Instability and topology bifurcations on a hemisphere-cylinder at high angle of attack

La configuración de un cilindro acoplado a una semi-esfera, conocida como ’hemispherecylinder’, se considera como un modelo simplificado para numerosas aplicaciones industriales tales como fuselaje de aviones o submarinos. Por tanto, el estudio y entendimiento de los fenómenos fluidos que ocurren alrededor de dicha geometría presenta gran interés. En esta tesis se muestra la investigación del origen y evolución de los, ya conocidos, patrones de flujo (burbuja de separación, vórtices ’horn’ y vórtices ’leeward’) que se dan en esta geometría bajo condiciones de flujo separado. Para ello se han llevado a cabo simulaciones numéricas (DNS) y ensayos experimentales usando la técnica de Particle Image Velocimetry (PIV), para una variedad de números de Reynolds (Re) y ángulos de ataque (AoA). Se ha aplicado sobre los resultados numéricos la teoría de puntos críticos obteniendo, por primera vez para esta geometría, un diagrama de bifurcaciones que clasifica los diferentes regímenes topológicos en función del número de Reynolds y del ángulo de ataque. Se ha llevado a cabo una caracterización completa sobre el origen y la evolución de los patrones estructurales característicos del cuerpo estudiado. Puntos críticos de superficie y líneas de corriente tridimensionales han ayudado a describir el origen y la evolución de las principales estructuras presentes en el flujo hasta alcanzar un estado de estabilidad desde el punto de vista topológico. Este estado se asocia con el patrón de los vórtices ’horn’, definido por una topología característica que se encuentra en un rango de números de Reynolds muy amplio y en regímenes compresibles e incompresibles. Por otro lado, con el objeto de determinar las estructuras presentes en el flujo y sus frecuencias asociadas, se han usado distintas técnicas de análisis: Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD) y análisis de Fourier. Dichas técnicas se han aplicado sobre los datos experimentales y numéricos, demostrándose la buena concordancia entre ambos resultados. Finalmente, se ha encontrado en ambos casos, una frecuencia dominante asociada con una inestabilidad de los vórtices ’leeward’. ABSTRACT The hemisphere-cylinder may be considered as a simplified model for several geometries found in industrial applications such as aircrafts’ fuselages or submarines. Understanding the complex flow phenomena that surrounds this particular geometry is therefore of major industrial interest. This thesis presents an investigation of the origin and evolution of the complex flow pattern; i.e. separation bubbles, horn vortices and leeward vortices, around the hemisphere-cylinder under separated flow conditions. To this aim, threedimensional Direct Numerical Simulations (DNS) and experimental tests, using Particle Image Velocimetry (PIV) techniques, have been performed for a variety of Reynolds numbers (Re) and angles of attack (AoA). Critical point theory has been applied to the numerical simulations to provide, for the first time for this geometry, a bifurcation diagram that classifies the different flow topology regimes as a function of the Reynolds number and the angle of attack. A complete characterization about the origin and evolution of the complex structural patterns of this geometry has been put in evidence. Surface critical points and surface and volume streamlines were able to describe the main flow structures and their strong dependence with the flow conditions up to reach the structurally stable state. This state was associated with the pattern of the horn vortices, found on ranges from low to high Reynolds numbers and from incompressible to compressible regimes. In addition, different structural analysis techniques have been employed: Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD) and Fourier analysis. These techniques have been applied to the experimental and numerical data to extract flow structure information (i.e. modes and frequencies). Experimental and numerical modes are shown to be in good agreement. A dominant frequency associated with an instability of the leeward vortices has been identified in both, experimental and numerical results.

Flow around a hemisphere-cylinder at high angle of attack and low Reynolds number. Part I: Experimental and numerical investigation

Three-dimensional Direct Numerical Simulations combined with Particle Image Velocimetry experiments have been performed on a hemisphere-cylinder at Reynolds number 1000 and angle of attack 20◦. At these flow conditions, a pair of vortices, so-called “horn” vortices, are found to be associated with flow separation. In order to understand the highly complex phenomena associated with this fully threedimensional massively separated flow, different structural analysis techniques have been employed: Proper Orthogonal and Dynamic Mode Decompositions, POD and DMD, respectively, as well as criticalpoint theory. A single dominant frequency associated with the von Karman vortex shedding has been identified in both the experimental and the numerical results. POD and DMD modes associated with this frequency were recovered in the analysis. Flow separation was also found to be intrinsically linked to the observed modes. On the other hand, critical-point theory has been applied in order to highlight possible links of the topology patterns over the surface of the body with the computed modes. Critical points and separation lines on the body surface show in detail the presence of different flow patterns in the base flow: a three-dimensional separation bubble and two pairs of unsteady vortices systems, the horn vortices, mentioned before, and the so-called “leeward” vortices. The horn vortices emerge perpendicularly from the body surface at the separation region. On the other hand, the leeward vortices are originated downstream of the separation bubble, as a result of the boundary layer separation. The frequencies associated with these vortical structures have been quantified.

