Direct numerical simulation of bubble-induced turbulence

We report on an investigation of bubble-induced turbulence. Bubbles of a size larger than the dissipative scale cannot be treated as pointwise inclusions, and generate important hydrodynamic fields in the carrier fluid when in motion. Furthermore, bubble motions may induce a collective agitation due to hydrodynamic interactions which display some turbulent-like features. We tackle this complex phenomenon numerically, performing direct numerical simulations with a volume-of-fluid method. In the first part of the work, we perform both two-dimensional and three-dimensional tests in order to determine appropriate numerical and physical parameters. We then carry out a highly resolved simulation of a three-dimensional bubble column, with a set-up and physical parameters similar to those used in laboratory experiments. This is the largest simulation attempted for such a configuration and is only possible thanks to adaptive grid refinement. Results are compared both with experiments and previous coarse-mesh numerical simulations. In particular, the one-point probability density function of the velocity fluctuations is in good agreement with experiments. The spectra of the kinetic energy show a clear k(-3) scaling. The mechanisms underlying the energy transfer and notably the possible presence of a cascade are unveiled by a local scale-by-scale analysis in physical space. The comparison with previous simulations indicates to what extent simulations not fully resolved may yet give correct results, from a statistical point of view

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Adaptive mesh refinement method for CFD applications

