Numerical Simulation of Three-Dimensional Free Surface Flows Using the K-BKZ-PSM Integral Constitutive Equation

This work introduces a novel numerical method designed to address three-dimensional unsteady free surface flows incorporating integral viscoelastic constitutive equations, specifically the K-BKZ-PSM (Kaye-Bernstein, Kearsley, Zapas-Papanastasiou, Scriven, Macosko) model. The new proposed methodology employs a second-order finite difference approach along with the deformation fields method to solve the integral constitutive equation and the marker particle method (known as marker-and-cell) to accurately capture the evolution of the fluid's free surface. The newly developed numerical method has proven its effectiveness in handling complex fluid flow scenarios, including confined flows and extrudate swell simulations of Boger fluids. Furthermore, a new semi-analytical solution for velocity and stress fields is derived, considering fully developed flows of a K-BKZ-PSM fluid in a pipe.

Automated summary

This work introduces a novel numerical method for addressing three-dimensional unsteady free surface flows incorporating integral viscoelastic constitutive equations. The newly developed method has proven effective in handling complex fluid flow scenarios and a semi-analytical solution for the velocity and stress fields of the fluid in a pipe has also been derived.