Contribución al estudio de las metodologías de cálculo realista con incertidumbre (BEPU), dentro del análisis determinista de seguridad de plantas nucleares

El análisis determinista de seguridad (DSA) es el procedimiento que sirve para diseñar sistemas, estructuras y componentes relacionados con la seguridad en las plantas nucleares. El DSA se basa en simulaciones computacionales de una serie de hipotéticos accidentes representativos de la instalación, llamados escenarios base de diseño (DBS). Los organismos reguladores señalan una serie de magnitudes de seguridad que deben calcularse en las simulaciones, y establecen unos criterios reguladores de aceptación (CRA), que son restricciones que deben cumplir los valores de esas magnitudes. Las metodologías para realizar los DSA pueden ser de 2 tipos: conservadoras o realistas. Las metodologías conservadoras utilizan modelos predictivos e hipótesis marcadamente pesimistas, y, por ello, relativamente simples. No necesitan incluir un análisis de incertidumbre de sus resultados. Las metodologías realistas se basan en hipótesis y modelos predictivos realistas, generalmente mecanicistas, y se suplementan con un análisis de incertidumbre de sus principales resultados. Se les denomina también metodologías BEPU (“Best Estimate Plus Uncertainty”). En ellas, la incertidumbre se representa, básicamente, de manera probabilista. Para metodologías conservadores, los CRA son, simplemente, restricciones sobre valores calculados de las magnitudes de seguridad, que deben quedar confinados en una “región de aceptación” de su recorrido. Para metodologías BEPU, el CRA no puede ser tan sencillo, porque las magnitudes de seguridad son ahora variables inciertas. En la tesis se desarrolla la manera de introducción de la incertidumbre en los CRA. Básicamente, se mantiene el confinamiento a la misma región de aceptación, establecida por el regulador. Pero no se exige el cumplimiento estricto sino un alto nivel de certidumbre. En el formalismo adoptado, se entiende por ello un “alto nivel de probabilidad”, y ésta corresponde a la incertidumbre de cálculo de las magnitudes de seguridad. Tal incertidumbre puede considerarse como originada en los inputs al modelo de cálculo, y propagada a través de dicho modelo. Los inputs inciertos incluyen las condiciones iniciales y de frontera al cálculo, y los parámetros empíricos de modelo, que se utilizan para incorporar la incertidumbre debida a la imperfección del modelo. Se exige, por tanto, el cumplimiento del CRA con una probabilidad no menor a un valor P0 cercano a 1 y definido por el regulador (nivel de probabilidad o cobertura). Sin embargo, la de cálculo de la magnitud no es la única incertidumbre existente. Aunque un modelo (sus ecuaciones básicas) se conozca a la perfección, la aplicación input-output que produce se conoce de manera imperfecta (salvo que el modelo sea muy simple). La incertidumbre debida la ignorancia sobre la acción del modelo se denomina epistémica; también se puede decir que es incertidumbre respecto a la propagación. La consecuencia es que la probabilidad de cumplimiento del CRA no se puede conocer a la perfección; es una magnitud incierta. Y así se justifica otro término usado aquí para esta incertidumbre epistémica: metaincertidumbre. Los CRA deben incorporar los dos tipos de incertidumbre: la de cálculo de la magnitud de seguridad (aquí llamada aleatoria) y la de cálculo de la probabilidad (llamada epistémica o metaincertidumbre). Ambas incertidumbres pueden introducirse de dos maneras: separadas o combinadas. En ambos casos, el CRA se convierte en un criterio probabilista. Si se separan incertidumbres, se utiliza una probabilidad de segundo orden; si se combinan, se utiliza una probabilidad única. Si se emplea la probabilidad de segundo orden, es necesario que el regulador imponga un segundo nivel de cumplimiento, referido a la incertidumbre epistémica. Se denomina nivel regulador de confianza, y debe ser un número cercano a 1. Al par formado por los dos niveles reguladores (de probabilidad y de confianza) se le llama nivel regulador de tolerancia. En la Tesis se razona que la mejor manera de construir el CRA BEPU es separando las incertidumbres, por dos motivos. Primero, los expertos defienden el tratamiento por separado de incertidumbre aleatoria y epistémica. Segundo, el CRA separado es (salvo en casos excepcionales) más conservador que el CRA combinado. El CRA BEPU no es otra cosa que una hipótesis sobre una distribución de probabilidad, y su comprobación se realiza de forma estadística. En la tesis, los métodos estadísticos para comprobar el CRA BEPU en 3 categorías, según estén basados en construcción de regiones de tolerancia, en estimaciones de cuantiles o en estimaciones de probabilidades (ya sea de cumplimiento, ya sea de excedencia de límites reguladores). Según denominación propuesta recientemente, las dos primeras categorías corresponden a los métodos Q, y la tercera, a los métodos P. El propósito de la clasificación no es hacer un inventario de los distintos métodos en cada categoría, que son muy numerosos y variados, sino de relacionar las distintas categorías y citar los métodos más utilizados y los mejor considerados desde el punto de vista regulador. Se hace mención especial del método más utilizado hasta el momento: el método no paramétrico de Wilks, junto con su extensión, hecha por Wald, al caso multidimensional. Se decribe su método P homólogo, el intervalo de Clopper-Pearson, típicamente ignorado en el ámbito BEPU. En este contexto, se menciona el problema del coste computacional del análisis de incertidumbre. Los métodos de Wilks, Wald y Clopper-Pearson requieren que la muestra aleatortia utilizada tenga un tamaño mínimo, tanto mayor cuanto mayor el nivel de tolerancia exigido. El tamaño de muestra es un indicador del coste computacional, porque cada elemento muestral es un valor de la magnitud de seguridad, que requiere un cálculo con modelos predictivos. Se hace especial énfasis en el coste computacional cuando la magnitud de seguridad es multidimensional; es decir, cuando el CRA es un criterio múltiple. Se demuestra que, cuando las distintas componentes de la magnitud se obtienen de un mismo cálculo, el carácter multidimensional no introduce ningún coste computacional adicional. Se prueba así la falsedad de una creencia habitual en el ámbito BEPU: que el problema multidimensional sólo es atacable desde la extensión de Wald, que tiene un coste de computación creciente con la dimensión del problema. En el caso (que se da a veces) en que cada componente de la magnitud se calcula independientemente de los demás, la influencia de la dimensión en el coste no se puede evitar. Las primeras metodologías BEPU hacían la propagación de incertidumbres a través de un modelo sustitutivo (metamodelo o emulador) del modelo predictivo o código. El objetivo del metamodelo no es su capacidad predictiva, muy inferior a la del modelo original, sino reemplazar a éste