Game Theory Models for Multi-Robot Patrolling of Infraestructures

Abstract This work is focused on the problem of performing multi‐robot patrolling for infrastructure security applications in order to protect a known environment at critical facilities. Thus, given a set of robots and a set of points of interest, the patrolling task consists of constantly visiting these points at irregular time intervals for security purposes. Current existing solutions for these types of applications are predictable and inflexible. Moreover, most of the previous centralized and deterministic solutions and only few efforts have been made to integrate dynamic methods. Therefore, the development of new dynamic and decentralized collaborative approaches in order to solve the aforementioned problem by implementing learning models from Game Theory. The model selected in this work that includes belief‐based and reinforcement models as special cases is called Experience‐Weighted Attraction. The problem has been defined using concepts of Graph Theory to represent the environment in order to work with such Game Theory techniques. Finally, the proposed methods have been evaluated experimentally by using a patrolling simulator. The results obtained have been compared with previous available

Electron temperature versus laser intensity times wavelength squared: a comparison of theory and experiments

The peak temperature in the corona of plasma ejected by a laser-irradiated slab is discussed in terms of a one-electron-temperature model. Both heat-flux saturation and pulse rise-time effects are considered;the intensity in the rising half of the pulse is approximated by a linear function of time, I(t) = Iot/r. The temperature is found to be proportional to (IQX2)273 and a function of I0X4/r. Above a certain value of I0X4/T, the plasma presents two characteristic temperatures (at saturation and at the critical surface) which can be identified with experimentally observed cold- and hot-electron temperatures. The results are compared with extensive experimental data available for both nd and CO2 lasers, I0(W'cnf2) X2 (/um) starting around 1012. The agreement is good if substantial flux inhibition is assumed (flux-limit factor f = 0.03), and fails for I0X2 above 1O1S. Results for both ablation pressure and mass ablation rate are also given.

Cooperative Multi-robot Patrolling: A study of distributed approaches based on mathematical models of game theory to protect infrastructures

El principio de Teoría de Juegos permite desarrollar modelos estocásticos de patrullaje multi-robot para proteger infraestructuras criticas. La protección de infraestructuras criticas representa un gran reto para los países al rededor del mundo, principalmente después de los ataques terroristas llevados a cabo la década pasada. En este documento el termino infraestructura hace referencia a aeropuertos, plantas nucleares u otros instalaciones. El problema de patrullaje se define como la actividad de patrullar un entorno determinado para monitorear cualquier actividad o sensar algunas variables ambientales. En esta actividad, un grupo de robots debe visitar un conjunto de puntos de interés definidos en un entorno en intervalos de tiempo irregulares con propósitos de seguridad. Los modelos de partullaje multi-robot son utilizados para resolver este problema. Hasta el momento existen trabajos que resuelven este problema utilizando diversos principios matemáticos. Los modelos de patrullaje multi-robot desarrollados en esos trabajos representan un gran avance en este campo de investigación. Sin embargo, los modelos con los mejores resultados no son viables para aplicaciones de seguridad debido a su naturaleza centralizada y determinista. Esta tesis presenta cinco modelos de patrullaje multi-robot distribuidos e impredecibles basados en modelos matemáticos de aprendizaje de Teoría de Juegos. El objetivo del desarrollo de estos modelos está en resolver los inconvenientes presentes en trabajos preliminares. Con esta finalidad, el problema de patrullaje multi-robot se formuló utilizando conceptos de Teoría de Grafos, en la cual se definieron varios juegos en cada vértice de un grafo. Los modelos de patrullaje multi-robot desarrollados en este trabajo de investigación se han validado y comparado con los mejores modelos disponibles en la literatura. Para llevar a cabo tanto la validación como la comparación se ha utilizado un simulador de patrullaje y un grupo de robots reales. Los resultados experimentales muestran que los modelos de patrullaje desarrollados en este trabajo de investigación trabajan mejor que modelos de trabajos previos en el 80% de 150 casos de estudio. Además de esto, estos modelos cuentan con varias características importantes tales como distribución, robustez, escalabilidad y dinamismo. Los avances logrados con este trabajo de investigación dan evidencia del potencial de Teoría de Juegos para desarrollar modelos de patrullaje útiles para proteger infraestructuras. ABSTRACT Game theory principle allows to developing stochastic multi-robot patrolling models to protect critical infrastructures. Critical infrastructures protection is a great concern for countries around the world, mainly due to terrorist attacks in the last decade. In this document, the term infrastructures includes airports, nuclear power plants, and many other facilities. The patrolling problem is defined as the activity of traversing a given environment to monitoring any activity or sensing some environmental variables If this activity were performed by a fleet of robots, they would have to visit some places of interest of an environment at irregular intervals of time for security purposes. This problem is solved using multi-robot patrolling models. To date, literature works have been solved this problem applying various mathematical principles.The multi-robot patrolling models developed in those works represent great advances in this field. However, the models that obtain the best results are unfeasible for security applications due to their centralized and predictable nature. This thesis presents five distributed and unpredictable multi-robot patrolling models based on mathematical learning models derived from Game Theory. These multi-robot patrolling models aim at overcoming the disadvantages of previous work. To this end, the multi-robot patrolling problem was formulated using concepts of Graph Theory to represent the environment. Several normal-form games were defined at each vertex of a graph in this formulation. The multi-robot patrolling models developed in this research work have been validated and compared with best ranked multi-robot patrolling models in the literature. Both validation and comparison were preformed by using both a patrolling simulator and real robots. Experimental results show that the multirobot patrolling models developed in this research work improve previous ones in as many as 80% of 150 cases of study. Moreover, these multi-robot patrolling models rely on several features to highlight in security applications such as distribution, robustness, scalability, and dynamism. The achievements obtained in this research work validate the potential of Game Theory to develop patrolling models to protect infrastructures.