Fourier analysis of the aerodynamic behavior of cup anemometers

The calibration results (the transfer function) of an anemometer equipped with several cup rotors were analyzed and correlated with the aerodynamic forces measured on the isolated cups in a wind tunnel. The correlation was based on a Fourier analysis of the normal-to-the-cup aerodynamic force. Three different cup shapes were studied: typical conical cups, elliptical cups and porous cups (conical-truncated shape). Results indicated a good correlation between the anemometer factor, K, and the ratio between the first two coefficients in the Fourier series decomposition of the normal-to-the-cup aerodynamic force

Influence of aerodynamic characteristics of H beams on galloping stability

This paper presents the experimental study developed on a prismatic beam with H section, sometimes used in bridges as suspenders, vertical bars or decks. The purpose of this study is to understand the physical behavior of the air around this type of section, in order to reduce the aerodynamic loads, the onset speed of galloping and even to avoid it. To achieve this, a study of the influence of all geometric parameters that define the section has been developed. Previously, the most interesting configurations have been selected using a smoke flow visualization technique in the wind-tunnel, then the corresponding static aerodynamic loads were measured, completed with dynamic tests and, finally, the parameters governing the phenomenon of galloping determined.

Static and Dynamic Experimental Analysis of the Galloping Stability of Porous H-Section Beams

The phenomenon of self-induced vibrations of prismatic beams in a cross-flow has been studied for decades, but it is still of great interest due to their important effects in many different industrial applications. This paper presents the experimental study developed on a prismatic beam with H-section.The aim of this analysis is to add some additional insight into the behaviour of the flow around this type of bodies, in order to reduce galloping and even to avoid it. The influence of some relevant geometrical parameters that define the H-section on the translational galloping behaviour of these beams has been analysed. Wind loads coefficients have been measured through static wind tunnel tests and the Den Hartog criterion applied to elucidate the influence of geometrical parameters on the galloping properties of the bodies under consideration.These results have been completed with surface pressure distribution measurements and, besides, dynamic tests have been also performed to verify the static criterion. Finally, the morphology of the flow past the tested bodies has been visualised by using smoke visualization techniques. Since the rectangular section beam is a limiting case of the H-section configuration, the results here obtained are compared with the ones published in the literature concerning rectangular configurations; the agreement is satisfactory.