The main objective of this thesis is the development of an adaptive mesh refinement (AMR) algorithm for computational fluid dynamics simulations using hexahedral and tetrahedral meshes. This numerical methodology is applied in the context of large-eddy simulations (LES) of turbulent flows and direct numerical simulations (DNS) of interfacial flows, to bring new numerical research and physical insight. For the fluid dynamics simulations, the governing equations, the spatial discretization on unstructured grids and the numerical schemes for solving Navier-Stokes equations are presented. The equations follow a discretization by conservative finite-volume on collocated meshes. For the turbulent flows formulation, the spatial discretization preserves symmetry properties of the continuous differential operators and the time integration follows a self-adaptive strategy, which has been well tested on unstructured grids. Moreover, LES model consisting of a wall adapting local-eddy-viscosity within a variational multi-scale formulation is used for the applications showed in this thesis. For the two-phase flow formulation, a conservative level-set method is applied for capturing the interface between two fluids and is implemented with a variable density projection scheme to simulate incompressible two-phase flows on unstructured meshes. The AMR algorithm developed in this thesis is based on a quad/octree data structure and keeps a relation of 1:2 between levels of refinement. In the case of tetrahedral meshes, a geometrical criterion is followed to keep the quality metric of the mesh on a reasonable basis. The parallelization strategy consists mainly in the creation of mesh elements in each sub-domain and establishes a unique global identification number, to avoid duplicate elements. Load balance is assured at each AMR iteration to keep the parallel performance of the CFD code. Moreover, a mesh multiplication algorithm (MM) is reported to create large meshes, with different kind of mesh elements, but preserving the topology from a coarser original mesh. This thesis focuses on the study of turbulent flows and two-phase flows using an AMR framework. The cases studied for LES of turbulent flows applications are the flow around one and two separated square cylinders, and the flow around a simplified car model. In this context, a physics-based refinement criterion is developed, consisting of the residual velocity calculated from a multi-scale decomposition of the instantaneous velocity. This criteria ensures grid adaptation following the main vortical structures and giving enough mesh resolution on the zones of interest, i.e., flow separation, turbulent wakes, and vortex shedding. The cases studied for the two-phase flows are the DNS of 2D and 3D gravity-driven bubble, with a particular focus on the wobbling regime. A study of rising bubbles in the wobbling regime and the effect of dimensionless numbers on the dynamic behavior of the bubbles are presented. Moreover, the use of tetrahedral AMR is applied for the numerical simulation of gravity-driven bubbles in complex domains. On this topic, the methodology is validated on bubbles rising in cylindrical channels with different topology, where the study of these cases contributed to having new numerical research and physical insight in the development of a rising bubble with wall effects.El objetivo principal de esta tesis es el desarrollo de un algoritmo adaptativo de refinamiento de malla (AMR) para simulaciones de dinámica de fluidos computacional utilizando mallas hexaédricas y tetraédricas. Esta metodología numérica se aplica en el contexto de simulaciones Large-eddie (LES) de flujos turbulentos y simulaciones numéricas directas (DNS) de flujos interfaciales, para traer nuevas investigaciones numéricas y entendimiento físicas. Para las simulaciones de dinámica de fluidos, se presentan las ecuaciones governantes, la discretización espacial en mallas no estructuradas y los esquemas numéricos para resolver las ecuaciones de Navier-Stokes. Las ecuaciones siguen una discretización conservativa por volumenes finitos en mallas colocadas. Para la formulación de flujos turbulentos, la discretización espacial preserva las propiedades de simetría de los operadores diferenciales continuos y la integración de tiempo sigue una estrategia autoadaptativa, que ha sido bien probada en mallas no estructuradas. Además, para las aplicaciones que se muestran en esta tesis, se utiliza el modelo LES que consiste en una viscosidad local que se adapta a la pared dentro de una formulación multiescala variable. Para la formulación de flujo de dos fases, se aplica un método de conjunto de niveles conservador para capturar la interfaz entre dos fluidos y se implementa con un esquema de proyección de densidad variable para simular flujos de dos fases incompresibles en mallas no estructuradas. El algoritmo AMR desarrollado en esta tesis se basa en una estructura de datos de quad / octree y mantiene una relación de 1: 2 entre los niveles de refinamiento. En el caso de las mallas tetraédricas, se sigue un criterio geométrico para mantener la calidad de la malla en una base razonable. La estrategia de paralelización consiste principalmente en la creación de elementos de malla en cada subdominio y establece un número de identificación global único, para evitar elementos duplicados. El equilibrio de carga está asegurado en cada iteración de AMR para mantener el rendimiento paralelo del código CFD. Además, se ha desarrollado un algoritmo de multiplicación de malla (MM) para crear mallas grandes, con diferentes tipos de elementos de malla, pero preservando la topología de una malla original más pequeña. Esta tesis se centra en el estudio de flujos turbulentos y flujos de dos fases utilizando un marco AMR. Los casos estudiados para aplicaciones de LES de flujos turbulentos son el flujo alrededor de uno y dos cilindros separados de sección cuadrada, y el flujo alrededor de un modelo de automóvil simplificado. En este contexto, se desarrolla un criterio de refinamiento basado en la física, que consiste en la velocidad residual calculada a partir de una descomposición de escala múltiple de la velocidad instantánea. Este criterio garantiza la adaptación de la malla siguiendo las estructuras vorticales principales y proporcionando una resolución de malla suficiente en las zonas de interés, es decir, separación de flujo, estelas turbulentas y desprendimiento de vórtices. Los casos estudiados para los flujos de dos fases son el DNS de la burbuja impulsada por la gravedad en 2D y 3D, con un enfoque particular en el régimen de oscilación. Además, el uso de AMR tetraédrico se aplica para la simulación numérica de burbujas impulsadas por la gravedad en dominios complejos. En este tema, la metodología se valida en burbujas que ascienden en canales cilíndricos con topología diferente, donde el estudio de estos casos contribuyó a tener una nueva investigación numérica y una visión física en el desarrollo de una burbuja con efectos de pared

