.