Investigación experimental del flujo aerodinámico sobre helipuertos embarcados

La investigación del flujo aerodinámico sobre helipuertos embarcados se encuentra estrechamente relacionada con la operación segura de las aeronaves, pues las condiciones del flujo que tiene lugar en ese entorno pueden exceder los límites para los que están certificadas dichas aeronaves. El ambiente aerodinámico en las inmediaciones de un barco es altamente complejo y se encuentra influenciado por gran número de factores (chimeneas, antenas, mástiles, etc.) relacionados con la configuración específica del propio barco. El flujo objeto de investigación corresponde a la estela que se desarrolla sobre la cubierta de vuelo de una fragata, el cual está fuertemente influenciado por la superestructura de la misma, y que cualitativamente es similar al flujo que tiene lugar entre edificios altos o helipuertos situados en áreas urbanas, pues comprende estructuras tipo caja, con bordes afilados, que generan flujos tridimensionales altamente turbulentos. En esta Tesis se aborda el estudio del problema desde el punto de vista experimental, mediante simulación en túnel aerodinámico y medida de las variables del campo fluido sobre maquetas de fragatas a escala reducida. Las herramientas empleadas para tal cometido, han sido técnicas experimentales, tales como la visualización del flujo, la velocimetría láser por imágenes de partículas, la anemometría láser Doppler y los scanners electrónicos de presión, que han permitido investigar el flujo problema con objeto de obtener información, y adquirir así, un conocimiento más profundo de dicho flujo. La explotación de este conocimiento, ha dado lugar al diseño de una nueva solución, basada en la modificación de geometría básica de la fragata, por medio del cambio de la curvatura del techo del hangar, permitiendo suavizar el escalón descendente que se produce aguas abajo del mismo. Las geometrías modificadas han sido ensayada en túnel mediante la misma metodología empleada para la fragata original, de modo que, ha podido establecerse un análisis comparativo, para valorar la efectividad de la solución propuesta, el cual ha mostrado resultados satisfactorios, retirando el flujo adverso de la zona de operación de helicópteros y desplazándolo hacia el hangar, donde resulta menos peligroso, de modo que se reduce la carga del piloto y los riesgos de accidente durante las operaciones a bordo de embarcaciones. ABSTRACT The investigation of aerodynamic flow above the ship’s heliports is directly related to the aircraft safe operation, because the environment flow conditions may exceed the aircraft certification limits. Aerodynamic ship’s environment is highly complex and it is influenced by a large number of factors (stacks, antennae, masts, …) related to each specific ship configuration. The flow under investigation occurs into the wake produced above the flight deck of a frigate, that is strongly influenced by the superstructure. This flow is similar to one produced around tall buildings or heliports located in urban areas, thus in both of them, the air is flowing around sharp-edges box-like structures, producing three-dimensional and highly turbulent flows. This Thesis studies the problem from an experimental point of view, by means of wind tunnel simulations and measurements of the flow field around reduced scale frigates models. Tools used in this work are the experimental techniques, as flow visualization, particle image velocimetry, laser Doppler anemometry and pressure electronic scanners. These techniques provide information about the flow in order to obtain a more complete insight of this kind of flows. The exploitation of this insight is used for the design of a new flow control concept, based on the modification of the basic frigate geometry. This new design consists in the hangar roof curvature modification that produces a smoothing of the descendent step located downstream the hangar. Modified geometries are tested in wind tunnel by means of the same methodology as the original frigate, thus a comparative analysis is established in order to perform an assessment of effectiveness. This analysis has shown good results in displacing the adverse flow from the helicopter operation path to the nearest hangar region, reducing the pilot load and the accident risks during on board operations.

Aerodynamic Study of Airfoils with Leading Edge Imperfections at Low Reynolds Number

A study has been made on the influence of the leading edge imperfections in airfoils used in different devices relating their aerodynamic performances. Wind tunnel tests have been made at different Reynolds numbers and angle of attacks in order to show this effect. Later, a quantitative study of the aerodynamic properties has been made based on the different leading edge imperfections and their size.

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.

Transverse galloping of two-dimensional bodies having a rhombic cross-section

Transverse galloping is a type of aeroelastic instability characterized by oscillations perpendicular to wind direction, large amplitude and low frequency, which appears in some elastic two-dimensional bluff bodies when they are subjected to an incident flow, provided that the flow velocity exceeds a threshold critical value. Understanding the galloping phenomenon of different cross-sectional geometries is important in a number of engineering applications: for energy harvesting applications the interest relies on strongly unstable configurations but in other cases the purpose is to avoid this type of aeroelastic phenomenon. In this paper the aim is to analyze the transverse galloping behavior of rhombic bodies to understand, on the one hand, the dependence of the instability with a geometrical parameter such as the relative thickness and, on the other hand, why this cross-section shape, that is generally unstable, shows a small range of relative thickness values where it is stable. Particularly, the non-galloping rhombus-shaped prism?s behavior is revised through wind tunnel experiments. The bodies are allowed to freely move perpendicularly to the incoming flow and the amplitude of movement and pressure distributions on the surfaces is measured.

On the harmonic analysis of cup anemometer rotation speed: A principle to monitor performance and maintenance status of rotating meteorological sensors

The calibration results of one anemometer equipped with several rotors, varying their size, were analyzed. In each case, the 30-pulses pert turn output signal of the anemometer was studied using Fourier series decomposition and correlated with the anemometer factor (i.e., the anemometer transfer function). Also, a 3-cup analytical model was correlated to the data resulting from the wind tunnel measurements. Results indicate good correlation between the post-processed output signal and the working condition of the cup anemometer. This correlation was also reflected in the results from the proposed analytical model. With the present work the possibility of remotely checking cup anemometer status, indicating the presence of anomalies and, therefore, a decrease on the wind sensor reliability is revealed.