exclusivamente en la propagación de incertidumbres. Para ello, el metamodelo se debe construir con los parámetros de input que más contribuyan a la incertidumbre del resultado, y eso requiere un análisis de importancia o de sensibilidad previo. Por su simplicidad, el modelo sustitutivo apenas supone coste computacional, y puede estudiarse exhaustivamente, por ejemplo mediante muestras aleatorias. En consecuencia, la incertidumbre epistémica o metaincertidumbre desaparece, y el criterio BEPU para metamodelos se convierte en una probabilidad simple. En un resumen rápido, el regulador aceptará con más facilidad los métodos estadísticos que menos hipótesis necesiten; los exactos más que los aproximados; los no paramétricos más que los paramétricos, y los frecuentistas más que los bayesianos. El criterio BEPU se basa en una probabilidad de segundo orden. La probabilidad de que las magnitudes de seguridad estén en la región de aceptación no sólo puede asimilarse a una probabilidad de éxito o un grado de cumplimiento del CRA. También tiene una interpretación métrica: representa una distancia (dentro del recorrido de las magnitudes) desde la magnitud calculada hasta los límites reguladores de aceptación. Esta interpretación da pie a una definición que propone esta tesis: la de margen de seguridad probabilista. Dada una magnitud de seguridad escalar con un límite superior de aceptación, se define el margen de seguridad (MS) entre dos valores A y B de la misma como la probabilidad de que A sea menor que B, obtenida a partir de las incertidumbres de A y B. La definición probabilista de MS tiene varias ventajas: es adimensional, puede combinarse de acuerdo con las leyes de la probabilidad y es fácilmente generalizable a varias dimensiones. Además, no cumple la propiedad simétrica. El término margen de seguridad puede aplicarse a distintas situaciones: distancia de una magnitud calculada a un límite regulador (margen de licencia); distancia del valor real de la magnitud a su valor calculado (margen analítico); distancia desde un límite regulador hasta el valor umbral de daño a una barrera (margen de barrera). Esta idea de representar distancias (en el recorrido de magnitudes de seguridad) mediante probabilidades puede aplicarse al estudio del conservadurismo. El margen analítico puede interpretarse como el grado de conservadurismo (GC) de la metodología de cálculo. Utilizando la probabilidad, se puede cuantificar el conservadurismo de límites de tolerancia de una magnitud, y se pueden establecer indicadores de conservadurismo que sirvan para comparar diferentes métodos de construcción de límites y regiones de tolerancia. Un tópico que nunca se abordado de manera rigurosa es el de la validación de metodologías BEPU. Como cualquier otro instrumento de cálculo, una metodología, antes de poder aplicarse a análisis de licencia, tiene que validarse, mediante la comparación entre sus predicciones y valores reales de las magnitudes de seguridad. Tal comparación sólo puede hacerse en escenarios de accidente para los que existan valores medidos de las magnitudes de seguridad, y eso ocurre, básicamente en instalaciones experimentales. El objetivo último del establecimiento de los CRA consiste en verificar que se cumplen para los valores reales de las magnitudes de seguridad, y no sólo para sus valores calculados. En la tesis se demuestra que una condición suficiente para este objetivo último es la conjunción del cumplimiento de 2 criterios: el CRA BEPU de licencia y un criterio análogo, pero aplicado a validación. Y el criterio de validación debe demostrarse en escenarios experimentales y extrapolarse a plantas nucleares. El criterio de licencia exige un valor mínimo (P0) del margen probabilista de licencia; el criterio de validación exige un valor mínimo del margen analítico (el GC). Esos niveles mínimos son básicamente complementarios; cuanto mayor uno, menor el otro. La práctica reguladora actual impone un valor alto al margen de licencia, y eso supone que el GC exigido es pequeño. Adoptar valores menores para P0 supone menor exigencia sobre el cumplimiento del CRA, y, en cambio, más exigencia sobre el GC de la metodología. Y es importante destacar que cuanto mayor sea el valor mínimo del margen (de licencia o analítico) mayor es el coste computacional para demostrarlo. Así que los esfuerzos computacionales también son complementarios: si uno de los niveles es alto (lo que aumenta la exigencia en el cumplimiento del criterio) aumenta el coste computacional. Si se adopta un valor medio de P0, el GC exigido también es medio, con lo que la metodología no tiene que ser muy conservadora, y el coste computacional total (licencia más validación) puede optimizarse. ABSTRACT Deterministic Safety Analysis (DSA) is the procedure used in the design of safety-related systems, structures and components of nuclear power plants (NPPs). DSA is based on computational simulations of a set of hypothetical accidents of the plant, named Design Basis Scenarios (DBS). Nuclear regulatory authorities require the calculation of a set of safety magnitudes, and define the regulatory acceptance criteria (RAC) that must be fulfilled by them. Methodologies for performing DSA van be categorized as conservative or realistic. Conservative methodologies make use of pessimistic model and assumptions, and are relatively simple. They do not need an uncertainty analysis of their results. Realistic methodologies are based on realistic (usually mechanistic) predictive models and assumptions, and need to be supplemented with uncertainty analyses of their results. They are also termed BEPU (“Best Estimate Plus Uncertainty”) methodologies, and are typically based on a probabilistic representation of the uncertainty. For conservative methodologies, the RAC are simply the restriction of calculated values of safety magnitudes to “acceptance regions” defined on their range. For BEPU methodologies, the RAC cannot be so simple, because the safety magnitudes are now uncertain. In the present Thesis, the inclusion of uncertainty in RAC is studied. Basically, the restriction to the acceptance region must be fulfilled “with a high certainty level”. Specifically, a high probability of fulfillment is required. The calculation uncertainty of the magnitudes is considered as propagated from inputs through the predictive model. Uncertain inputs include model empirical parameters, which store the uncertainty due to the model imperfection. The fulfillment of the RAC is required with a probability not less than a value P0 close to 1 and defined by the regulator (probability or coverage level). Calculation uncertainty is not the only one involved. Even if a model (i.e. the basic equations) is perfectly known, the input-output mapping produced by the model is imperfectly known (unless the model is very simple). This ignorance is called epistemic uncertainty, and it is associated to the process of propagation). In fact, it is propagated to the probability