On the effects of turbulence modelling in design optimisation for high-lift devices

Aerodynamic shape optimisation is being increasingly utilised as a design tool in the aerospace industry. In order to provide accurate results, design optimisation methods rely on the accuracy of the underlying CFD methods applied to obtain aerodynamic forces for a given configuration. Previous studies of the authors have highlighted that the variation of the order of accuracy of the CFD solver with a fixed turbulence model affects the resulting optimised airfoil shape for a single element airfoil. The accuracy of the underlying CFD model is even more relevant in the context of high-lift configurations where an accurate prediction of flow is challenging due to the complex flow physics involving transition and flow separation phenomena. This paper explores the effect of the fidelity of CFD results for a range of turbulence models within the context of the computational design of aircraft configurations. The NLR7301 multi-element airfoil (main wing and flap) is selected as the baseline configuration, because of the wealth of experimental an computational results available for this configuration. An initial validation study is conducted in order to establish optimal mesh parameters. A bi-objective shape optimisation problem is then formulated, by trying to reveal the trade-off between lift and drag coefficients at high angles of attack. Optimisation of the airfoil shape is performed with Spalart-Allmaras, k - ω SST and k - ε realisable models. The results indicate that there is consistent and complementary impact to the optimum level achieved from all the three different turbulence models considered in the presented case study. Without identifying particular superiority of any of the turbu- lence models, we can say though that each of them expressed favourable influence towards different optimality routes. These observations lead to the exploration of new avenues for future research. © 2012 by the authors.

Young's modulus varies with differential orientation of keratin in feathers

Feathers are composed of a structure that, whilst being very light, is able to withstand the large aerodynamic forces exerted upon them during flight. To explore the contribution of molecular orientation to feather keratin mechanical properties, we have examined the nanoscopic organisation of the keratin molecules by X-ray diffraction techniques and have confirmed a link between this and the Young's modulus of the feather rachis. Our results indicate that along the rachis length, from calamus to tip, the keratin molecules become more aligned than at the calamus before returning to a state of higher mis-orientation towards the tip of the rachis. We have also confirmed the general trend of increasing Young's modulus with distance along the rachis. Furthermore, we report a distinct difference in the patterns of orientation of beta-keratin in the feathers of flying and flightless birds. The trend for increased modulus along the feathers of volant birds is absent in the flightless ostrich.

Stochastic field processes in the mathematical modelling of damped transmission line vibrations

Wind-excited vibrations in the frequency range of 10 to 50 Hz due to vortex shedding often cause fatigue failures in the cables of overhead transmission lines. Damping devices, such as the Stockbridge dampers, have been in use for a long time for supressing these vibrations. The dampers are conveniently modelled by means of their driving point impedance, measured in the lab over the frequency range under consideration. The cables can be modelled as strings with additional small bending stiffness. The main problem in modelling the vibrations does however lay in the aerodynamic forces, which usually are approximated by the forces acting on a rigid cylinder in planar flow. In the present paper, the wind forces are represented by stochastic processes with arbitrary crosscorrelation in space; the case of a Kármán vortex street on a rigid cylinder in planar flow is contained as a limit case in this approach. The authors believe that this new view of the problem may yield useful results, particularly also concerning the reliability of the lines and the probability of fatigue damages. © 1987.

Aeroelastic stability analysis using linear matrix inequalities

The present work describes an alternative methodology for identification of aeroelastic stability in a range of varying parameters. Analysis is performed in time domain based on Lyapunov stability and solved by convex optimization algorithms. The theory is outlined and simulations are carried out on a benchmark system to illustrate the method. The classical methodology with the analysis of the system's eigenvalues is presented for comparing the results and validating the approach. The aeroelastic model is represented in state space format and the unsteady aerodynamic forces are written in time domain using rational function approximation. The problem is formulated as a polytopic differential inclusion system and the conceptual idea can be used in two different applications. In the first application the method verifies the aeroelastic stability in a range of air density (or its equivalent altitude range). In the second one, the stability is verified for a rage of velocities. These analyses are in contrast to the classical discrete analysis performed at fixed air density/velocity values. It is shown that this method is efficient to identify stability regions in the flight envelope and it offers promise for robust flutter identification.

Control of Limit Cycle Oscillation in a Three Degrees of Freedom Airfoil Section Using Fuzzy Takagi-Sugeno Modeling

This work presents a strategy to control nonlinear responses of aeroelastic systems with control surface freeplay. The proposed methodology is developed for the three degrees of freedom typical section airfoil considering aerodynamic forces from Theodorsen's theory. The mathematical model is written in the state space representation using rational function approximation to write the aerodynamic forces in time domain. The control system is designed using the fuzzy Takagi-Sugeno modeling to compute a feedback control gain. It useds Lyapunov's stability function and linear matrix inequalities (LMIs) to solve a convex optimization problem. Time simulations with different initial conditions are performed using a modified Runge-Kutta algorithm to compare the system with and without control forces. It is shown that this approach can compute linear control gain able to stabilize aeroelastic systems with discontinuous nonlinearities.

