Elementos finitos mixtos estabilizados para flujos viscoplásticos. Formulación y aplicaciones

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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