Galloping instabilities of Z-shaped shading louvers

Modern design of civil constructions such as office blocks, airport terminal buildings, factories, etc. incorporates more and more environmental considerations that lead to, amongst other elements, the use of glazed façades with shading devices to optimize energy consumption. These shading devices, normally slats or louvers, are very flexible structures exposed to the action of wind, and therefore aeroelastic effects such as galloping must be taken into account in their design. A typical cross-section for such elements is a Z-shaped profile made out of a central web and two side wings. The results of a parametric analysis based on static wind tunnel tests and performed on different Z-shaped louvers to determine translational galloping instability regions are presented in this paper.

Bridge windshield design to avoid aeroelastic phenomena

Since in 1940 the Tacoma Narrows Bridge was destroyed by the wind, aeroelastic instabilities have been recognized as one of the most challenging aspects of bridge design. They can produce long-term fatigue failure through vortex induced vibrations, or sudden collapse through self-excited flutter. These vibrations may also cause discomfort for the users and temporary closure of the bridge. Wind tunnel studies are a very helpful tool to understand these phenomena. By means of them, the critical wind speed at which vortex induced vibration and flutter appear can be precisely determined and the design of the bridge can be reconsidered in the early steps of the process. In this paper, an optimum design of the bridge section is sought. One of the most relevant parameters that influence the stability of a certain deck is the porosity of the barriers. Section model tests have been carried out to find whether an optimum value of the porosity of the barrier exists. This value or range of values must present neither vortex induced vibration nor flutter.

Vibroacoustic Problems in High Speed Trains

Passengers comfort in terms of acoustic noise levels is a key train design parameter, especially relevant in high speed trains, where the aerodynamic noise is dominant. The aim of the work, described in this paper, is to make progress in the understanding of the flow field around high speed trains in an open field, which is a subject of interest for many researchers with direct industrial applications, but also the critical configuration of the train inside a tunnel is studied in order to evaluate the external loads arising from noise sources of the train. The airborne noise coming from the wheels (wheelrail interaction), which is the dominant source at a certain range of frequencies, is also investigated from the numerical and experimental points of view. The numerical prediction of the noise in the interior of the train is a very complex problem, involving many different parameters: complex geometries and materials, different noise sources, complex interactions among those sources, broad range of frequencies where the phenomenon is important, etc. During recent years a research plan is being developed at IDR/UPM (Instituto de Microgravedad Ignacio Da Riva, Universidad Politécnica de Madrid) involving both numerical simulations, wind tunnel and full-scale tests to address this problem. Comparison of numerical simulations with experimental data is a key factor in this process.

On the effects of windbreaks on the aerodynamic loads over parabolic solar troughs

Parabolic reflectors, also known as parabolic troughs, are widely used in solar thermal power plants. This kind of power plants is usually located on desert climates, where the combined action of wind and dust can be of paramount importance. In some cases it becomes necessary to protect these devices from the joined wind and sand action, which is normally accomplished through solid windbreaks. In this paper the results of a wind tunnel test campaign, of a scale parabolic trough row having different windward windbreaks, are reported. The windbreaks herein considered consist of a solid wall with an upper porous fence. Different geometrical configurations, varying the solid wall height and the separation between the parabolic trough row and the windbreak have been considered. From the measured time series, both the mean and peak values of the aerodynamic loads were determined. As it would be expected, mean aerodynamic drag, as well as peak values, decrease as the distance between the windbreak and the parabolic increases, and after a threshold value, such drag loads increase with the distance.

Optimization of the Integrated Guidance and Control for a Dual Aerodynamic Control Missile