Structural response and dynamics of fluid-structure-control interaction in wind turbine blades

Reducing the uncertainties related to blade dynamics by the improvement of the quality of numerical simulations of the fluid structure interaction process is a key for a breakthrough in wind-turbine technology. A fundamental step in that direction is the implementation of aeroelastic models capable of capturing the complex features of innovative prototype blades, so they can be tested at realistic full-scale conditions with a reasonable computational cost. We make use of a code based on a combination of two advanced numerical models implemented in a parallel HPC supercomputer platform: First, a model of the structural response of heterogeneous composite blades, based on a variation of the dimensional reduction technique proposed by Hodges and Yu. This technique has the capacity of reducing the geometrical complexity of the blade section into a stiffness matrix for an equivalent beam. The reduced 1-D strain energy is equivalent to the actual 3-D strain energy in an asymptotic sense, allowing accurate modeling of the blade structure as a 1-D finite-element problem. This substantially reduces the computational effort required to model the structural dynamics at each time step. Second, a novel aerodynamic model based on an advanced implementation of the BEM(Blade ElementMomentum) Theory; where all velocities and forces are re-projected through orthogonal matrices into the instantaneous deformed configuration to fully include the effects of large displacements and rotation of the airfoil sections into the computation of aerodynamic forces. This allows the aerodynamic model to take into account the effects of the complex flexo-torsional deformation that can be captured by the more sophisticated structural model mentioned above. In this thesis we have successfully developed a powerful computational tool for the aeroelastic analysis of wind-turbine blades. Due to the particular features mentioned above in terms of a full representation of the combined modes of deformation of the blade as a complex structural part and their effects on the aerodynamic loads, it constitutes a substantial advancement ahead the state-of-the-art aeroelastic models currently available, like the FAST-Aerodyn suite. In this thesis, we also include the results of several experiments on the NREL-5MW blade, which is widely accepted today as a benchmark blade, together with some modifications intended to explore the capacities of the new code in terms of capturing features on blade-dynamic behavior, which are normally overlooked by the existing aeroelastic models.

Hysteresis phenomena in transverse galloping of triangular cross-section bodies

Transverse galloping is a type of aeroelastic instability characterised by large amplitude, low frequency oscillation of a structure in the direction normal to the mean wind direction. It normally appears in bodies with small stiffness and structural damping, provided the incident flow velocity is high enough. In the simplest approach transverse galloping can be considered as a one-degree-of-freedom oscillator subjected to aerodynamic forces, which in turn can be described by using a quasi-steady description. In this frame it has been demonstrated that hysteresis phenomena in transverse galloping is related to the existence of inflection points in the curve giving the dependence with the angle of attack of the aerodynamic coefficient normal to the incident flow. Aiming at experimentally checking such a relationship between these inflection points and hysteresis, wind tunnel experiments have been conducted. Experiments have been restricted to isosceles triangular cross-section bodies, whose galloping behaviour is well documented. Experimental results show that, according to theoretical predictions, hysteresis takes place at the angles of attack where there are inflection points in the lift coefficient curve, provided that the body is prone to gallop at these angles of attack.

Analysis of the geometric altimetry to support aircraft optimal profiles within future 4D trajectory management

The use of barometric altimetry is to some extent a limiting factor on safety, predictability and efficiency of aircraft operations, and reduces the potential of the trajectory based operations capabilities. However, geometric altimetry could be used to improve all of these aspects. Nowadays aircraft altitude is estimated by applying the International Standard Atmosphere which differs from real altitude. At different temperatures for an assigned barometric altitude, aerodynamic forces are different and this has a direct relationship with time, fuel consumption and range of the flight. The study explores the feasibility of using sensors providing geometric reference altitude, in particular, to supply capabilities for the optimization of vertical profiles and also, their impact on the vertical Air Traffic Management separation assurance processes. One of the aims of the thesis is to assess if geometric altitude fulfils the aeronautical requirements through existing sensors. Also the thesis will elaborate on the advantages of geometric altitude over the barometric altitude in terms of efficiency for vertical navigation. The evidence that geometric altitude is the best choice to improve the efficiency in vertical profile and aircraft capacity by reducing vertical uncertainties will also be shown. In this paper, an atmospheric study is presented, as well as the impact of temperature deviation from International Standard Atmosphere model is analyzed in order to obtain relationship between geometric and barometric altitude. Furthermore, an aircraft model to study aircraft vertical profile is provided to analyse trajectories based on geometric altitudes.