of fulfilling the RAC. Another term used on the Thesis for this epistemic uncertainty is metauncertainty. The RAC must include the two types of uncertainty: one for the calculation of the magnitude (aleatory uncertainty); the other one, for the calculation of the probability (epistemic uncertainty). The two uncertainties can be taken into account in a separate fashion, or can be combined. In any case the RAC becomes a probabilistic criterion. If uncertainties are separated, a second-order probability is used; of both are combined, a single probability is used. On the first case, the regulator must define a level of fulfillment for the epistemic uncertainty, termed regulatory confidence level, as a value close to 1. The pair of regulatory levels (probability and confidence) is termed the regulatory tolerance level. The Thesis concludes that the adequate way of setting the BEPU RAC is by separating the uncertainties. There are two reasons to do so: experts recommend the separation of aleatory and epistemic uncertainty; and the separated RAC is in general more conservative than the joint RAC. The BEPU RAC is a hypothesis on a probability distribution, and must be statistically tested. The Thesis classifies the statistical methods to verify the RAC fulfillment in 3 categories: methods based on tolerance regions, in quantile estimators and on probability (of success or failure) estimators. The former two have been termed Q-methods, whereas those in the third category are termed P-methods. The purpose of our categorization is not to make an exhaustive survey of the very numerous existing methods. Rather, the goal is to relate the three categories and examine the most used methods from a regulatory standpoint. Special mention deserves the most used method, due to Wilks, and its extension to multidimensional variables (due to Wald). The counterpart P-method of Wilks’ is Clopper-Pearson interval, typically ignored in the BEPU realm. The problem of the computational cost of an uncertainty analysis is tackled. Wilks’, Wald’s and Clopper-Pearson methods require a minimum sample size, which is a growing function of the tolerance level. The sample size is an indicator of the computational cost, because each element of the sample must be calculated with the predictive models (codes). When the RAC is a multiple criteria, the safety magnitude becomes multidimensional. When all its components are output of the same calculation, the multidimensional character does not introduce additional computational cost. In this way, an extended idea in the BEPU realm, stating that the multi-D problem can only be tackled with the Wald extension, is proven to be false. When the components of the magnitude are independently calculated, the influence of the problem dimension on the cost cannot be avoided. The former BEPU methodologies performed the uncertainty propagation through a surrogate model of the code, also termed emulator or metamodel. The goal of a metamodel is not the predictive capability, clearly worse to the original code, but the capacity to propagate uncertainties with a lower computational cost. The emulator must contain the input parameters contributing the most to the output uncertainty, and this requires a previous importance analysis. The surrogate model is practically inexpensive to run, so that it can be exhaustively analyzed through Monte Carlo. Therefore, the epistemic uncertainty due to sampling will be reduced to almost zero, and the BEPU RAC for metamodels includes a simple probability. The regulatory authority will tend to accept the use of statistical methods which need a minimum of assumptions: exact, nonparametric and frequentist methods rather than approximate, parametric and bayesian methods, respectively. The BEPU RAC is based on a second-order probability. The probability of the safety magnitudes being inside the acceptance region is a success probability and can be interpreted as a fulfillment degree if the RAC. Furthermore, it has a metric interpretation, as a distance (in the range of magnitudes) from calculated values of the magnitudes to acceptance regulatory limits. A probabilistic definition of safety margin (SM) is proposed in the thesis. The same from a value A to other value B of a safety magnitude is defined as the probability that A is less severe than B, obtained from the uncertainties if A and B. The probabilistic definition of SM has several advantages: it is nondimensional, ranges in the interval (0,1) and can be easily generalized to multiple dimensions. Furthermore, probabilistic SM are combined according to the probability laws. And a basic property: probabilistic SM are not symmetric. There are several types of SM: distance from a calculated value to a regulatory limit (licensing margin); or from the real value to the calculated value of a magnitude (analytical margin); or from the regulatory limit to the damage threshold (barrier margin). These representations of distances (in the magnitudes’ range) as probabilities can be applied to the quantification of conservativeness. Analytical margins can be interpreted as the degree of conservativeness (DG) of the computational methodology. Conservativeness indicators are established in the Thesis, useful in the comparison of different methods of constructing tolerance limits and regions. There is a topic which has not been rigorously tackled to the date: the validation of BEPU methodologies. Before being applied in licensing, methodologies must be validated, on the basis of comparisons of their predictions ad real values of the safety magnitudes. Real data are obtained, basically, in experimental facilities. The ultimate goal of establishing RAC is to verify that real values (aside from calculated values) fulfill them. In the Thesis it is proved that a sufficient condition for this goal is the conjunction of 2 criteria: the BEPU RAC and an analogous criterion for validation. And this las criterion must be proved in experimental scenarios and extrapolated to NPPs. The licensing RAC requires a minimum value (P0) of the probabilistic licensing margin; the validation criterion requires a minimum value of the analytical margin (i.e., of the DG). These minimum values are basically complementary; the higher one of them, the lower the other one. The regulatory practice sets a high value on the licensing margin, so that the required DG is low. The possible adoption of lower values for P0 would imply weaker exigence on the RCA fulfillment and, on the other hand, higher exigence on the conservativeness of the methodology. It is important to highlight that a higher minimum value of the licensing or analytical margin requires a higher computational cost. Therefore, the computational efforts are also complementary. If medium levels are adopted, the required DG is also medium, and the methodology does not need to be very conservative. The total computational effort (licensing plus validation) could be optimized.

