Discrete linear stability and sensitivity analysis of fluid flows

Este trabajo presenta un método discreto para el cálculo de estabilidad hidrodinámica y análisis de sensibilidad a perturbaciones externas para ecuaciones diferenciales y en particular para las ecuaciones de Navier-Stokes compressible. Se utiliza una aproximación con variable compleja para obtener una precisión analítica en la evaluación de la matriz Jacobiana. Además, mapas de sensibilidad para la sensibilidad a las modificaciones del flujo de base y a una fuerza constante permiten identificar las regiones del campo fluido donde una modificacin (ej. fuerza puntual) tiene un efecto estabilizador del flujo. Se presentan cuatro casos de prueba: (1) un caso analítico para comprobar la derivación discreta, (2) una cavidad cerrada a bajo Reynolds para mostrar la mayor precisión en el cálculo de los valores propios con la aproximación de paso complejo, (3) flujo 2D en un cilindro circular para validar la metodología, y (4) flujo en un cavidad abierta, presentado para validar el método en casos de inestabilidades convectivamente inestables. Los tres últimos casos mencionados (2-4) se resolvieron con las ecuaciones de Navier-Stokes compresibles, utilizando un método Discontinuous Galerkin Spectral Element Method. Se obtuvo una buena concordancia para el caso de validación (3), cuando se comparó el nuevo método con resultados de la literatura. Además, este trabajo muestra que para el cálculo de los modos propios directos y adjuntos, así como para los mapas de sensibilidad, el uso de variables complejas es de suprema importancia para obtener una predicción precisa. El método descrito es aplicado al análisis para la estabilización de la estela generada por un disco actuador, que representa un modelo sencillo para hélices, rotores de helicópteros o turbinas eólicas. Se explora la primera bifurcación del flujo para un disco actuador, y se sugiere que está asociada a una inestabilidad de tipo Kelvin-Helmholtz, cuya estabilidad se controla con en el número de Reynolds y en la resistencia del disco actuador (o fuerza resistente). En primer lugar, se verifica que la disminución de la resistencia del disco tiene un efecto estabilizador parecido a una disminución del Reynolds. En segundo lugar, el análisis hidrodinmico discreto identifica dos regiones para la colocación de una fuerza puntual que controle las inestabilidades, una cerca del disco y otra en una zona aguas abajo. En tercer lugar, se muestra que la inclusión de un forzamiento localizado cerca del actuador produce una estabilización más eficiente que al forzar aguas abajo. El análisis de los campos de flujo controlados confirma que modificando el gradiente de velocidad cerca del actuador es más eficiente para estabilizar la estela. Estos resultados podrían proporcionar nuevas directrices para la estabilización de la estela de turbinas de viento o de marea cuando estén instaladas en un parque eólico y minimizar las interacciones no estacionarias entre turbinas. ABSTRACT A discrete framework for computing the global stability and sensitivity analysis to external perturbations for any set of partial differential equations is presented. In particular, a complex-step approximation is used to achieve near analytical accuracy for the evaluation of the Jacobian matrix. Sensitivity maps for the sensitivity to base flow modifications and to a steady force are computed to identify regions of the flow field where an input could have a stabilising effect. Four test cases are presented: (1) an analytical test case to prove the theory of the discrete framework, (2) a lid-driven cavity at low Reynolds case to show the improved accuracy in the calculation of the eigenvalues when using the complex-step approximation, (3) the 2D flow past a circular cylinder at just below the critical Reynolds number is used to validate the methodology, and finally, (4) the flow past an open cavity is presented to give an example of the discrete method applied to a convectively unstable case. The latter three (2–4) of the aforementioned cases were solved with the 2D compressible Navier–Stokes equations using a Discontinuous Galerkin Spectral Element Method. Good agreement was obtained for the validation test case, (3), with appropriate results in the literature. Furthermore, it is shown that for the calculation of the direct and adjoint eigenmodes and their sensitivity maps to external perturbations, the use of complex variables is paramount for obtaining an accurate prediction. An analysis for stabilising the wake past an actuator disc, which represents a simple model for propellers, helicopter rotors or wind turbines is also presented. We explore the first flow bifurcation for an actuator disc and it suggests that it is associated to a Kelvin- Helmholtz type instability whose stability relies on the Reynolds number and the flow resistance applied through the disc (or actuator forcing). First, we report that decreasing the disc resistance has a similar stabilising effect to an decrease in the Reynolds number. Second, a discrete sensitivity analysis identifies two regions for suitable placement of flow control forcing, one close to the disc and one far downstream where the instability originates. Third, we show that adding a localised forcing close to the actuator provides more stabilisation that forcing far downstream. The analysis of the controlled flow fields, confirms that modifying the velocity gradient close to the actuator is more efficient to stabilise the wake than controlling the sheared flow far downstream. An interesting application of these results is to provide guidelines for stabilising the wake of wind or tidal turbines when placed in an energy farm to minimise unsteady interactions.