Predicción de la velocidad crítica de flameo mediante el uso de modelos aeroelásticos extrapolados en tiempo real con datos de vuelo

La Aeroelasticidad fue definida por Arthur Collar en 1947 como "el estudio de la interacción mutua entre fuerzas inerciales, elásticas y aerodinámicas actuando sobre elementos estructurales expuestos a una corriente de aire". Actualmente, esta definición se ha extendido hasta abarcar la influencia del control („Aeroservoelasticidad‟) e, incluso, de la temperatura („Aerotermoelasticidad‟). En el ámbito de la Ingeniería Aeronáutica, los fenómenos aeroelásticos, tanto estáticos (divergencia, inversión de mando) como dinámicos (flameo, bataneo) son bien conocidos desde los inicios de la Aviación. Las lecciones aprendidas a lo largo de la Historia Aeronáutica han permitido establecer criterios de diseño destinados a mitigar la probabilidad de sufrir fenómenos aeroelásticos adversos durante la vida operativa de una aeronave. Adicionalmente, el gran avance experimentado durante esta última década en el campo de la Aerodinámica Computacional y en la modelización aeroelástica ha permitido mejorar la fiabilidad en el cálculo de las condiciones de flameo de una aeronave en su fase de diseño. Sin embargo, aún hoy, los ensayos en vuelo siguen siendo necesarios para validar modelos aeroelásticos, verificar que la aeronave está libre de inestabilidades aeroelásticas y certificar sus distintas envolventes. En particular, durante el proceso de expansión de la envolvente de una aeronave en altitud/velocidad, se requiere predecir en tiempo real las condiciones de flameo y, en consecuencia, evitarlas. A tal efecto, en el ámbito de los ensayos en vuelo, se han desarrollado diversas metodologías que predicen, en tiempo real, las condiciones de flameo en función de condiciones de vuelo ya verificadas como libres de inestabilidades aeroelásticas. De entre todas ellas, aquella que relaciona el amortiguamiento y la velocidad con un parámetro específico definido como „Margen de Flameo‟ (Flutter Margin), permanece como la técnica más común para proceder con la expansión de Envolventes en altitud/velocidad. No obstante, a pesar de su popularidad y facilidad de aplicación, dicha técnica no es adecuada cuando en la aeronave a ensayar se hallan presentes no-linealidades mecánicas como, por ejemplo, holguras. En particular, en vuelos de ensayo dedicados específicamente a expandir la envolvente en altitud/velocidad, las condiciones de „Oscilaciones de Ciclo Límite‟ (Limit Cycle Oscillations, LCOs) no pueden ser diferenciadas de manera precisa de las condiciones de flameo, llevando a una determinación excesivamente conservativa de la misma. La presente Tesis desarrolla una metodología novedosa, basada en el concepto de „Margen de Flameo‟, que permite predecir en tiempo real las condiciones de „Ciclo Límite‟, siempre que existan, distinguiéndolas de las de flameo. En una primera parte, se realiza una revisión bibliográfica de la literatura acerca de los diversos métodos de ensayo existentes para efectuar la expansión de la envolvente de una aeronave en altitud/velocidad, el efecto de las no-linealidades mecánicas en el comportamiento aeroelástico de dicha aeronave, así como una revisión de las Normas de Certificación civiles y militares respecto a este tema. En una segunda parte, se propone una metodología de expansión de envolvente en tiempo real, basada en el concepto de „Margen de Flameo‟, que tiene en cuenta la presencia de no-linealidades del tipo holgura en el sistema aeroelástico objeto de estudio. Adicionalmente, la metodología propuesta se valida contra un modelo aeroelástico bidimensional paramétrico e interactivo programado en Matlab. Para ello, se plantean las ecuaciones aeroelásticas no-estacionarias de un perfil bidimensional en la formulación espacio-estado y se incorpora la metodología anterior a través de un módulo de análisis de señal y otro módulo de predicción. En una tercera parte, se comparan las conclusiones obtenidas con las expuestas en la literatura actual y se aplica la metodología propuesta a resultados experimentales de ensayos en vuelo reales. En resumen, los principales resultados de esta Tesis son: 1. Resumen del estado del arte en los métodos de ensayo aplicados a la expansión de envolvente en altitud/velocidad y la influencia de no-linealidades mecánicas en la determinación de la misma. 2. Revisión de la normas de Certificación Civiles y las normas Militares en relación a la verificación aeroelástica de aeronaves y los límites permitidos en presencia de no-linealidades. 