Bases y procesos de certificación de sistemas aéreos no tripulados

El objetivo de la tesis es el de crear unas bases de certificación para sistemas aéreos remotamente pilotados teniendo en consideración los siguientes requisitos: 1) La base ha de tener una estructura similar a la existente para los aviones tripulados. De esta manera se favorecerá una futura convergencia entre las bases de certificación según las misiones realizadas y las tecnologías empleadas por aviones tripulados y pilotados a distancia vayan convergiendo. La CS 23 y FAR 23 van a ser modificadas en profundidad en un futuro inmediato. Se ha considerado la redacción de la nueva normativa propuesta. 2) Los requisitos han de considerar los cambios definidos por las autoridades que gestionan el espacio aéreo. En Europa es SESAR JU quien gestiona el proceso. 3) Los organismos reguladores de la aviación están emitiendo consejos y recomendaciones para permitir la operación de los RPAS en el espacio aéreo no segregado. Asimismo han establecido unos principios fundamentales en los que han de basarse las bases de certificación. Se analizarán los documentos publicados al respecto por OACI, FAA y EASA que han aumentado significativamente en 2015. 4) Los altos niveles de seguridad alcanzados por la aviación han sido principalmente conseguidos gracias a la existencia de unas bases de certificación que se han actualizado frecuentemente considerando la experiencia en el diseño y la operación. Esta experiencia en los RPAS es reducida pero puede aportar importante información de seguridad. ABSTRACT The Goal of the Thesis is to create a certification specification for remotely piloted systems (RPAS). The methodology used for the development of the standard considers the following constrains: 1. The Base shall be defined in a similar way as the standards used for manned aircraft of the same category. This procedure will make possible a future merging of the standards for manned and unmanned system. It is foreseen that the missions performed and the technology used will be similar in a near future. CS23 and FAR 23 are going to be completely modified in a near future. The changed proposed will also be considered. 2. The standards developed must consider all the changes that are being defined by the air traffic management authorities around the globe. In Europe the program is being managed by SESAR Joint Undertaking. 3. The regulatory organizations are providing technical advice and recommendations in order to permit the operation of the RPAS in non-segregated airspace. There has been a big amount of documentation issued in the last year by ICAO, EASA and FAA. The standards developed should consider and implement these requirements. 4. The high safety record obtained by the manned aviation has been mainly due to the continuous update of the certifications standards based on the experience. The experience in the design and operation of RPAS is reduced but can already provide important safety information.

Recubrimientos autolubricantes cuasicristalinos tipo composite depositados mediante proyección térmica para aplicaciones espaciales y de alta temperatura