Las futuras misiones para misiles aire-aire operando dentro de la atmósfera requieren la interceptación de blancos a mayores velocidades y más maniobrables, incluyendo los esperados vehículos aéreos de combate no tripulados. La intercepción tiene que lograrse desde cualquier ángulo de lanzamiento. Una de las principales discusiones en la tecnología de misiles en la actualidad es cómo satisfacer estos nuevos requisitos incrementando la capacidad de maniobra del misil y en paralelo, a través de mejoras en los métodos de guiado y control modernos. Esta Tesis aborda estos dos objetivos simultáneamente, al proponer un diseño integrando el guiado y el control de vuelo (autopiloto) y aplicarlo a misiles con control aerodinámico simultáneo en canard y cola. Un primer avance de los resultados obtenidos ha sido publicado recientemente en el Journal of Aerospace Engineering, en Abril de 2015, [Ibarrondo y Sanz-Aranguez, 2015]. El valor del diseño integrado obtenido es que permite al misil cumplir con los requisitos operacionales mencionados empleando únicamente control aerodinámico. El diseño propuesto se compara favorablemente con esquemas más tradicionales, consiguiendo menores distancias de paso al blanco y necesitando de menores esfuerzos de control incluso en presencia de ruidos. En esta Tesis se demostrará cómo la introducción del doble mando, donde tanto el canard como las aletas de cola son móviles, puede mejorar las actuaciones de un misil existente. Comparado con un misil con control en cola, el doble control requiere sólo introducir dos servos adicionales para accionar los canards también en guiñada y cabeceo. La sección de cola será responsable de controlar el misil en balanceo mediante deflexiones diferenciales de los controles. En el caso del doble mando, la complicación añadida es que los vórtices desprendidos de los canards se propagan corriente abajo y pueden incidir sobre las superficies de cola, alterando sus características de control. Como un primer aporte, se ha desarrollado un modelo analítico completo para la aerodinámica no lineal de un misil con doble control, incluyendo la caracterización de este efecto de acoplamiento aerodinámico. Hay dos modos de funcionamiento en picado y guiñada para un misil de doble mando: ”desviación” y ”opuesto”. En modo ”desviación”, los controles actúan en la misma dirección, generando un cambio inmediato en la sustentación y produciendo un movimiento de translación en el misil. La respuesta es rápida, pero en el modo ”desviación” los misiles con doble control pueden tener dificultades para alcanzar grandes ángulos de ataque y altas aceleraciones laterales. Cuando los controles actúan en direcciones opuestas, el misil rota y el ángulo de ataque del fuselaje se incrementa para generar mayores aceleraciones en estado estacionario, aunque el tiempo de respuesta es mayor. Con el modelo aerodinámico completo, es posible obtener una parametrización dependiente de los estados de la dinámica de corto periodo del misil. Debido al efecto de acoplamiento entre los controles, la respuesta en bucle abierto no depende linealmente de los controles. El autopiloto se optimiza para obtener la maniobra requerida por la ley de guiado sin exceder ninguno de los límites aerodinámicos o mecánicos del misil. Una segunda contribución de la tesis es el desarrollo de un autopiloto con múltiples entradas de control y que integra la aerodinámica no lineal, controlando los tres canales de picado, guiñada y cabeceo de forma simultánea. Las ganancias del autopiloto dependen de los estados del misil y se calculan a cada paso de integración mediante la resolución de una ecuación de Riccati de orden 21x21. Las ganancias obtenidas son sub-óptimas, debido a que una solución completa de la ecuación de Hamilton-Jacobi-Bellman no puede obtenerse de manera práctica, y se asumen ciertas simplificaciones. Se incorpora asimismo un mecanismo que permite acelerar la respuesta en caso necesario. Como parte del autopiloto, se define una estrategia para repartir el esfuerzo de control entre el canard y la cola. Esto se consigue mediante un controlador aumentado situado antes del bucle de optimización, que minimiza el esfuerzo total de control para maniobrar. Esta ley de alimentación directa mantiene al misil cerca de sus condiciones de equilibrio, garantizando una respuesta transitoria adecuada. El controlador no lineal elimina la respuesta de fase no-mínima característica de la cola. En esta Tesis se consideran dos diseños para el guiado y control, el control en Doble-Lazo y el control Integrado. En la aproximación de Doble-Lazo, el autopiloto se sitúa dentro de un bucle interior y se diseña independientemente del guiado, que conforma el bucle más exterior del control. Esta estructura asume que existe separación espectral entre los dos, esto es, que los tiempos de respuesta del autopiloto son mucho mayores que los tiempos característicos del guiado. En el estudio se combina el autopiloto desarrollado con una ley de guiado óptimo. Los resultados obtenidos demuestran que se consiguen aumentos muy importantes en las actuaciones frente a misiles con control canard