3. Desarrollo de una metodología de expansión de envolvente basada en el Margen de Flameo. 4. Validación de la metodología anterior contra un modelo aeroelástico bidimensional paramétrico e interactivo programado en Matlab/Simulink. 5. Análisis de los resultados obtenidos y comparación con resultados experimentales. ABSTRACT Aeroelasticity was defined by Arthur Collar in 1947 as “the study of the mutual interaction among inertia, elastic and aerodynamic forces when acting on structural elements surrounded by airflow”. Today, this definition has been updated to take into account the Controls („Aeroservoelasticity‟) and even the temperature („Aerothermoelasticity‟). Within the Aeronautical Engineering, aeroelastic phenomena, either static (divergence, aileron reversal) or dynamic (flutter, buzz), are well known since the early beginning of the Aviation. Lessons learned along the History of the Aeronautics have provided several design criteria in order to mitigate the probability of encountering adverse aeroelastic phenomena along the operational life of an aircraft. Additionally, last decade improvements experienced by the Computational Aerodynamics and aeroelastic modelization have refined the flutter onset speed calculations during the design phase of an aircraft. However, still today, flight test remains as a key tool to validate aeroelastic models, to verify flutter-free conditions and to certify the different envelopes of an aircraft. Specifically, during the envelope expansion in altitude/speed, real time prediction of flutter conditions is required in order to avoid them in flight. In that sense, within the flight test community, several methodologies have been developed to predict in real time flutter conditions based on free-flutter flight conditions. Among them, the damping versus velocity technique combined with a Flutter Margin implementation remains as the most common technique used to proceed with the envelope expansion in altitude/airspeed. However, although its popularity and „easy to implement‟ characteristics, several shortcomings can adversely affect to the identification of unstable conditions when mechanical non-linearties, as freeplay, are present. Specially, during test flights devoted to envelope expansion in altitude/airspeed, Limits Cycle Oscillations (LCOs) conditions can not be accurately distinguished from those of flutter and, in consequence, it leads to an excessively conservative envelope determination. The present Thesis develops a new methodology, based on the Flutter Margin concept, that enables in real time the prediction of the „Limit Cycle‟ conditions, whenever they exist, without degrading the capability of predicting the flutter onset speed. The first part of this Thesis presents a review of the state of the art regarding the test methods available to proceed with the envelope expansion of an aircraft in altitude/airspeed and the effect of mechanical non-linearities on the aeroelastic behavior. Also, both civil and military regulations are reviewed with respect aeroelastic investigation of air vehicles. The second part of this Thesis proposes a new methodology to perform envelope expansion in real time based on the Flutter Margin concept when non-linearities, as freeplay, are present. Additionally, this methodology is validated against a Matlab/Slimulink bidimensional aeroelastic model. This model, parametric and interactive, is formulated within the state-space field and it implements the proposed methodology through two main real time modules: A signal processing module and a prediction module. The third part of this Thesis compares the final conclusions derived from the proposed methodology with those stated by the flight test community and experimental results. In summary, the main results provided by this Thesis are: 1. State of the Art review of the test methods applied to envelope expansion in altitude/airspeed and the influence of mechanical non-linearities in its identification. 2. Review of the main civil and military regulations regarding the aeroelastic verification of air vehicles and the limits set when non-linearities are present. 3. Development of a methodology for envelope expansion based on the Flutter Margin concept. 4. A Matlab/Simulink 2D-[aeroelastic model], parametric and interactive, used as a tool to validate the proposed methodology. 5. Conclusions driven from the present Thesis and comparison with experimental results.