Los recubrimientos lubricantes sólidos son requeridos para reducir la fricción y prevenir el desgaste en componentes que operan a altas temperaturas o en vacío (vehículos espaciales, industria química, motores diésel, turbinas aeronáuticas y de generación de energía…). Los lubricantes líquidos pierden sus características cuando las condiciones de presión, temperatura o ambientales son severas (oxidación, inestabilidad térmica, volatilidad,…), por ejemplo los aceites minerales convencionales se descomponen a temperaturas próximas a 200 ºC. Por tanto, la única manera de poder conseguir una adecuada lubricación a temperaturas extremas es por medio de sólidos, que cada vez más, se aplican en forma de recubrimientos. Estos recubrimientos podrían ser empleados en componentes de vehículos espaciales reutilizables, donde se pueden alcanzar, en la reentrada en la atmósfera, temperaturas de 700 ºC (bisagras, rodamientos, articulaciones y zonas de sellado en las superficies de control, y rodamientos de las turbobombas y las cajas de engranajes). Dichos recubrimientos también deberían ser capaces de proporcionar una lubricación efectiva a bajas temperaturas para las operaciones en tierra, para las operaciones de arranque en frío, incluso en el espacio. El conjunto de requisitos que tendrían que satisfacer las capas tribológicas relacionadas con estas condiciones extremas es muy diverso, lo que hace que el concepto de capas tipo composite (aquéllas constituidas por varios componentes) sea, en principio, muy adecuado para estas aplicaciones. Recubrimientos composite proyectados térmicamente constituidos por una matriz dura y conteniendo lubricantes sólidos pueden ser una buena solución desde el punto de vista tribológico. El “Lewis Research Centre” de la NASA ha estado desarrollando recubrimientos autolubricantes tipo composite, constituidos por la combinación de materiales duros como el carburo de cromo, junto con lubricantes sólidos como plata o la eutéctica de fluoruros de calcio y bario, en una matriz de NiCr, para su uso en aplicaciones terrestres a alta temperatura. Estos recubrimientos han sido aplicados mediante proyección térmica, siendo denominados como series PS100, PS200, PS300 y PS400, reduciendo de forma significativa el coeficiente de fricción y mejorando la resistencia al desgaste en un amplio margen de temperaturas. Otra nueva familia de materiales con comportamiento tribológico prometedor son las aleaciones cuasicristalinas (QC). Presentan características muy atractivas: alta dureza, baja fricción, alto límite elástico de compresión... Son muy frágiles como materiales másicos, por lo que se intentan aplicar en forma de recubrimientos. Se pueden depositar mediante proyección térmica. Algunos de estos materiales cuasicristalinos, como AlCoFeCr, poseen coeficientes de dilatación próximos al de los materiales metálicos, alta estabilidad térmica, baja conductividad térmica y una elevada resistencia a la oxidación y a la corrosión en caliente. En esta tesis se han desarrollado recubrimientos tipo composite conteniendo cuasicristales como componente antidesgaste, NiCr como componente tenaz, y Ag y la eutéctica de BaF2-CaF2, como lubricantes sólidos. Estos recubrimientos han sido depositados con diferentes composiciones (denominadas TH100, TH103, TH200, TH400, TH600…) mediante distintos procesos de proyección térmica: plasma en aire (PS), plasma en baja presión (LPPS) y combustión a alta velocidad (HVOF). Los recubrimientos se han generado sobre el sustrato X-750, una superaleación base níquel, endurecible por precipitación, con muy buena resistencia mecánica y a la oxidación hasta temperaturas de 870 ºC y, además, es empleada en aplicaciones aeroespaciales e industriales. Los recubrimientos han sido caracterizados microestructuralmente en INTA (Instituto Nacional de Técnica Aeroespacial), mediante SEM-EDS (Scanning Electronic Microscopy-Energy Dispersive Spectroscopy) y XRD (X-Ray Diffraction), y tribológicamente mediante medidas de microdureza y ensayos en tribómetro POD (Pin On Disc) para determinar los coeficientes de fricción y de desgaste. Los recubrimientos han sido ensayados tribológicamente a alta temperatura en INTA y en vacío en AMTTARC (Aerospace and Space Materials Technology Testhouse – Austrian Research Centres), en Seibersdorf (Austria). Se ha estudiado la influencia de la carga normal aplicada, la velocidad lineal y el material del pin. De entre las diferentes series de recubrimientos cuasicristalinos tipo composite desarrolladas, dos de ellas, TH100 y TH103 han presentado una excelente calidad microestructural (baja porosidad, distribución uniforme de fases…) y se han mostrado como excelentes recubrimientos antidesgaste. Sin embargo, estas capas presentan un pobre comportamiento como autolubricantes a temperatura ambiente, aunque mejoran mucho a alta temperatura o en vacío. Los resultados del trabajo presentado en esta tesis han proporcionado nuevo conocimiento respecto al comportamiento tribológico de recubrimientos autolubricantes cuasicristalinos tipo composite depositados por proyección térmica. Sin embargo, dichos resultados, aunque son muy prometedores, no han puesto de manifiesto el adecuado comportamiento autolubricante que se pretendía y, además, como ocurre en cualquier trabajo de investigación, durante el desarrollo del mismo siempre aparecen nuevas dudas por resolver. Se proponen nuevas líneas de trabajo futuro que complementen los resultados obtenidos y que puedan encaminar hacia la obtención de un recubrimiento que mejore su comportamiento autolubricante. ABSTRACT Solid lubricant coatings are required to reduce friction and prevent wear in components that operate at high temperatures or under vacuum (space vehicles, chemical industry, diesel engines, power generation turbines and aeronautical turbines, for instance). In these cases neither greases nor liquid lubricants can be employed and the only practicable approach to lubrication in such conditions is by means of solids. These are increasingly applied in the form of coatings which should exhibit low shear strength, whilst maintaining their chemical stability at extremes temperatures and in the space environment. In the space field, these coatings would be employed in re-usable space plane applications, such as elevon hinges, where temperatures of 700 ºC are reached during re-entry into the Earth’s atmosphere. These coatings should also be capable of providing effective lubrication at lower temperatures since “cold start” operation may be necessary, even in the space environment. The diverse and sometimes conflictive requirements in high temperature and space-related tribological coatings make the concept of composite coatings highly suitable for these applications. Thermal-sprayed composites containing solid lubricants in a hard matrix perform well tribologically. NASA‘s Lewis Research Centre had developed self-lubricating composite coatings for terrestrial use, comprising hard materials like chromium carbide as well as solid lubricant additives such as silver and BaF2-CaF2 eutectic on a Ni-Cr matrix. These coatings series, named PS100, PS200, PS300 and PS400, are applied by thermal spray and significantly reduce friction coefficients, improving wear resistance over a wide temperature range. Quasicrystalline alloys (QC) constitute a new family of materials with promising tribological behaviour. Some QC materials exhibit a combination of adequate antifriction properties: low friction coefficient, high hardness and high yield strength under compression, and can be easily produced as coatings on top of metallic and non-metallic materials. Among these QC alloys, AlCoFeCr has high hardness (700 HV0.1), a thermal expansion coefficient close to that of metals, high thermal stability, low thermal conductivity and good oxidation and hot corrosion resistance. However most QC materials have the disadvantage of being very brittle. In order to take advantage of the excellent tribological properties of QCs, thick composite lubricant coatings were prepared containing them as the hard phase for wear resistance, Ag and BaF2-CaF2 eutectic as lubricating materials and NiCr as the tough component. These coatings were deposited in different composition mixtures (named TH100, TH103, TH200, TH400, TH600…) by different thermal spray processes: air plasma spray (PS), low pressure plasma spray (LPPS) and high velocity oxy-fuel (HVOF), on X-750 substrates. X-750 is an age-hardenable nickel-base superalloy with very good strength and a good resistance to oxidising combustion gas environments at temperatures up to about 870 ºC and it is widely used in aerospace and industrial applications. Coatings have been characterized microstructurally, at INTA (National Institute for Aerospace Technology), by means of SEM-EDS (Scanning Electronic Microscopy- Energy Dispersive Spectroscopy) and XRD (X-Ray Diffraction), and tribologically by microhardness measurements and pin-on-disc testing to determine friction coefficients as well as wear resistance. The coatings were tested tribologically at high temperature at INTA and under vacuum at AMTT-ARC (Aerospace and Space Materials Technology Testhouse – Austrian Research Centres), in Seibersdorf (Austria). Different loads, linear speeds and pin materials were studied. TH100 and TH103 QC alloy matrix composite coatings were deposited by HVOF with excellent microstructural quality (low porosity, uniform phase distribution) and showed to be excellent wear resistant coatings. However these QC alloy matrix composite coatings are poor as a self-lubricant at room temperature but much better at high temperature or in vacuum. The results from the work performed within the scope of this thesis have provided new knowledge concerning the tribological behavior of self-lubricating quasicrystalline composite coatings deposited by thermal spraying. Although these results are very promising, they have not shown an adequate self-lubricating behavior as was intended, and also, as in any research, the results have in addition raised new questions. Future work is suggested to complement the results of this thesis in order to improve the selflubricating behaviour of the coatings.