o control en cola, y que la interceptación, cuando se lanza cerca del curso de colisión, se consigue desde cualquier ángulo alrededor del blanco. Para el misil de doble mando, la estrategia óptima resulta en utilizar el modo de control opuesto en la aproximación al blanco y utilizar el modo de desviación justo antes del impacto. Sin embargo la lógica de doble bucle no consigue el impacto cuando hay desviaciones importantes con respecto al curso de colisión. Una de las razones es que parte de la demanda de guiado se pierde, ya que el misil solo es capaz de modificar su aceleración lateral, y no tiene control sobre su aceleración axial, a no ser que incorpore un motor de empuje regulable. La hipótesis de separación mencionada, y que constituye la base del Doble-Bucle, puede no ser aplicable cuando la dinámica del misil es muy alta en las proximidades del blanco. Si se combinan el guiado y el autopiloto en un único bucle, la información de los estados del misil está disponible para el cálculo de la ley de guiado, y puede calcularse la estrategia optima de guiado considerando las capacidades y la actitud del misil. Una tercera contribución de la Tesis es la resolución de este segundo diseño, la integración no lineal del guiado y del autopiloto (IGA) para el misil de doble control. Aproximaciones anteriores en la literatura han planteado este sistema en ejes cuerpo, resultando en un sistema muy inestable debido al bajo amortiguamiento del misil en cabeceo y guiñada. Las simplificaciones que se tomaron también causan que el misil se deslice alrededor del blanco y no consiga la intercepción. En nuestra aproximación el problema se plantea en ejes inerciales y se recurre a la dinámica de los cuaterniones, eliminado estos inconvenientes. No se limita a la dinámica de corto periodo del misil, porque se construye incluyendo de modo explícito la velocidad dentro del bucle de optimización. La formulación resultante en el IGA es independiente de la maniobra del blanco, que sin embargo se ha de incluir en el cálculo del modelo en Doble-bucle. Un típico inconveniente de los sistemas integrados con controlador proporcional, es el problema de las escalas. Los errores de guiado dominan sobre los errores de posición del misil y saturan el controlador, provocando la pérdida del misil. Este problema se ha tratado aquí con un controlador aumentado previo al bucle de optimización, que define un estado de equilibrio local para el sistema integrado, que pasa a actuar como un regulador. Los criterios de actuaciones para el IGA son los mismos que para el sistema de Doble-Bucle. Sin embargo el problema matemático resultante es muy complejo. El problema óptimo para tiempo finito resulta en una ecuación diferencial de Riccati con condiciones terminales, que no puede resolverse. Mediante un cambio de variable y la introducción de una matriz de transición, este problema se transforma en una ecuación diferencial de Lyapunov que puede resolverse mediante métodos numéricos. La solución resultante solo es aplicable en un entorno cercano del blanco. Cuando la distancia entre misil y blanco es mayor, se desarrolla una solución aproximada basada en la solución de una ecuación algebraica de Riccati para cada paso de integración. Los resultados que se han obtenido demuestran, a través de análisis numéricos en distintos escenarios, que la solución integrada es mejor que el sistema de Doble-Bucle. Las trayectorias resultantes son muy distintas. El IGA preserva el guiado del misil y consigue maximizar el uso de la propulsión, consiguiendo la interceptación del blanco en menores tiempos de vuelo. El sistema es capaz de lograr el impacto donde el Doble-Bucle falla, y además requiere un orden menos de magnitud en la cantidad de cálculos necesarios. El efecto de los ruidos radar, datos discretos y errores del radomo se investigan. El IGA es más robusto, resultando menos afectado por perturbaciones que el Doble- Bucle, especialmente porque el núcleo de optimización en el IGA es independiente de la maniobra del blanco. La estimación de la maniobra del blanco es siempre imprecisa y contaminada por ruido, y degrada la precisión de la solución de Doble-Bucle. Finalmente, como una cuarta contribución, se demuestra que el misil con guiado IGA es capaz de realizar una maniobra de defensa contra un blanco que ataque por su cola, sólo con control aerodinámico. Las trayectorias estudiadas consideran una fase pre-programada de alta velocidad de giro, manteniendo siempre el misil dentro de su envuelta de vuelo. Este procedimiento no necesita recurrir a soluciones técnicamente más complejas como el control vectorial del empuje o control por chorro para ejecutar esta maniobra. En todas las demostraciones matemáticas se utiliza el producto de Kronecker como una herramienta practica para manejar las parametrizaciones dependientes de variables, que resultan en matrices de grandes dimensiones. ABSTRACT Future missions for air to air endo-atmospheric missiles require the interception of targets with higher speeds and more maneuverable, including forthcoming unmanned supersonic combat vehicles. The interception will need to