Adaptive mesh refinement method for CFD applications

The main objective of this thesis is the development of an adaptive mesh refinement (AMR) algorithm for computational fluid dynamics simulations using hexahedral and tetrahedral meshes. This numerical methodology is applied in the context of large-eddy simulations (LES) of turbulent flows and direct numerical simulations (DNS) of interfacial flows, to bring new numerical research and physical insight. For the fluid dynamics simulations, the governing equations, the spatial discretization on unstructured grids and the numerical schemes for solving Navier-Stokes equations are presented. The equations follow a discretization by conservative finite-volume on collocated meshes. For the turbulent flows formulation, the spatial discretization preserves symmetry properties of the continuous differential operators and the time integration follows a self-adaptive strategy, which has been well tested on unstructured grids. Moreover, LES model consisting of a wall adapting local-eddy-viscosity within a variational multi-scale formulation is used for the applications showed in this thesis. For the two-phase flow formulation, a conservative level-set method is applied for capturing the interface between two fluids and is implemented with a variable density projection scheme to simulate incompressible two-phase flows on unstructured meshes. The AMR algorithm developed in this thesis is based on a quad/octree data structure and keeps a relation of 1:2 between levels of refinement. In the case of tetrahedral meshes, a geometrical criterion is followed to keep the quality metric of the mesh on a reasonable basis. The parallelization strategy consists mainly in the creation of mesh elements in each sub-domain and establishes a unique global identification number, to avoid duplicate elements. Load balance is assured at each AMR iteration to keep the parallel performance of the CFD code. Moreover, a mesh multiplication algorithm (MM) is reported to create large meshes, with different kind of mesh elements, but preserving the topology from a coarser original mesh. This thesis focuses on the study of turbulent flows and two-phase flows using an AMR framework. The cases studied for LES of turbulent flows applications are the flow around one and two separated square cylinders, and the flow around a simplified car model. In this context, a physics-based refinement criterion is developed, consisting of the residual velocity calculated from a multi-scale decomposition of the instantaneous velocity. This criteria ensures grid adaptation following the main vortical structures and giving enough mesh resolution on the zones of interest, i.e., flow separation, turbulent wakes, and vortex shedding. The cases studied for the two-phase flows are the DNS of 2D and 3D gravity-driven bubble, with a particular focus on the wobbling regime. A study of rising bubbles in the wobbling regime and the effect of dimensionless numbers on the dynamic behavior of the bubbles are presented. Moreover, the use of tetrahedral AMR is applied for the numerical simulation of gravity-driven bubbles in complex domains. On this topic, the methodology is validated on bubbles rising in cylindrical channels with different topology, where the study of these cases contributed to having new numerical research and physical insight in the development of a rising bubble with wall effects.El objetivo principal de esta tesis es el desarrollo de un algoritmo adaptativo de refinamiento de malla (AMR) para simulaciones de dinámica de fluidos computacional utilizando mallas hexaédricas y tetraédricas. Esta metodología numérica se aplica en el contexto de simulaciones Large-eddie (LES) de flujos turbulentos y simulaciones numéricas directas (DNS) de flujos interfaciales, para traer nuevas investigaciones numéricas y entendimiento físicas. Para las simulaciones de dinámica de fluidos, se presentan las ecuaciones governantes, la discretización espacial en mallas no estructuradas y los esquemas numéricos para resolver las ecuaciones de Navier-Stokes. Las ecuaciones siguen una discretización conservativa por volumenes finitos en mallas colocadas. Para la formulación de flujos turbulentos, la discretización espacial preserva las propiedades de simetría de los operadores diferenciales continuos y la integración de tiempo sigue una estrategia autoadaptativa, que ha sido bien probada en mallas no estructuradas. Además, para las aplicaciones que se muestran en esta tesis, se utiliza el modelo LES que consiste en una viscosidad local que se adapta a la pared dentro de una formulación multiescala variable. Para la formulación de flujo de dos fases, se aplica un método de conjunto de niveles conservador para capturar la interfaz entre dos fluidos y se implementa con un esquema de proyección de densidad variable para simular flujos de dos fases incompresibles en mallas no estructuradas. El algoritmo AMR desarrollado en esta tesis se basa en una estructura de datos de quad / octree y mantiene una relación de 1: 2 entre los niveles de refinamiento. En el caso de las mallas tetraédricas, se sigue un criterio geométrico para mantener la calidad de la malla en una base razonable. La estrategia de paralelización consiste principalmente en la creación de elementos de malla en cada subdominio y establece un número de identificación global único, para evitar elementos duplicados. El equilibrio de carga está asegurado en cada iteración de AMR para mantener el rendimiento paralelo del código CFD. Además, se ha desarrollado un algoritmo de multiplicación de malla (MM) para crear mallas grandes, con diferentes tipos de elementos de malla, pero preservando la topología de una malla original más pequeña. Esta tesis se centra en el estudio de flujos turbulentos y flujos de dos fases utilizando un marco AMR. Los casos estudiados para aplicaciones de LES de flujos turbulentos son el flujo alrededor de uno y dos cilindros separados de sección cuadrada, y el flujo alrededor de un modelo de automóvil simplificado. En este contexto, se desarrolla un criterio de refinamiento basado en la física, que consiste en la velocidad residual calculada a partir de una descomposición de escala múltiple de la velocidad instantánea. Este criterio garantiza la adaptación de la malla siguiendo las estructuras vorticales principales y proporcionando una resolución de malla suficiente en las zonas de interés, es decir, separación de flujo, estelas turbulentas y desprendimiento de vórtices. Los casos estudiados para los flujos de dos fases son el DNS de la burbuja impulsada por la gravedad en 2D y 3D, con un enfoque particular en el régimen de oscilación. Además, el uso de AMR tetraédrico se aplica para la simulación numérica de burbujas impulsadas por la gravedad en dominios complejos. En este tema, la metodología se valida en burbujas que ascienden en canales cilíndricos con topología diferente, donde el estudio de estos casos contribuyó a tener una nueva investigación numérica y una visión física en el desarrollo de una burbuja con efectos de pared.Postprint (published version