Atmospheric Propagation at 100 and 300 GHz: Assessment of a Method to Identify Rainy Conditions during Radiosoundings

The influence of atmospheric gases and tropospheric phenomena becomes more relevant at frequencies within the THz band (100 GHz to 10 THz), severely affecting the propagation conditions. The use of radiosoundings in propagation studies is a well established measurement technique in order to collect information about the vertical structure of the atmosphere, from which gaseous and cloud attenuation can be estimated with the use of propagation models. However, some of these prediction models are not suitable to be used under rainy conditions. In the present study, a method to identify the presence of rainy conditions during radiosoundings is introduced, with the aim of filtering out these events from yearly statistics of predicted atmospheric attenuation. The detection procedure is based on the analysis of a set of parameters, some of them extracted from synoptical observations of weather (SYNOP reports) and other derived from radiosonde observations (RAOBs). The performance of the method has been evaluated under different climatic conditions, corresponding to three locations in Spain, where colocated rain gauge data were available. Rain events detected by the method have been compared with those precipitations identified by the rain gauge. The pertinence Received 26 June 2012, Accepted 31 July 2012, Scheduled 15 August 2012 * Corresponding author: Gustavo Adolfo Siles Soria (gsiles@grc.ssr.upm.es). 258 Siles et al. of the method is discussed on the basis of an analysis of cumulative distributions of total attenuation at 100 and 300 GHz. This study demonstrates that the proposed method can be useful to identify events probably associated to rainy conditions. Hence, it can be considered as a suitable algorithm in order to filter out this kind of events from annual attenuation statistics.

Ferromanganese nodules and micro-hardgrounds associated with the Cadiz Contourite Channel (NE Atlantic): Palaeoenvironmental records of fluid venting and bottom currents