Analysis and optimization of trajectories for Ballistic Missiles Interception

Intercontinental Ballistic Missiles are capable of placing a nuclear warhead at more than 5,000 km away from its launching base. With the lethal power of a nuclear warhead a whole city could be wiped out by a single weapon causing millions of deaths. This means that the threat posed to any country from a single ICBM captured by a terrorist group or launched by a 'rogue' state is huge. This threat is increasing as more countries are achieving nuclear and advanced launcher capabilities. In order to suppress or at least reduce this threat the United States created the National Missile Defense System which involved, among other systems, the development of long-range interceptors whose aim is to destroy incoming ballistic missiles in their midcourse phase. The Ballistic Missile Defense is a high-profile topic that has been the focus of political controversy lately when the U.S. decided to expand the Ballistic Missile system to Europe, with the opposition of Russia. However the technical characteristics of this system are mostly unknown by the general public. The Interception of an ICBM using a long range Interceptor Missile as intended within the Ground-Based Missile Defense System by the American National Missile Defense (NMD) implies a series of problems of incredible complexity: - The incoming missile has to be detected almost immediately after launch. - The incoming missile has to be tracked along its trajectory with a great accuracy. - The Interceptor Missile has to implement a fast and accurate guidance algorithm in order to reach the incoming missile as soon as possible. - The Kinetic Kill Vehicle deployed by the interceptor boost vehicle has to be able to detect the reentry vehicle once it has been deployed by ICBM, when it offers a very low infrared signature, in order to perform a final rendezvous manoeuvre. - The Kinetic Kill Vehicle has to be able to discriminate the reentry vehicle from the surrounding debris and decoys. - The Kinetic Kill Vehicle has to be able to implement an accurate guidance algorithm in order to perform a kinetic interception (direct collision) of the reentry vehicle, at relative speeds of more than 10 km/s. All these problems are being dealt simultaneously by the Ground-Based Missile Defense System that is developing very complex and expensive sensors, communications and control centers and long-range interceptors (Ground-Based Interceptor Missile) including a Kinetic Kill Vehicle. Among all the technical challenges involved in this interception scenario, this thesis focuses on the algorithms required for the guidance of the Interceptor Missile and the Kinetic Kill Vehicle in order to perform the direct collision with the ICBM. The involved guidance algorithms are deeply analysed in this thesis in part III where conventional guidance strategies are reviewed and optimal guidance algorithms are developed for this interception problem. The generation of a realistic simulation of the interception scenario between an ICBM and a Ground Based Interceptor designed to destroy it was considered as necessary in order to be able to compare different guidance strategies with meaningful results. As a consequence, a highly representative simulator for an ICBM and a Kill Vehicle has been implemented, as detailed in part II, and the generation of these simulators has also become one of the purposes of this thesis. In summary, the main purposes of this thesis are: - To develop a highly representative simulator of an interception scenario between an ICBM and a Kill Vehicle launched from a Ground Based Interceptor. -To analyse the main existing guidance algorithms both for the ascent phase and the terminal phase of the missiles. Novel conclusions of these analyses are obtained. - To develop original optimal guidance algorithms for the interception problem. - To compare the results obtained using the different guidance strategies, assess the behaviour of the optimal guidance algorithms, and analyse the feasibility of the Ballistic Missile Defense system in terms of guidance (part IV). As a secondary objective, a general overview of the state of the art in terms of ballistic missiles and anti-ballistic missile defence is provided (part I).

