Ausas, Roberto F. (2010) Simulación numérica en flujo de dos fases inmiscibles con aplicaciones en lubricación hidrodinámica / Numerical simulation of immiscible two-phase flows with applications to hydrodynamic lubrication. Tesis Doctoral en Ciencias de la Ingeniería, Universidad Nacional de Cuyo, Instituto Balseiro.
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Resumen en español
En esta tesis se discute el modelado numérico del problema de lubricación hidrodinámica en los aros de pistón de motores a explosión. Este modelado ha sido abordado con dos enfoques bien distintos. Por un lado, se ha propuesto una formulación numérica basada en el método de volúmenes finitos para resolver el modelo p–θ de Elrod–Adams, que no es otra cosa que un modelo de orden reducido para el problema de lubricación en presencia de cavitación. Por otro lado, se ha propuesto una formulación numérica completa para la simulación de flujos de dos fases inmiscibles, es decir, un modelo de mayor orden para el problema fluido–dinámico considerando la presencia por separado del lubricante y los gases. Con respecto al primer enfoque considerado, la formulación que proponemos permite resolver la ecuación de Reynolds e imponer las llamadas condiciones JFO, propuestas por Jacobson & Floberg y Olsson, resultando en una formulación estrictamente conservativa. El método está basado en un esquema de relajación y permite resolver al mismo tiempo la dinámica de las partes lubricadas. Luego de describir detalladamente el esquema, se aplica a varias situaciones prácticas y luego al problema de los aros de pistón. Si bien el método es ampliamente usado, notamos que debe ser modificado para estudiar esta clase específica de dispositivos, por lo cual proponemos una variación del mismo. La evidencia numérica en este caso parece indicar que el modelo matem ático, con esta modificación, presenta multiplicidad de soluciones, lo cual motiva el estudio del problema por medio de las ecuaciones de Navier–Stokes incompresibles. En relación con el segundo enfoque, en esta tesis se adopta una formulación de elementos finitos para las ecuaciones de Navier–Stokes, con un método de tipo level set para el seguimiento de la interfase móvil que separa las dos fases presentes en el sistema. La formulación propuesta utiliza interpolación lineal para la velocidad, presión y función de level set. Se estudian varias cuestiones particulares que deben ser tomadas en cuenta en una formulación de este tipo. Por un lado se estudia de manera exhaustiva un método de reinicialización para mantener la regularidad de la función de level set y se lo extiende al caso de mallas curvilíneas. Además, proponemos un nuevo espacio de elementos finitos, que no introduce incógnitas adicionales y está basado en simples modificaciones del espacio P_1 conforme, para capturar las discontinuidades en el campo de presiones debido a la presencia de la tensión superficial, la cual es incluida mediante una formulación de Laplace–Beltrami. La formulaciódn propuesta es monolítica, es decir, se computan simultáneamente todas las variables fluido–dinámicas (velocidad y presión) y la posición de la interfase (embebida en la función de level set), con un esquema iterativo de Newton–Raphson, para lo cual se propone un cómputo mejorado del Jacobiano. Luego, se introduce un nuevo método para acondicionar la velocidad de transporte en las cercanías de la interfase y mejorar así, en algunos casos, la precisión de los cálculos. El método está basado en la resolución de una ecuación a derivadas parciales y es por lo tanto mucho más simple de implementar que otras metodologías de tipo geométrico. Finalmente, se aplica la formulación numérica al problema fluido–dinámico en aros de pistón y los resultados son comparados con los correspondientes al modelo de lubricación propuesto.
Resumen en inglés
This thesis deals with the numerical modeling of the piston ring lubrication problem typical of internal combustion engines in the hydrodynamic regime. This modeling has been addressed by means of two very distinct approaches. On the one hand, we have proposed a numerical formulation based on a finite volume method to solve the Elrod–Adams p–θ model, which is a low order model of the lubrication problem in the presence of cavitation. On the other hand, we have proposed a complete numerical formulation for the simulation of two phase inmiscible flows, i.e. a higher order model of the problem, considering separately the presence of the lubricant fluid and the combustion gases. With respect to the first approach, the proposed formulation allows us to solve the Reynolds equation imposing the so called JFO conditions introduced by Jacobson & Floberg and Olsson, leading to a formulation that exactly preserves mass. The computational method that we propose is based on a relaxation scheme and also allows a simulataneous computation of the dynamical behavior of the lubricated device. After detailed description of the scheme, we apply it to various practical cases and then to the piston ring lubrication problem. Though widely used, we notice that the model fails for this specific type of lubricated devices, thus needing a suitable modification. The numerical evidence in this case, seems to indicate that the mathematical model, with the aforementioned modification, exhibits multiplicity of solutions, which motivates to study the problem by means of the incompresible Navier–Stokes equations. Regarding the second approach, in this thesis we adopt a finite element formulation of the Navier–Stokes problem with a level set method to follow the moving interface that separates both phases present in the system. The proposed formulation uses linear interpolation for the velocity, pressure and level set function. We study several issues that need to be addressed in this type formulations. On the one hand, we study with great detail a reinitialization method to keep the distorsion of the level set function under control and extend it for the case of curvilinear grids. We also propose a new finite element space with no additional degrees of freedom based on extremely simple modifications to the P1–conforming space, to capture the discontinuities that appear in the pressure field due to the presence of surface tension, which is included by means of a Laplace–Beltrami formulation. The proposed methodology is monolithic, i.e., all variables, velocity, pressure and interface position (which is embedded in the level set function) are computed simultaneously by means of a Newton–Raphson iterative procedure, for which we propose an improved computation of the Jacobian. Additionally, we introduce a new method to increase, in some cases, the accuracy of computations by means of a fix near the interface in the velocity field used for transport of the level set function. The method is based on the resolution of a partial differential equation and thus much easier to implement than other geometrical methodologies. We finally apply the numerical methodology to the piston ring system and compare results with those of the previously mentioned lubrication models.
| Tipo de objeto: | Tesis (Tesis Doctoral en Ciencias de la Ingeniería) |
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| Palabras Clave: | Two-phase flow; Flujo bifásico; Simulación numérica |
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| Materias: | Matemática > Lógica matemática |
| Divisiones: | Aplicaciones de la energía nuclear > Tecnología de materiales y dispositivos > Mecánica computacional |
| Código ID: | 168 |
| Depositado Por: | Marisa G. Velazco Aldao |
| Depositado En: | 12 Aug 2010 15:06 |
| Última Modificación: | 07 Feb 2012 11:43 |
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