Mathematical Analysis of the Effect of Rotor Geometry on Cup Anemometer Response

The calibration coefficients of two commercial anemometers equipped with different rotors were studied. The rotor cups had the same conical shape, while the size and distance to the rotation axis varied.The analysis was based on the 2-cup positions analytical model, derived using perturbation methods to include second-order effects such as pressure distribution along the rotating cups and friction.Thecomparison with the experimental data indicates a nonuniformdistribution of aerodynamic forces on the rotating cups, with higher forces closer to the rotating axis. The 2-cup analytical model is proven to be accurate enough to study the effect of complex forces on cup anemometer performance.

Metodología de Ejecución y Explotación de los Ensayos en Vuelo de Flameo

El flameo o flutter es un fenómeno vibratorio debido a la interacción de fuerzas inerciales, elásticas y aerodinámicas. Consiste en un intercambio de energía, que se puede observar en el cambio de amortiguamientos, entre dos o más modos estructurales, denominados modos críticos, cuyas frecuencias tienden a acercarse (coalescencia de frecuencias). Los ensayos en vuelo de flameo suponen un gran riesgo debido a la posibilidad de una perdida brusca de estabilidad aeroelástica (flameo explosivo) con la posibilidad de destrucción de la aeronave. Además existen otros fenómenos asociados que pueden aparecer como el LCO (Limit Cycle Oscillation) y la interacción con los mandos de vuelo. Debido a esto, se deben llevar a cabo análisis exhaustivos, que incluyen GVT (vibraciones en tierra), antes de comenzar los ensayos en vuelo, y estos últimos deben ser ejecutados con robustos procedimientos. El objetivo de los ensayos es delimitar la frontera de estabilidad sin llegar a ella, manteniéndose siempre dentro de la envolvente estable de vuelo. Para lograrlo se necesitan métodos de predicción, siendo el “Flutter Margin”, el más utilizado. Para saber cuánta estabilidad aeroelástica tiene el avión y lo lejos que está de la frontera de estabilidad (a través de métodos de predicción) los parámetros modales, en particular la frecuencia y el amortiguamiento, son de vital importancia. El ensayo en vuelo consiste en la excitación de la estructura a diferentes condiciones de vuelo, la medición de la respuesta y su análisis para obtener los dos parámetros mencionados. Un gran esfuerzo se dedica al análisis en tiempo real de las señales como un medio de reducir el riesgo de este tipo de ensayos. Existen numerosos métodos de Análisis Modal, pero pocos capaces de analizar las señales procedentes de los ensayos de flameo, debido a sus especiales características. Un método novedoso, basado en la Descomposición por Valores Singulares (SVD) y la factorización QR, ha sido desarrollado y aplicado al análisis de señales procedentes de vuelos de flameo del F-18. El método es capaz de identificar frecuencia y amortiguamiento de los modos críticos. El algoritmo se basa en la capacidad del SVD para el análisis, modelización y predicción de series de datos con características periódicas y en su capacidad de identificar el rango de una matriz, así como en la aptitud del QR para seleccionar la mejor base vectorial entre un conjunto de vectores para representar el campo vectorial que forman. El análisis de señales de flameo simuladas y reales demuestra, bajo ciertas condiciones, la efectividad, robustez, resistencia al ruido y capacidad de automatización del método propuesto. ABSTRACT Flutter involves the interaction between inertial, elastic and aerodynamic forces. It consists on an exchange of energy, identified by change in damping, between two or more structural modes, named critical modes, whose frequencies tend to get closer to each other (frequency coalescence). Flight flutter testing involves high risk because of the possibility of an abrupt lost in aeroelastic stability (hard flutter) that may lead to aircraft destruction. Moreover associated phenomena may happen during the flight as LCO (Limit Cycle Oscillation) and coupling with flight controls. Because of that, intensive analyses, including GVT (Ground Vibration Test), have to be performed before beginning the flights test and during them consistent procedures have to be followed. The test objective is to identify the stability border, maintaining the aircraft always inside the stable domain. To achieve that flutter speed prediction methods have to be used, the most employed being the “Flutter Margin”. In order to know how much aeroelastic stability remains and how far the aircraft is from the stability border (using the prediction methods), modal parameters, in particular frequency and damping are paramount. So flight test consists in exciting the structure at various flight conditions, measuring the response and identifying in real-time these two parameters. A great deal of effort is being devoted to real-time flight data analysis as an effective way to reduce the risk. Numerous Modal Analysis algorithms are available, but very few are suitable to analyze signals coming from flutter testing due to their special features. A new method, based on Singular Value Decomposition (SVD) and QR factorization, has been developed and applied to the analysis of F-18 flutter flight-test data. The method is capable of identifying the frequency and damping of the critical aircraft modes. The algorithm relies on the capability of SVD for the analysis, modelling and prediction of data series with periodic features and also on its power to identify matrix rank as well as QR competence for selecting the best basis among a set of vectors in order to represent a given vector space of such a set. The analysis of simulated and real flutter flight test data demonstrates, under specific conditions, the effectiveness, robustness, noise-immunity and the capability for automation of the method proposed.