A panel method free-wake code for aeroelastic rotor predictions

A panel method free-wake model to analyse the rotor flapping is presented. The aerodynamic model consists of a panel method, which takes into account the three-dimensional rotor geometry, and a free-wake model, to determine the wake shape. The main features of the model are the wake division into a near-wake sheet and a far wake represented by a single tip vortex, and the modification of the panel method formulation to take into account this particular wake description. The blades are considered rigid with a flap degree of freedom. The problem solution is approached using a relaxation method, which enforces periodic boundary conditions. Finally, several code validations against helicopter and wind turbine experimental data are performed, showing good agreement

OSIRIS – The scientific camera system onboard Rosetta

The Optical, Spectroscopic, and Infrared Remote Imaging System OSIRIS is the scientific camera system onboard the Rosetta spacecraft (Figure 1). The advanced high performance imaging system will be pivotal for the success of the Rosetta mission. OSIRIS will detect 67P/Churyumov-Gerasimenko from a distance of more than 106 km, characterise the comet shape and volume, its rotational state and find a suitable landing spot for Philae, the Rosetta lander. OSIRIS will observe the nucleus, its activity and surroundings down to a scale of ~2 cm px−1. The observations will begin well before the onset of cometary activity and will extend over months until the comet reaches perihelion. During the rendezvous episode of the Rosetta mission, OSIRIS will provide key information about the nature of cometary nuclei and reveal the physics of cometary activity that leads to the gas and dust coma. OSIRIS comprises a high resolution Narrow Angle Camera (NAC) unit and a Wide Angle Camera (WAC) unit accompanied by three electronics boxes. The NAC is designed to obtain high resolution images of the surface of comet 7P/Churyumov-Gerasimenko through 12 discrete filters over the wavelength range 250–1000 nm at an angular resolution of 18.6 μrad px−1. The WAC is optimised to provide images of the near-nucleus environment in 14 discrete filters at an angular resolution of 101 μrad px−1. The two units use identical shutter, filter wheel, front door, and detector systems. They are operated by a common Data Processing Unit. The OSIRIS instrument has a total mass of 35 kg and is provided by institutes from six European countries

Observations of Comet 9P/Tempel 1 around the Deep Impact event by the OSIRIS cameras onboard Rosetta

The OSIRIS cameras on the Rosetta spacecraft observed Comet 9P/Tempel 1 from 5 days before to 10 days after it was hit by the Deep Impact projectile. The Narrow Angle Camera (NAC) monitored the cometary dust in 5 different filters. The Wide Angle Camera (WAC) observed through filters sensitive to emissions from OH, CN, Na, and OI together with the associated continuum. Before and after the impact the comet showed regular variations in intensity. The period of the brightness changes is consistent with the rotation period of Tempel 1. The overall brightness of Tempel 1 decreased by about 10% during the OSIRIS observations. The analysis of the impact ejecta shows that no new permanent coma structures were created by the impact. Most of the material moved with View the MathML source∼200ms−1. Much of it left the comet in the form of icy grains which sublimated and fragmented within the first hour after the impact. The light curve of the comet after the impact and the amount of material leaving the comet (View the MathML source4.5–9×106kg of water ice and a presumably larger amount of dust) suggest that the impact ejecta were quickly accelerated by collisions with gas molecules. Therefore, the motion of the bulk of the ejecta cannot be described by ballistic trajectories, and the validity of determinations of the density and tensile strength of the nucleus of Tempel 1 with models using ballistic ejection of particles is uncertain.

Model of the aerodynamic behavior of a pararotor

Asimple semi-empirical model for the aerodynamic behavior of a low-aspect ratio pararotor in autorotation at low Reynolds numbers is presented. The paper is split into three sections: Sec. II deals with the theoretical model derivation, Sec. III deals with the wind-tunnel measurements needed for tuning the theoretical model, and Sec. IV deals with the tuning between the theoretical model and the experimental data. The study is focused on the effect of both the blade pitch angle and the blade roughness and also on the stream velocity, on the rotation velocity, and on the drag of a model. Flow pattern visualizations have also been performed. The value of the free aerodynamic parameters of the semi-empirical model that produces the best fit with the experimental results agrees with the expected ones for the blades at the test conditions. Finally, the model is able to describe the behavior of a pararotor in autorotation that rotates fixed to a shaft, validated for a range of blade pitch angles. The movement of the device is found to be governed by a reduced set of dimensionless parameters.

IDR/UPM facilities for liquid bridge experimentation on earth under microgravity conditions

Besides space laboratories for in-orbit experimentation, Earth based facilities for laboratory experimentation are of paramount importance for the enhancement on liquid bridge knowledge. In spite of the constraints imposed by simulated microgravity (which force to work either with very small size liquid bridges or by using the Plateau tank technique, amongst other techniques), the availability and accessibility of Earth facilities can circumvent in many cases the drawbacks associated with simulated microgravity conditions. To support theoretical and in orbit experimental studies on liquid bridges under reduced gravity conditions, several ground facilities were developed at IDR. In the following these ground facilities are briefly described, and main results obtained by using them are cited.

Pedestrian wind comfort: feasibility study of criteria homogenisation

One of the aims of COST C14 action is the assessment and evaluation of pedestrian wind comfort. At present there is no general rule available that is applied across Europe. There are several criteria that have been developed and applied in different countries. These criteria are based on the definition of two independent parameters, a threshold effective wind speed and a probability of exceedence of this threshold speed. The difficulty of the criteria comparison arises from the two-dimensional character of the criteria definition. An effort is being made to compare these criteria, trying both to find commonalities and to clearly identify differences, in order to build up the basis for the next step: to try to define common criteria (perhaps with regional and seasonal variations). The first point is to define clearly the threshold effective wind speed (mean velocity definition parameters: averaging interval and reference height) and equivalence between different ways of defining the threshold effective wind speed (mean wind speed, gust equivalent mean, etc.) in comparable terms (as far as possible). It can be shown that if the wind speed at a given location is defined in terms of a probability distribution, e.g. Weibull function, a given criterion is satisfied by an infinite set of wind conditions, that is, of probability distributions. The criterion parameters and the Weibull function parameters are linked to each other, establishing a set called iso-criteria lines (the locus of the Weibull function parameters that fulfil a given criterion). The relative position of iso-criteria lines when displayed in a suitable two-dimensional plane facilitates the comparison of comfort criteria. The comparison of several wind comfort criteria, coming from several institutes is performed, showing the feasibility and limitations of the method.

