Revision as of 15:31, 24 October 2017

Abstract

The objective of this work is to develop and evaluate a methodology for the solution of the Navier-Stokes equations for Bingham Herschel-Bulkley viscoplastic fluids using stabilized mixed velocity/pressure finite elements. The theoretical formulation is developed and implemented in a computer code. Numerical solutions for these viscoplastic flows are presented and assessed.

Viscoplastic fluids are characterized by 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 and two immiscible fluids considering free surface are presented. A review of the Newtonian and non-Newtonian rheological models is included, with a detailed description of the viscoplastic models. The regularized viscoplastic models due to Papanastasiou are described. Double viscosity regularized models are proposed.

The analytical solutions for parallel flows are deduced for Newtonian, Bingham, and Herschel-Bulkley, pseudoplastic and dilatant fluids. 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. For the cases of flows with a free surface, the simplified Eulerian method is employed, with the level set method to solve the motion of the free.

A convergence study is performed to compare the ASGS and OSS stabilization methods in parallel flows with Bingham and Herschel-Bulkley fluids. The double viscosity regularized models show lower convergence error convergence than the regularized models used commonly.

Numerical solutions developed in this work are applied to a broad set of benchmark problems. They can be divided into three groups: Bingham flows, Herschel-Bulkley flows and free surface flows.

The solutions obtained validate the methodology proposed in this research and compare well with the analytical and numerical solutions, experimental and field data.

The methodology proposed in this work provides a computational tool to study confined viscoplastic flows, common in industry, and debris viscoplastic flows with free surface.

References

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