be achieved from any angle and off-boresight launch conditions. One of the most significant discussions in missile technology today is how to satisfy these new operational requirements by increasing missile maneuvering capabilities and in parallel, through the development of more advanced guidance and control methods. This Thesis addresses these two objectives by proposing a novel optimal integrated guidance and autopilot design scheme, applicable to more maneuverable missiles with forward and rearward aerodynamic controls. A first insight of these results have been recently published in the Journal of Aerospace Engineering in April 2015, [Ibarrondo and Sanz-Aránguez, 2015]. The value of this integrated solution is that it allows the missile to comply with the aforementioned requirements only by applying aerodynamic control. The proposed design is compared against more traditional guidance and control approaches with positive results, achieving reduced control efforts and lower miss distances with the integrated logic even in the presence of noises. In this Thesis it will be demonstrated how the dual control missile, where canard and tail fins are both movable, can enhance the capabilities of an existing missile airframe. Compared to a tail missile, dual control only requires two additional servos to actuate the canards in pitch and yaw. The tail section will be responsible to maintain the missile stabilized in roll, like in a classic tail missile. The additional complexity is that the vortices shed from the canard propagate downstream where they interact with the tail surfaces, altering the tail expected control characteristics. These aerodynamic phenomena must be properly described, as a preliminary step, with high enough precision for advanced guidance and control studies. As a first contribution we have developed a full analytical model of the nonlinear aerodynamics of a missile with dual control, including the characterization of this cross-control coupling effect. This development has been produced from a theoretical model validated with reliable practical data obtained from wind tunnel experiments available in the scientific literature, complement with computer fluid dynamics and semi-experimental methods. There are two modes of operating a missile with forward and rear controls, ”divert” and ”opposite” modes. In divert mode, controls are deflected in the same direction, generating an increment in direct lift and missile translation. Response is fast, but in this mode, dual control missiles may have difficulties in achieving large angles of attack and high level of lateral accelerations. When controls are deflected in opposite directions (opposite mode) the missile airframe rotates and the body angle of attack is increased to generate greater accelerations in steady-state, although the response time is larger. With the aero-model, a state dependent parametrization of the dual control missile short term dynamics can be obtained. Due to the cross-coupling effect, the open loop dynamics for the dual control missile is not linearly dependent of the fin positions. The short term missile dynamics are blended with the servo system to obtain an extended autopilot model, where the response is linear with the control fins turning rates, that will be the control variables. The flight control loop is optimized to achieve the maneuver required by the guidance law without exceeding any of the missile aerodynamic or mechanical limitations. The specific aero-limitations and relevant performance indicators for the dual control are set as part of the analysis. A second contribution of this Thesis is the development of a step-tracking multi-input autopilot that integrates non-linear aerodynamics. The designed dual control missile autopilot is a full three dimensional autopilot, where roll, pitch and yaw are integrated, calculating command inputs simultaneously. The autopilot control gains are state dependent, and calculated at each integration step solving a matrix Riccati equation of order 21x21. The resulting gains are sub-optimal as a full solution for the Hamilton-Jacobi-Bellman equation cannot be resolved in practical terms and some simplifications are taken. Acceleration mechanisms with an λ-shift is incorporated in the design. As part of the autopilot, a strategy is defined for proper allocation of control effort between canard and tail channels. This is achieved with an augmented feed forward controller that minimizes the total control effort of the missile to maneuver. The feedforward law also maintains the missile near trim conditions, obtaining a well manner response of the missile. The nonlinear controller proves to eliminate the non-minimum phase effect of the tail. Two guidance and control designs have been considered in this Thesis: the Two- Loop and the Integrated approaches. In the Two-Loop approach, the autopilot is placed in an inner loop and designed separately from an outer guidance loop. This structure assumes that spectral separation holds, meaning that the autopilot response times are much higher than the guidance command updates. The developed