Stability analysis of a free falling pararotor

The pararotor is a decelerator device based on the autorotation of a rotating wing. When it is dropped, it generates an aerodynamic force parallel to the main motion direction, acting as a decelerating force. In this paper, the rotational motion equations are shown for the vertical flight without any lateral wind component and some simplifying assumptions are introduced to obtain analytic solutions of the motion. First, the equilibrium state is obtained as a function of the main parameters. Then the equilibrium stability is analyzed. The motion stability depends on two nondimensional parameters, which contain geometric, inertia, and aerodynamic characteristics of the device. Based on these two parameters a stability diagram can be defined. Some stability regions with different types of stability trajectories (nodes, spirals, focuses) can be identified for spinning motion around axes close to the major, minor, and intermediate principal axes. It is found that the blades contribute to stability in a case of spin around the intermediate principal inertia axis, which is otherwise unstable. Subsequently, the equations for determining the angles of nutation and spin of the body are obtained, thus defining the orientation of the body for a stationary motion and the parameters on which that position depends.

The extended Betz–Lanchester limit

A proposal for an extended formulation of the power coefficient of a wind turbine is presented. This new formulation is a generalization of the Betz–Lanchester expression for the power coefficient as function of the axial deceleration of the wind speed provoked by the wind turbine in operation. The extended power coefficient takes into account the benefits of the power produced and the cost associated to the production of this energy. By the simple model proposed is evidenced that the purely energetic optimum operation condition giving rise to the Betz–Lanchester limit (maximum energy produced) does not coincide with the global optimum operational condition (maximum benefit generated) if cost of energy and degradation of the wind turbine during operation is considered. The new extended power coefficient is a general parameter useful to define global optimum operation conditions for wind turbines, considering not only the energy production but also the maintenance cost and the economic cost associated to the life reduction of the machine.

Singularities and undefinitions in the calibration functions of sonic anemometers

A mathematical model of the process employed by a sonic anemometer to build up the measured wind vector in a steady flow is presented to illustrate the way the geometry of these sensors as well as the characteristics of aerodynamic disturbance on the acoustic path can lead to singularities in the transformation function that relates the measured (disturbed) wind vector with the real (corrected) wind vector, impeding the application of correction/calibration functions for some wind conditions. An implicit function theorem allows for the identification of those combinations of real wind conditions and design parameters that lead to undefined correction/ calibration functions. In general, orthogonal path sensors do not show problematic combination of parameters. However, some geometric sonic sensor designs, available in the market, with paths forming smaller angles could lead to undefined correction functions for some levels of aerodynamic disturbances and for certain wind directions. The parameters studied have a strong influence on the existence and number of singularities in the correction/ calibration function as well as on the number of singularities for some combination of parameters. Some conclusions concerning good design practices are included.

Vehicle induced loads on pedestrian barriers

This paper is a continuation of a previous one, Sanz-Andrés, Santiago-Prowald, Baker and Quinn (J. Wind Eng. Ind. Aerodyn. 91 (2003) 925) concerning the loads generated on a structural panel (traffic sign) by vehicle running along the road, although obviously, the results are also applicable to the effects of other moving vehicles such as trains. The structural panel was modelized as a large plate whose largest dimension is perpendicular to the vehicle motion direction. In this paper a similar approach is used to develop a mathematical model for the vehicle-induced load on pedestrian barriers, modelized as a large plate whose largest dimension is parallel to the vehicle motion direction. The purpose of the work is to develop a model simple enough to give analytical results, although with the physical phenomena correctly accounted for, such as to be able to explain, at least qualitatively, the main characteristics of the phenomenon, as observed in the experiments performed by Quinn et al. (J. Wind Eng. Ind. Aerodyn. 89 (2001) 831). Actually, in spite of the model simplicity, results of the theoretical model show a reasonable good quantitative agreement with the experimental results. The aim of this and previous publications is to provide to the transport infrastructure community with some simple tools that can help to explain, and in some cases also to compute, the unsteady loading produced by moving vehicles on persons and installations placed close to the roads or tracks.

The forced oscillations of submerged bodies

The increasing use of very light structures in aerospace applications are given rise to the need of taking into account the effects of the surrounding media in the motion of a structure (as for instance, in modal testing of solar panels or antennae) as it is usually performed in the motion of bodies submerged in water in marine applications. New methods are in development aiming at to determine rigid-body properties (the center of mass position and inertia properties) from the results of oscillations tests (at low frequencies during modal testing, by exciting the rigid-body modes only) by using the equations of the rigid-body dynamics. As it is shown in this paper, the effect of the surrounding media significantly modifies the oscillation dynamics in the case of light structures and therefore this effect should be taken into account in the development of the above-mentioned methods. The aim of the paper is to show that, if a central point exists for the aerodynamic forces acting on the body, the motion equations for the small amplitude rotational and translational oscillations can be expressed in a form which is a generalization of the motion equations for a body in vacuum, thus allowing to obtain a physical idea of the motion and aerodynamic effects and also significantly simplifying the calculation of the solutions and the interpretation of the results. In the formulation developed here the translational oscillations and the rotational motion around the center of mass are decoupled, as is the case for the rigid-body motion in vacuum, whereas in the classical added mass formulation the six motion equations are coupled. Also in this paper the nonsteady motion of small amplitude of a rigid body submerged in an ideal, incompressible fluid is considered in order to define the conditions for the existence of the central point in the case of a three-dimensional body. The results here presented are also of interest in marine applications.