Fogliatto, Ezequiel O. (2022) Simulación numérica del fenómeno de ebullición empleando el método de lattice Boltzmann / Numerical simulation of boiling using the lattice Boltzmann method. Tesis Doctoral en Ciencias de la Ingeniería, Universidad Nacional de Cuyo, Instituto Balseiro.
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Resumen en español
En la presente tesis se analiza la expansión de la técnica de lattice Boltzmann (LB) hacia la simulación del transporte de energía en fujos multifásicos, buscando una alternativa para resolver computacionalmente el complejo fenómeno de ebullición. Desde un punto de vista formal LB puede interpretarse como un camino para encontrar la solución de una ecuación de Boltzmann, donde en lugar de discretizar directamente las ecuaciones de conservación macroscópicas, el método propone transportar una función de distribución en una grilla regular. A través de técnicas de expansión multiescala, como el análisis de Chapman-Enskog, es posible verificar que la grilla espacial, las velocidades discretas del espacio de fases, y el operador de colisión, pueden ser combinados adecuadamente para obtener la solución de las ecuaciones de conservación típicas de la mecánica de fuidos. La aplicación de esta metodología produce, en general, algoritmos de sencilla implementación, con una elevada capacidad de paralelización y una eficiencia computacional significativa. El camino propuesto en este trabajo para abordar la simulación de ebullición con LB sigue una metodología incremental. En primer lugar se comienza con la evaluación de modelos multifásicos isotérmicos existentes, que consiste en el desarrollo y aplicación de un problema de prueba, con solución analítica, que permite evaluar la capacidad de un modelo LB para representar el equilibrio termodinámico de un sistema líquido-vapor bajo diferentes condiciones hidrodinámicas. A través de esta solución de referencia es posible cuantificar el efecto de la fuerza gravitacional en la existencia y posición de una interfase en equilibrio, junto con la verificación de la reproducción adecuada de densidades de coexistencia y la resolución espacial del método analizado. Los modelos hidrodinámicos son expandidos con nuevas propuestas para resolver el transporte de energía en dos y tres dimensiones. Para ello, en esta tesis se adicionan ecuaciones de LB que permiten recuperar adecuadamente una ecuación de energía termodinámicamente consistente con la formulación pseudopotencial. Típicamente, el uso de esquemas LB tradicionales en la resolución de ecuaciones de advección-difusión escalares produce la recuperación de términos macroscópicos no deseados. En los modelos propuestos en este trabajo se demuestra que estos efectos pueden evitarse mediante la utilización de una distribución de equilibrio definida explícitamente en el espacio de momentos, de una matriz de relajación con coeficientes no nulos fuera de la diagonal principal, y de un término fuente implícito. Los nuevos modelos son validados mediante la simulación de un conjunto de experimentos numéricos con solución analítica, y demuestran una excelente capacidad para reproducir la creación y movimiento de las interfases. Por otro lado, son utilizados para demostrar cuantitativamente que aspectos tradicionales de la técnica, como consistencia e independencia de grilla, pueden evaluarse mediante una adimensionalización adecuada de las simulaciones empleando unidades reducidas. Las capacidades de los nuevos modelos y procedimientos para simular eficientemente problemas de ebullición son finalmente evaluadas mediante la reproducción de un experimento de generación de burbujas individuales sobre una superficie calefaccionada. En particular, los modelos LB de la familia pseudopotencial reproducen el comportamiento de fluidos con propiedades macroscópicas que no pueden fijarse con exactitud antes de la simulación del experimento, y cuyos valores deben determinarse mediante experimentos numéricos adicionales. La validación propuesta en esta tesis no sólo incluye la comparación de las simulaciones con los resultados experimentales, sino que incorpora un análisis detallado de la construcción del modelo computacional. En el caso bajo análisis, se evidencia una excelente reproducción del proceso de formación, crecimiento y desprendimiento de las burbujas. Los modelos introducidos en esta tesis se encuentran implementados en una herramienta numérica desarrollada en C++ que permite efectuar las simulaciones en arquitecturas de alto desempeño. El diseño de las bibliotecas posibilita una sencilla expansión e incorporación de nuevos modelos y ecuaciones.
Resumen en inglés
In this thesis, the expansion of the lattice Boltzmann (LB) technique towards the resolution of energy transport in multiphase flows is analyzed, building a path to efficiently tackle the challenging boiling phenomena. From a formal viewpoint, LB is a particular alternative to find a solution of the Boltzmann equation, where a distribution function is transported on a regular grid instead of discretizing the target equations. Multiscale expansion techniques, such as the Chapman-Enskog analysis, show that a suitable combination of the spatial grid, the discrete velocities in the phase space, and the collision operator, can solve the typical conservation equations of fuid mechanics. The application of this methodology produces simple, highly-parallelizable algorithms that exhibit a remarkable computational efficiency. The approach to simulate boiling with LB follows an incremental methodology. In the first place, existing isothermal multiphase models are evaluated using a novel test problem, with an analytical solution, which evaluates the capability of an LB model to represent the thermodynamic equilibrium of a liquid-vapor system under different hydrodynamic conditions. The use of this reference solution enables the quantification of the effect of the gravitational force on the existence and position of interphase in equilibrium, together with the verification of the adequate reproduction of coexistence densities and the spatial resolution of the method. Isothermal models are further expanded to solve the energy transport in two and three dimensions. LB equations are added to adequately recover an energy equation that is thermodynamically consistent with the pseudopotential formulation. Typically, traditional LB schemes for scalar advection-diffusion equations bring about unwanted non-physical macroscopic terms. The models proposed in this thesis show that these effects can be avoided by using an equilibrium distribution explicitly defined in the moment space, a relaxation matrix with of-diagonal coefficients, and an implicit source term. The new models are validated by simulating a set of numerical experiments with an analytical solution, and they demonstrate an excellent ability to reproduce the creation and movement of interphases. On the other hand, they are used to demonstrate quantitatively that traditional aspects of the technique, such as consistency and grid independence, can be evaluated with an adequate representation of the simulation results in reduced units. The capabilities of the new models to simulate boiling problems are finally evaluated by reproducing a single bubble generation experiment on a heated surface. In particular, pseudopotential LB models reproduce macroscopic properties that are not known before the simulation and must be determined by conducting additional numerical experiments. The validation proposed in this thesis not only includes the comparison of the simulations with the experimental results but also incorporates a detailed analysis of the setup of the computational model. In this case, an excellent reproduction of the formation, growth, and release of the bubbles is observed. The models developed in this thesis are implemented in a numerical tool developed in C ++ that can be executed on high-performance architectures. The proposed library design allows the expansion and incorporation of new models and equations in a simple way.
| Tipo de objeto: | Tesis (Tesis Doctoral en Ciencias de la Ingeniería) |
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| Palabras Clave: | Heat transfer; Transferencia de calor; Boiling; Ebullición; Multiphase flow; Flujo multifásico; [Lattice Boltzmann; Pseudopotential; Pseudopotencial; Numerical methods; Métodos numéricos] |
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| Materias: | Ingeniería nuclear > Mecánica de fluidos |
| Divisiones: | Aplicaciones de la energía nuclear > Tecnología de materiales y dispositivos > Mecánica computacional |
| Código ID: | 1071 |
| Depositado Por: | Tamara Cárcamo |
| Depositado En: | 12 Jul 2022 15:40 |
| Última Modificación: | 12 Jul 2022 15:40 |
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