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==Abstract==
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==Resumen==
  
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The objective of this work is to develop and evaluate a methodology for the solution
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El objetivo de este trabajo es formular y evaluar una metodología para la resolución de las ecuaciones de Navier-Stokes para los fluidos viscoplásticos de Bingham y de Herschel-Bulkley mediante el método de los elementos finitos mixtos estabilizados velocidad/presión. Se desarrolla una formulación teórica, se realiza la implementación computacional y se presentan y evalúan soluciones numéricas para estos fluidos viscoplásticos.
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of the Navier-Stokes equations for Bingham Herschel-Bulkley viscoplastic fluids using stabilized
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mixed velocity/pressure finite elements. The theoretical formulation is developed and
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implemented in a computer code. Numerical solutions for these viscoplastic flows are presented
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and assessed.
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Viscoplastic fluids are characterized by minimum shear stress called yield stress.
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Above this yield stress, the fluid is able to flow. Below this yield stress, the fluid behaves as a
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quasi-rigid body, with zero strain-rate.
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First, the Navier-Stokes equations for incompressible fluid and two immiscible fluids
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considering free surface are presented. A review of the Newtonian and non-Newtonian rheological
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models is included, with a detailed description of the viscoplastic models. The regularized
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viscoplastic models due to Papanastasiou are described. Double viscosity regularized
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models are proposed.
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The analytical solutions for parallel flows are deduced for Newtonian, Bingham, and
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Herschel-Bulkley, pseudoplastic and dilatant fluids.
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The discrete model is developed, and the Algebraic SubGrid Scale (ASGS) stabilization
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method, the Orthogonal Subgrid scale (OSS) method and the split orthogonal subscales
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method are introduced. For the cases of flows with a free surface, the simplified Eulerian
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method is employed, with the level set method to solve the motion of the free.
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A convergence study is performed to compare the ASGS and OSS stabilization
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methods in parallel flows with Bingham and Herschel-Bulkley fluids. The double viscosity
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regularized models show lower convergence error convergence than the regularized models
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used commonly.
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Numerical solutions developed in this work are applied to a broad set of benchmark
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problems. They can be divided into three groups: Bingham flows, Herschel-Bulkley flows
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and free surface flows.
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The solutions obtained validate the methodology proposed in this research and compare
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well with the analytical and numerical solutions, experimental and field data.
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The methodology proposed in this work provides a computational tool to study confined
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viscoplastic flows, common in industry, and debris viscoplastic flows with free surface.
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Los fluidos viscoplásticos se caracterizan por presentar una tensión de corte mínima, denominada tensión de fluencia. Por encima de esta tensión de corte mínima el fluido comienza a moverse. En caso de no superarse esta tensión de fluencia, el fluido se comporta como un cuerpo rígido o quasi-rígido, con velocidad de deformación nula.
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Se presentan inicialmente las ecuaciones de Navier-Stokes para un fluido y dos fluidos incompresibles e inmiscibles considerando superficie libre. Se presenta una revisión de los modelos reológicos Newtonianos y los modelos no-Newtonianos. Se hace una descripción detallada de los modelos viscoplásticos. Se describen los modelos viscoplásticos regularizados de Papanastasiou. Se proponen modelos regualarizados de doble viscosidad como alternativa a los comúnmente usados.
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Se deducen las soluciones analítica en flujos paralelos para el fluido Newtoniano, el fluido de Bingham, de Herschel-Bulkley, el fluido pseudoplástico y dilatante.
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Se desarrolla el modelo discreto, así como la formulación estabilizada con los métodos de subescalas algebraica (Algebraic subgrid scale, ASGS), de subescalas ortogonales (Orthogonal subgrid scale, OSS) y de subescalas ortogonales con la presión y el termino convectivo desacoplados, split-OSS. En el caso del fluido con superficie libre se presenta el método euleriano simplificado, el cual usa el método de superficie de nivel level set para resolver el movimiento de esta superficie libre.
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Se presenta un estudio de convergencia con los métodos de estabilización OSS y ASGS en los flujos paralelos de Bingham y de Herschel-Bulkley. Los modelos regularizados se doble viscosidad muestran menor error de convergencia que los usados regularmente.
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Se presentan las soluciones numéricas desarrolladas en este trabajo para un amplio conjunto de problemas benchmark. Pueden dividirse en tres grupos: flujos de Bingham, flujos de Herschel-Bulkley y flujos con superficie libre. Las soluciones obtenidas validan la metodología propuesta en este trabajo de investigación comparándose muy bien con las soluciones analíticas, numéricas, con resultados experimentales y datos de campo.
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La metodología propuesta en este trabajo proporciona una herramienta computacional para estudiar flujos viscoplásticos confinados, muy comunes en la industria, y los flujos detríticos viscoplásticos con superficie libre.
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<pdf>Media:Draft_Samper_187723667_2095_M142.pdf</pdf>
  
  
 
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Latest revision as of 10:06, 11 June 2019

Resumen

El objetivo de este trabajo es formular y evaluar una metodología para la resolución de las ecuaciones de Navier-Stokes para los fluidos viscoplásticos de Bingham y de Herschel-Bulkley mediante el método de los elementos finitos mixtos estabilizados velocidad/presión. Se desarrolla una formulación teórica, se realiza la implementación computacional y se presentan y evalúan soluciones numéricas para estos fluidos viscoplásticos.

Los fluidos viscoplásticos se caracterizan por presentar una tensión de corte mínima, denominada tensión de fluencia. Por encima de esta tensión de corte mínima el fluido comienza a moverse. En caso de no superarse esta tensión de fluencia, el fluido se comporta como un cuerpo rígido o quasi-rígido, con velocidad de deformación nula.

Se presentan inicialmente las ecuaciones de Navier-Stokes para un fluido y dos fluidos incompresibles e inmiscibles considerando superficie libre. Se presenta una revisión de los modelos reológicos Newtonianos y los modelos no-Newtonianos. Se hace una descripción detallada de los modelos viscoplásticos. Se describen los modelos viscoplásticos regularizados de Papanastasiou. Se proponen modelos regualarizados de doble viscosidad como alternativa a los comúnmente usados.

Se deducen las soluciones analítica en flujos paralelos para el fluido Newtoniano, el fluido de Bingham, de Herschel-Bulkley, el fluido pseudoplástico y dilatante.

Se desarrolla el modelo discreto, así como la formulación estabilizada con los métodos de subescalas algebraica (Algebraic subgrid scale, ASGS), de subescalas ortogonales (Orthogonal subgrid scale, OSS) y de subescalas ortogonales con la presión y el termino convectivo desacoplados, split-OSS. En el caso del fluido con superficie libre se presenta el método euleriano simplificado, el cual usa el método de superficie de nivel level set para resolver el movimiento de esta superficie libre.

Se presenta un estudio de convergencia con los métodos de estabilización OSS y ASGS en los flujos paralelos de Bingham y de Herschel-Bulkley. Los modelos regularizados se doble viscosidad muestran menor error de convergencia que los usados regularmente.

Se presentan las soluciones numéricas desarrolladas en este trabajo para un amplio conjunto de problemas benchmark. Pueden dividirse en tres grupos: flujos de Bingham, flujos de Herschel-Bulkley y flujos con superficie libre. Las soluciones obtenidas validan la metodología propuesta en este trabajo de investigación comparándose muy bien con las soluciones analíticas, numéricas, con resultados experimentales y datos de campo.

La metodología propuesta en este trabajo proporciona una herramienta computacional para estudiar flujos viscoplásticos confinados, muy comunes en la industria, y los flujos detríticos viscoplásticos con superficie libre.


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