Ferromanganese nodule fields and hardgrounds have recently been discovered in the Cadiz Contourite Channel in the Gulf of Cadiz (850–1000 m). This channel is part of a large contourite depositional system generated by the Mediterranean Outflow Water. Ferromanganese deposits linked to contourites are interesting tools for palaeoenviromental studies and show an increasing economic interest as potential mineral resources for base and strategic metals. We present a complete characterisation of these deposits based on submarine photographs and geophysical, petrographic, mineralogical and geochemical data. The genesis and growth of ferromanganese deposits, strongly enriched in Fe vs. Mn (av. 39% vs. 6%) in this contourite depositional system result from the combination of hydrogenetic and diagenetic processes. The interaction of the Mediterranean Outflow Water with the continental margin has led to the formation of Late Pleistocene–Holocene ferromanganese mineral deposits, in parallel to the evolution of the contourite depositional system triggered by climatic and tectonic events. The diagenetic growth was fuelled by the anaerobic oxidation of thermogenic hydrocarbons (δ13CPDB=−20 to −37‰) and organic matter within the channel floor sediments, promoting the formation of Fe–Mn carbonate nodules. High 87Sr/86Sr isotopic values (up to 0.70993±0.00025) observed in the inner parts of nodules are related to the influence of radiogenic fluids fuelled by deep-seated fluid venting across the fault systems in the diapirs below the Cadiz Contourite Channel. Erosive action of the Mediterranean Outflow Water undercurrent could have exhumed the Fe–Mn carbonate nodules, especially in the glacial periods, when the lower core of the undercurrent was more active in the study area. The growth rate determined by 230Thexcess/232Th was 113±11 mm/Ma, supporting the hypothesis that the growth of the nodules records palaeoenvironmental changes during the last 70 ka. Ca-rich layers in the nodules could point to the interaction between the Mediterranean Outflow Water and the North Atlantic Deep Water during the Heinrich events. Siderite–rhodochrosite nodules exposed to the oxidising seabottom waters were replaced by Fe–Mn oxyhydroxides. Slow hydrogenetic growth of goethite from the seawaters is observed in the outermost parts of the exhumed nodules and hardgrounds, which show imprints of the Mediterranean Outflow Water with low 87Sr/86Sr isotopic values (down to 0.70693±0.00081). We propose a new genetic and evolutionary model for ferromanganese oxide nodules derived from ferromanganese carbonate nodules formed on continental margins above the carbonate compensation depth and dominated by hydrocarbon seepage structures and strong erosive action of bottom currents. We also compare and discuss the generation of ferromanganese deposits in the Cadiz Contourite Channel with that in other locations and suggest that our model can be applied to ferromanganiferous deposits in other contouritic systems affected by fluid venting.

Assessing the landscape value of public works: validation of the method in the lowlands of the middle section of the Tajo river (Spain)

This paper proposes a method of landscape characterisation and assessment of public works associated with fluvial landscapes, which is validated in the middle section of the Tajo River. In this method, a set of criteria is identified that unifies various characteristics of the landscape associated to the infrastructures. A specific weight is then assigned to each criterion in such a way as to produce a semi-quantitative value ranging from a minimum value of 0 to a maximum value of 10. Taken together, these criteria enable us to describe and assess the value of the public works selected for study, in this case helping us to evaluate the sections of the River Tajo analysed in our study area. Accordingly, the value of all the infrastructures associated to a stretch of the river covering several hundred kilometres was determined and after dividing this stretch into sections, they were compared under equivalent conditions to provide a hierarchal ranking.

Estimate of the total ice volume of Svalbard glaciers and their potential contribution to sea-level rise = Estimación del volumen de hielo de Svalbard y su contribución potencial a la subida del nivel del mar