Fenómenos de galope en piezas prismáticas con sección en H

El objetivo de esta Tesis es el estudio sistemático del fenómeno aeroelástico de galope de una viga prismática con sección transversal en H. En particular, se pretende analizar la influencia de determinados parámetros geométricos que definen la geometría de la sección y el efecto del ángulo de ataque de la corriente sobre la estabilidad del fenómeno de oscilación. El interés en el estudio de esta forma de la sección transversal de una viga se basa en el hecho de que, con cierta frecuencia, se sigue utilizando, por su buen comportamiento estructural, en construcciones civiles como tableros y tirantes de puentes de gran longitud, señalizaciones, luminarias y, en general, en grandes estructuras metálicas. Los parámetros geométricos seleccionados para su estudio son tres: el espesor de las dos alas verticales, su porosidad y el espesor de sendas ranuras en la zona de unión entre el alma y las alas de la sección. Inicialmente se han realizado ensayos estáticos en un túnel aerodinámico con objeto de obtener las cargas aerodinámicas y poder aplicar el criterio casi-estático de Glauert - Den Hartog. En estos ensayos, se han medido tanto las fuerzas de sustentación y resistencia aerodinámicas como las distribuciones de presiones en la superficie de la zona central de la sección. Posteriormente, se han realizado ensayos de visualización de flujo, utilizando un túnel de humos, para poder comprender mejor el comportamiento físico del aire alrededor del cuerpo. El estudio estático se ha completado realizando ensayos con PIV, que permiten realizar una medida precisa de la velocidad del campo fluido. Por último, se han realizado ensayos dinámicos en otro túnel aerodinámico con objeto de contrastar la aplicabilidad del criterio casi-estático, la velocidad de inicio de galope y la amplitud de las oscilaciones producidas. Los resultados muestran que el espesor de las alas verticales, aunque modifica apreciablemente la magnitud de las cargas aerodinámicas, no afecta sustancialmente a la estabilidad a galope, mientras que su porosidad sí ejerce un control efectivo que permite reducir este fenómeno e incluso evitarlo, en determinados casos. En todas las situaciones el criterio de Glauert-Glauert - Den Hartog ha resultado ser aplicable y, en ocasiones, más restrictivo que los resultados obtenidos en ensayos dinámicos. La presencia de una ranura en la zona de unión entre el alma y las dos alas, o su combinación con la porosidad en las alas, reduce la intensidad de galope, incrementando la velocidad crítica de su inicio, pero no logra hacer que desaparezca, como se justificará en el desarrollo del trabajo. ABSTRACT Galloping is a type of aeroelastic instability characterized by a large amplitude oscillation at the natural frequency of the structure, producing normal motion to wind. It usually occurs in slender bodies lightly damped at sufficiently high speeds. In this thesis an experimental study has been developed on the galloping instability of a beam with H cross section, which is inscribed in a rectangle with a slender 1: 2. A systematic study has been carried out of the influence of three different geometric parameters on galloping, in the range of 0 to 90° angle of attack of the incoming stream. These parameters are the thickness of the flanges of the section, the porosity of the flanges, the thickness of two slots along the span, in the area between the flange and the central core of the section, and the combination effect of the last two parameters. First of all, static tests have been performed in a wind tunnel to determine the lift and drag forces by using a balance and then the quasi-static stability criterion due to Glauert-Den Hartog has been determined. Later, to better understand and verify the results previously obtained, it has also been tested the pressure distribution on the surface of the model, flow visualization in a second, smoke, wind tunnel, and Particle Image Velocimetry (PIV) study of the flow around the section, in a third tunnel. Finally, dynamic tests have been performed, on a fourth wind tunnel, for determining the amplitude and frequency of the oscillations in each case. The results have been collected in stability diagrams for each geometric parameter studied. These results show that the more critical angles of attack of the stream for galloping behavior are close to 0 and 90º. It has been found that the thickness of the flanges, although changes the galloping behavior on the section, does not reduce it substantially. However, the porosity in the flanges has been proved to be an efficient control mechanism on galloping, and even above 40% porosity, it disappears. The thickness of the slot studied and its combination with the porosity in the flanges in some cases reduces the aerodynamic forces appreciably but fail to prevent galloping at all angles of attack.

Influencia del viento transversal en sistemas ferroviarios = Cross-wind effects on railway infrastructure