Numerical analysis of oil injection in twin-screw compressors

Compressors are widely used in the manufacturing, process, construction, and energy industries. They consume nearly 20% of the electricity generated worldwide [1]. Nearly 66% of this electricity comes from burning fossil fuel that greatly impacts the environment. Improving compressor efficiency by even a small percentage will considerably reduce electricity and energy consumption. This thesis focuses on improvement in the efficiency of oil-injected compressors. The injection of oil in the working chamber of a screw compressor increases volumetric efficiency and reliability, but it increases power losses. Also, the oil needs to be separated from the gas, which requires additional equipment and energy losses, not to mention the contamination of the environment with the oil carryover. The injected oil has a significant influence on compressor performance and the environment. The distribution of oil injected in a compression chamber is critical for performance and reliability. Accordingly, investigations are carried out using Computational Fluid Dynamics (CFD), based on a Volume of Fluid (VOF) model, to determine the oil distribution. The predictions were compared with test results. This was applied to an industrial compressor with a traditional single oil injection point. Using different nozzle diameters allowed the evaluation of the oil and temperature distribution close to rotor surfaces to be determined. It was found out that the high gas temperatures coincided with the regions of low oil concentration. With increasing the oil flow rate through a single port, the cooling of these hot spots was not achieved beyond a certain point unless the second oil-injection port was introduced on the opposite rotor. The injection through ports on both rotors reduced the compressor chamber temperature by 30°-35°C and the specific power by 1.8%. Furthermore, the adaptive mesh refinement technique in a simplified compression domain was used to simulate the film formation and disintegration. The disintegration has shown various oil phase breakup levels due to interfacial shear, inertial, and centrifugal forces, leading to ligaments, lobes, and droplets. This study shows that computational methods could be exploited for improving compressor energy consumption through oil distribution. One such way is the enhancement of oil distribution to cool high temperature spots. Another is understanding the oil phase breakup due to the forces acting in a compression chamber that can affect the oil droplet sizes and cooling surface area. Techniques used in this research can be applied to improve efficiency for a wide range of screw compressors

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal