Elementos finitos mixtos estabilizados para flujos confinados de Bingham y de Herschel-Bulkley. Parte I: Formulación

Abstract

This work presents a methodology for the solution of the Navier-Stokes equations for Bingham and Herschel-Bulkley viscoplastic fluids using stabilized mixed velocity/pressure finite elements. The theoretical formulation is developed and implemented in a computer code.Viscoplastic fluids are characterized by a minimum shear stress called yield stress. Above this yield stress, the fluid is able to flow. Below this yield stress, the fluid behaves as a quasi-rigid body, with zero strain-rate.First, the Navier-Stokes equations for incompressible fluid are presented. A review of the viscoplastic rheological models is included, with a detailed description of these models. The regularized viscoplastic models due to Papanastasiou are described. Double viscosity regularized models are proposed as an alternative to the models commonly used.The discrete model is developed, and the Algebraic SubGrid Scale (ASGS) stabilization method, the Orthogonal Subgrid Scale (OSS) method and the split orthogonal subscales method are introduced.The methodology proposed in this work provides a computational tool to study confined viscoplastic flows, common in industry.