El viento, como factor medio-ambiental, ha sido objeto de numerosos estudios por los efectos que induce tanto en vehículos como en estructuras. Dentro del ámbito ferroviario, las cargas aerodinámicas debidas a la acción del viento transversal pueden poner en compromiso la seguridad de los vehículos en circulación, pudiendo llegar a ocasionar el vuelco del mismo. Incluso el sistema de cables encargado de realizar el suministro eléctrico necesario para la tracción del tren, conocido como catenaria, es sensible a la acción del viento. De hecho, al igual que ocurre en ciertas estructuras de cables, la interacción entre las fuerzas aerodinámicas no estacionarias y la catenaria puede ocasionar la aparición de oscilaciones de gran amplitud debido al fenómeno de galope. Una forma sencilla de reducir los efectos no deseados de la acción del viento, es la instalación de barreras cortavientos aguas arriba de la zona que se desea proteger. La instalación de estos dispositivos, reduce la velocidad en la estela generada, pero también modifica las propiedades del flujo dentro de la misma. Esta alteración de las condiciones del flujo puede contribuir a la aparición del fenómeno de galope en estructuras caracterizadas por su gran flexibilidad, como la catenaria ferroviaria. Estos dos efectos contrapuestos hacen evidente la importancia de mantener cierta visión global del efecto introducido por la instalación de barreras cortavientos en la plataforma ferroviaria. A lo largo de este documento, se evalúa desde un enfoque multidisciplinar el efecto inducido por las barreras cortavientos en varios subsistemas ferroviarios. Por un lado se analizan las mejoras en la estabilidad lateral del vehículo mediante una serie de ensayos en túnel de viento. La medición de la distribución de presiones en la superficie de un modelo bidimensional de vehículo ferroviario proporciona una buena estimación del nivel de protección que se consigue en función de la altura de una barrera cortavientos. Por otra parte, se analiza la influencia del mismo juego de barreras cortavientos en las características del flujo situado sobre la plataforma ferroviaria, mediante la utilización de anemometría de hilo caliente (HWA) y velocimetría de imágenes de párticulas (PIV). En particular se centra la atención en las características en la posición correspondiente a los hilos conductores de la catenaria. En la última parte del documento, se realiza un análisis simplificado de la aparición oscilaciones en la catenaria, por el efecto de la inestabilidad de galope. La información obtenida sobre las características del flujo se combinan con las propiedades aerodinámicas del hilo de contacto, obtenidas en mediante una serie de ensayos en túnel de viento. De esta manera se realiza una evaluación del riesgo a la aparición de este tipo de inestabilidad aeroeslástica aplicada a una catenaria ferroviaria situada sobre un viaducto tipo. ABSTRACT Wind as an environmental factor may induce undesirable effects on vehicles and structures. The analysis of those effects has caught the attention of several researchers. Concerning the railway system, cross-wind induces aerodynamic loads on rolling stock that may increase the overturning risk of the vehicle, threatening its safe operation. Even the cable system responsible to provide the electric current required for the train traction, known as the railway overhead or catenary, is sensitive to the wind action. In fact, the interaction between the unsteady aerodynamic forces and the railway overhead may trigger the development of undamped oscillations due to galloping phenomena. The inclusion of windbreaks upstream the area that needs wind protection is a simple mean to palliate the undesirable effects caused by the wind action. Although the presence of this wind protection devices reduces the wind speed downstream, they also modify the flow properties inside their wake. This modification on the flow characteristics may ease the apparition of the galloping phenomena on flexible structures, such as the railway overhead. This two opposite effects require to maintain a global perspective on the analysis of the influence of the windbreak presence. In the present document, a multidisciplinary analysis on the effect induced by windbreaks on several railways subsystems is conducted. On the one hand, a set of wind tunnel tests is conducted to assess the improvement on the rolling stock lateral stability. The qualitative estimation of the shelter effect, as function of the windbreak height, is established through the pressure distribution measured on the surface of a two-dimensional train model. On the other hand, the flow properties above the railway platform are assessed using the same set of windbreaks. Two experimental techniques are used to measure the flow properties, hot-wire anemometry (HWA) and particle image velocimetry (PIV). In particular, the attention is focused on the flow characteristics on the contact wire location. A simplified analysis on the catenary oscillations due to galloping phenomena is conducted in the last part of the document. Both, the flow characterization performed via PIV and the aerodynamic properties of the contact wire cross-section are combined. In this manner, the risk of the aeroelastic instabilities on a railway overhead placed on a railway bridge is assessed through a practical application.