nonlinear autopilot is linked in the study to an optimal guidance law. Simulations are carried on launching close to collision course against supersonic and highly maneuver targets. Results demonstrate a large boost in performance provided by the dual control versus more traditional canard and tail missiles, where interception with the dual control close to collision course is achieved form 365deg all around the target. It is shown that for the dual control missile the optimal flight strategy results in using opposite control in its approach to target and quick corrections with divert just before impact. However the Two-Loop logic fails to achieve target interception when there are large deviations initially from collision course. One of the reasons is that part of the guidance command is not followed, because the missile is not able to control its axial acceleration without a throttleable engine. Also the separation hypothesis may not be applicable for a high dynamic vehicle like a dual control missile approaching a maneuvering target. If the guidance and autopilot are combined into a single loop, the guidance law will have information of the missile states and could calculate the most optimal approach to the target considering the actual capabilities and attitude of the missile. A third contribution of this Thesis is the resolution of the mentioned second design, the non-linear integrated guidance and autopilot (IGA) problem for the dual control missile. Previous approaches in the literature have posed the problem in body axes, resulting in high unstable behavior due to the low damping of the missile, and have also caused the missile to slide around the target and not actually hitting it. The IGA system is posed here in inertial axes and quaternion dynamics, eliminating these inconveniences. It is not restricted to the missile short term dynamic, and we have explicitly included the missile speed as a state variable. The IGA formulation is also independent of the target maneuver model that is explicitly included in the Two-loop optimal guidance law model. A typical problem of the integrated systems with a proportional control law is the problem of scales. The guidance errors are larger than missile state errors during most of the flight and result in high gains, control saturation and loss of control. It has been addressed here with an integrated feedforward controller that defines a local equilibrium state at each flight point and the controller acts as a regulator to minimize the IGA states excursions versus the defined feedforward state. The performance criteria for the IGA are the same as in the Two-Loop case. However the resulting optimization problem is mathematically very complex. The optimal problem in a finite-time horizon results in an irresoluble state dependent differential Riccati equation with terminal conditions. With a change of variable and the introduction of a transition matrix, the equation is transformed into a time differential Lyapunov equation that can be solved with known numerical methods in real time. This solution results range limited, and applicable when the missile is in a close neighborhood of the target. For larger ranges, an approximate solution is used, obtained from solution of an algebraic matrix Riccati equation at each integration step. The results obtained show, by mean of several comparative numerical tests in diverse homing scenarios, than the integrated approach is a better solution that the Two- Loop scheme. Trajectories obtained are very different in the two cases. The IGA fully preserves the guidance command and it is able to maximize the utilization of the missile propulsion system, achieving interception with lower miss distances and in lower flight times. The IGA can achieve interception against off-boresight targets where the Two- Loop was not able to success. As an additional advantage, the IGA also requires one order of magnitude less calculations than the Two-Loop solution. The effects of radar noises, discrete radar data and radome errors are investigated. IGA solution is robust, and less affected by radar than the Two-Loop, especially because the target maneuvers are not part of the IGA core optimization loop. Estimation of target acceleration is always imprecise and noisy and degrade the performance of the two-Loop solution. The IGA trajectories are such that minimize the impact of radome errors in the guidance loop. Finally, as a fourth contribution, it is demonstrated that the missile with IGA guidance is capable of performing a defense against attacks from its rear hemisphere, as a tail attack, only with aerodynamic control. The studied trajectories have a preprogrammed high rate turn maneuver, maintaining the missile within its controllable envelope. This solution does not recur to more complex features in service today, like vector control of the missile thrust or side thrusters. In all the mathematical treatments and demonstrations, the Kronecker product has been introduced as a practical tool to handle the state dependent parametrizations that have resulted in very high order matrix equations.