Global Stability Analysis of Turbulent Transonic Flows on Airfoil geometries

La aparición de inestabilidades en un flujo es un problema importante que puede afectar a algunas aplicaciones aerodinámicas. De hecho existen diferentes tipos de fenómenos no-estacionarios que actualmente son tema de investigación; casos como la separación a altos ángulos de ataque o el buffet transónico son dos ejemplos de cierta relevancia. El análisis de estabilidad global permite identificar la aparición de dichas condiciones inestables, proporcionando información importante sobre la región donde la inestabilidad es dominante y sobre la frecuencia del fenómeno inestable. La metodología empleada es capaz de calcular un flujo base promediado mediante una discretización con volúmenes finitos y posteriormente la solución de un problema de autovalores asociado a la linealización que aparece al perturbar el flujo base. El cálculo numérico se puede dividir en tres pasos: primero se calcula una solución estacionaria para las ecuaciones RANS, luego se extrae la matriz del Jacobiano que representa el problema linealizado y finalmente se deriva y se resuelve el problema de autovalores generalizado mediante el método iterativo de Arnoldi. Como primer caso de validación, la técnica descrita ha sido aplicada a un cilindro circular en condiciones laminares para detectar el principio de las oscilaciones de los vórtices de von Karman, y se han comparado los resultados con experimentos y cálculos anteriores. La parte más importante del estudio se centra en el análisis de flujos compresibles en régimen turbulento. La predicción de la aparición y la progresión de flujo separado a altos ángulos de ataque se han estudiado en el perfil NACA0012 en condiciones tanto subsónicas como supersónicas y en una sección del ala del A310 en condiciones de despegue. Para todas las geometrías analizadas, se ha podido observar que la separación gradual genera la aparición de un modo inestable específico para altos ángulos de ataque siempre mayores que el ángulo asociado al máximo coeficiente de sustentación. Además, se ha estudiado el problema adjunto para obtener información sobre la zona donde una fuerza externa provoca el máximo cambio en el campo fluido. El estudio se ha completado calculando el mapa de sensibilidad estructural y localizando el centro de la inestabilidad. En el presente trabajo de tesis se ha analizado otro importante fenómeno: el buffet transónico. En condiciones transónicas, la interacción entre la onda de choque y la capa límite genera una oscilación de la posición de la onda de choque y, por consiguiente, de las fuerzas aerodinámicas. El conocimiento de las condiciones críticas y su origen puede ayudar a evitar la oscilación causada por estas fuerzas. Las condiciones para las cuales comienza la inestabilidad han sido calculadas y comparadas con trabajos anteriores. Por otra parte, los resultados del correspondiente problema adjunto y el mapa de sensibilidad se han obtenido por primera vez para el buffet, indicando la región del dominio que sera necesario modificar para crear el mayor cambio en las propiedades del campo fluido. Dado el gran consumo de memoria requerido para los casos 3D, se ha realizado un estudio sobre la reducción del domino con la finalidad de reducirlo a la región donde está localizada la inestabilidad. La eficacia de dicha reducción de dominio ha sido evaluada investigando el cambio en la dimensión de la matriz del Jacobiano, no resultando muy eficiente en términos del consumo de memoria. Dado que el buffet es un problema en general tridimensional, el análisis TriGlobal de una geometría 3D podría considerarse el auténtico reto futuro. Como aproximación al problema, un primer estudio se ha realizado empleando una geometría tridimensional extruida del NACA00f2. El cálculo del flujo 3D y, por primera vez en casos tridimensionales compresibles y turbulentos, el análisis de estabilidad TriGlobal, se han llevado a cabo. La comparación de los resultados obtenidos con los resultados del anterior modelo 2D, ha permitido, primero, verificar la exactitud del cálculo 2D realizado anteriormente y también ha proporcionado una estimación del consumo de memoria requerido para el caso 3D. ABSTRACT Flow unsteadiness is an important problem in aerodynamic applications. In fact, there are several types of unsteady phenomena that are still at the cutting edge of research in the field; separation at high angles of attack and transonic buffet are two important examples. Global Stability Analysis can identify the unstable onset conditions, providing important information about the instability location in the domain and the frequency of the unstable phenomenon. The methodology computes a base flow averaged state based on a finite volume discretization and a solution for a generalized eigenvalue problem corresponding to the perturbed linearized equations. The numerical computation is then performed in three steps: first, a steady solution for the RANS equation is computed; second, the Jacobian matrix that represents the linearized problem is obtained; and finally, the generalized eigenvalue problem is derived and solved with an Arnoldi iterative method. As a first validation test, the technique has been applied on a laminar circular cylinder in order to detect the von Karman vortex shedding onset, comparing the results with experiments and with previous calculations. The main part of the study focusses on turbulent and compressible cases. The prediction of the origin and progression of separated flows at high angles of attack has been studied on the NACA0012 airfoil at subsonic and transonic conditions and for the A310 airfoil in take-off configuration. For all the analyzed geometries, it has been found that gradual separation generates the appearance of one specific unstable mode for angles of attack always greater than the ones related to the maximum lift coefficient. In addition, the adjoint problem has been studied to suggest the location of an external force that results in the largest change to the flow field. From the direct and the adjoint analysis the structural sensitivity map has been computed and the core of the instability has been located. The other important phenomenon analyzed in this work is the transonic buffet. In transonic conditions, the interaction between the shock wave and the boundary layer leads to an oscillation of the shock location and, consequently, of the aerodynamic forces. Knowing the critical operational conditions and its origin can be helpful in preventing such fluctuating forces. The instability onset has then been computed and compared with the literature. Moreover, results of the corresponding adjoint problem and a sensitivity map have been provided for the first time for the buffet problem, indicating the region that must be modified to create the biggest change in flow field properties. Because of the large memory consumption required when a 3D case is approached, a domain reduction study has been carried out with the aim of limiting the domain size to the region where the instability is located. The effectiveness of the domain reduction has been evaluated by investigating the change in the Jacobian matrix size, not being very efficient in terms of memory consumption. Since buffet is a three-dimensional problem, TriGlobal stability analysis can be seen as a future challenge. To approximate the problem, a first study has been carried out on an extruded three-dimensional geometry of the NACA0012 airfoil. The 3D flow computation and the TriGlobal stability analysis have been performed for the first time on a compressible and turbulent 3D case. The results have been compared with a 2D model, confirming that the buffet onset evaluated in the 2D case is well detected. Moreover, the computation has given an indication about the memory consumption for a 3D case.

Hysteresis in transverse galloping: the role of the inflection points

Transverse galloping is here considered as a one-degree-of-freedom oscillator subjected to aerodynamic forces, which are described by using the quasi-steady hypothesis. The hysteresis of transverse galloping is also analyzed. Approximate solutions of the model are obtained by assuming that the aerodynamic and damping forces are much smaller than the inertial and stiffness ones. The analysis of the approximate solution, which is obtained by means of the method of Krylov–Bogoliubov, reveals the existing link between the hysteresis phenomenon and the number of inflection points at the aerodynamic force coefficient curve, Cy(α)Cy(α); CyCy and αα being, respectively, the force coefficient normal to the incident flow and the angle of attack. The influence of the position of these inflection points on the range of flow velocities in which hysteresis takes place is also analyzed.