Investigación de fenómenos de galope en cuerpos de diversa sección transversal

Los fenómenos aeroelásticos son relativamente frecuentes en las construcciones civiles modernas como edificios de oficinas, terminales de aeropuertos o fábricas. En este tipo de arquitectura aparecen con frecuencia estructuras flexibles sometidas a la acción del viento, como por ejemplo persianas formadas por láminas con distintos perfiles. Uno de estos perfiles es el perfil en Z, formado por un elemento central y dos alas laterales. Las inestabilidades de tipo galope se determinan en la práctica utilizando el criterio Glauert-Den Hartog. Este criterio precisa de la predicción exacta de la dependencia de los coeficientes aerodinámicos del ángulo de ataque. En esta tesis se presenta un estudio sistemático, tanto por métodos experimentales como numéricos de una familia completa de perfiles en Z que permite determinar sus regiones de inestabilidad frente al galope. Los análisis numéricos han sido validados con ensayos estáticos realizados en túnel de viento. Para la parte numérica se ha utilizado el código DLR TAU, que es un código de amplia utilización en la industria aeronáutica europea. En esta tesis se enfoca sobre todo a la predicción del galope en este tipo de perfiles en Z. Los resultados se presentan en forma de mapas de estabilidad. A lo largo del trabajo se realizan también comparaciones entre resultados numéricos y experimentales para varios niveles de detalle de las mallas empleadas y diversos modelos de turbulencia. ABSTRACT Aeroelastic effects are relatively common in the design of modern civil constructions such as office blocks, airport terminal buildings, and factories. Typical flexible structures exposed to the action of wind are shading devices, normally slats or louvers. A typical cross-section for such elements is a Z-shaped profile,made out of a central web and two-sidewings. Galloping instabilities are often determined in practice using the Glauert-DenHartog criterion.This criterion relies on accurate predictions of the dependence of the aerodynamic force coefficients with the angle of attack. The results of a parametric analysis based on both experimental and numerical analysis and performed on different Z-shaped louvers to determine translational galloping instability regions are presented in this thesis. These numerical analysis results have been validated with a parametric analysis of Z-shaped profiles based on static wind tunnel tests. In order to perform this validation, the DLR TAU Code, which is a standard code within the European aeronautical industry, has been used. This study highlights the focus on the numerical prediction of the effect of galloping, which is shown in a visible way, through stability maps. Comparisons between numerical and experimental data are presented with respect to various meshes and turbulence models.

Analysis of air flow past and through the 2415-3S airfoil for an unmanned aerial vehicle with internal propulsion system

This paper deals with the prediction of velocity fields on the 2415-3S airfoil which will be used for an unmanned aerial vehicle with internal propulsion system and in this way analyze the air flow through an internal duct of the airfoil using computational fluid dynamics. The main objective is to evaluate the effect of the internal air flow past the airfoil and how this affects the aerodynamic performance by means of lift and drag forces. For this purpose, three different designs of the internal duct were studied; starting from the base 2415-3S airfoil developed in previous investigation, basing on the hypothesis of decreasing the flow separation produced when the propulsive airflow merges the external flow, and in this way obtaining the best configuration. For that purpose, an exhaustive study of the mesh sensitivity was performed. It was used a non-structured mesh since the computational domain is three-dimensional and complex. The selected mesh contains approximately 12.5 million elements. Both the computational domain and the numerical solution were made with commercial CAD and CFD software, respectively. Air, incompressible and steady was analyzed. The boundary conditions are in concordance with experimental setup in the AF 6109 wind tunnel. The k-e model is utilized to describe the turbulent flow process as followed in references. Results allowed obtaining velocity contours as well as lift and drag coefficients and also the location of separation and reattachment regions in some cases for zero degrees of angle of attack on the internal and external surfaces of the airfoil. Finally, the selection of the configuration with the best aerodynamic performance was made, selecting the option without curved baffles.