El objetivo final de las investigaciones recogidas en esta tesis doctoral es la estimación del volumen de hielo total de los ms de 1600 glaciares de Svalbard, en el Ártico, y, con ello, su contribución potencial a la subida del nivel medio del mar en un escenario de calentamiento global. Los cálculos más exactos del volumen de un glaciar se efectúan a partir de medidas del espesor de hielo obtenidas con georradar. Sin embargo, estas medidas no son viables para conjuntos grandes de glaciares, debido al coste, dificultades logísticas y tiempo requerido por ellas, especialmente en las regiones polares o de montaña. Frente a ello, la determinación de áreas de glaciares a partir de imágenes de satélite sí es viable a escalas global y regional, por lo que las relaciones de escala volumen-área constituyen el mecanismo más adecuado para las estimaciones de volúmenes globales y regionales, como las realizadas para Svalbard en esta tesis. Como parte del trabajo de tesis, hemos elaborado un inventario de los glaciares de Svalbard en los que se han efectuado radioecosondeos, y hemos realizado los cálculos del volumen de hielo de más de 80 cuencas glaciares de Svalbard a partir de datos de georradar. Estos volúmenes han sido utilizados para calibrar las relaciones volumen-área desarrolladas en la tesis. Los datos de georradar han sido obtenidos en diversas campañas llevadas a cabo por grupos de investigación internacionales, gran parte de ellas lideradas por el Grupo de Simulación Numérica en Ciencias e Ingeniería de la Universidad Politécnica de Madrid, del que forman parte la doctoranda y los directores de tesis. Además, se ha desarrollado una metodología para la estimación del error en el cálculo de volumen, que aporta una novedosa técnica de cálculo del error de interpolación para conjuntos de datos del tipo de los obtenidos con perfiles de georradar, que presentan distribuciones espaciales con unos patrones muy característicos pero con una densidad de datos muy irregular. Hemos obtenido en este trabajo de tesis relaciones de escala específicas para los glaciares de Svalbard, explorando la sensibilidad de los parámetros a diferentes morfologías glaciares, e incorporando nuevas variables. En particular, hemos efectuado experimentos orientados a verificar si las relaciones de escala obtenidas caracterizando los glaciares individuales por su tamaño, pendiente o forma implican diferencias significativas en el volumen total estimado para los glaciares de Svalbard, y si esta partición implica algún patrón significativo en los parámetros de las relaciones de escala. Nuestros resultados indican que, para un valor constante del factor multiplicativo de la relacin de escala, el exponente que afecta al área en la relación volumen-área decrece según aumentan la pendiente y el factor de forma, mientras que las clasificaciones basadas en tamaño no muestran un patrón significativo. Esto significa que los glaciares con mayores pendientes y de tipo circo son menos sensibles a los cambios de área. Además, los volúmenes de la población total de los glaciares de Svalbard calculados con fraccionamiento en grupos por tamaño y pendiente son un 1-4% menores que los obtenidas usando la totalidad de glaciares sin fraccionamiento en grupos, mientras que los volúmenes calculados fraccionando por forma son un 3-5% mayores. También realizamos experimentos multivariable para obtener estimaciones óptimas del volumen total mediante una combinación de distintos predictores. Nuestros resultados muestran que un modelo potencial simple volumen-área explica el 98.6% de la varianza. Sólo el predictor longitud del glaciar proporciona significación estadística cuando se usa además del área del glaciar, aunque el coeficiente de determinación disminuye en comparación con el modelo más simple V-A. El predictor intervalo de altitud no proporciona información adicional cuando se usa además del área del glaciar. Nuestras estimaciones del volumen de la totalidad de glaciares de Svalbard usando las diferentes relaciones de escala obtenidas en esta tesis oscilan entre 6890 y 8106 km3, con errores relativos del orden de 6.6-8.1%. El valor medio de nuestras estimaciones, que puede ser considerado como nuestra mejor estimación del volumen, es de 7.504 km3. En términos de equivalente en nivel del mar (SLE), nuestras estimaciones corresponden a una subida potencial del nivel del mar de 17-20 mm SLE, promediando 19_2 mm SLE, donde el error corresponde al error en volumen antes indicado. En comparación, las estimaciones usando las relaciones V-A de otros autores son de 13-26 mm SLE, promediando 20 _ 2 mm SLE, donde el error representa la desviación estándar de las distintas estimaciones. ABSTRACT The final aim of the research involved in this doctoral thesis is the estimation of the total ice volume of the more than 1600 glaciers of Svalbard, in the Arctic region, and thus their potential contribution to sea-level rise under a global warming scenario. The most accurate calculations of glacier volumes are those based on ice-thicknesses measured by groundpenetrating radar (GPR). However, such measurements are not viable for very large sets of glaciers, due to their cost, logistic difficulties and time requirements, especially in polar or mountain regions. On the contrary, the calculation of glacier areas from satellite images is perfectly viable at global and regional scales, so the volume-area scaling relationships are the most useful tool to determine glacier volumes at global and regional scales, as done for Svalbard in this PhD thesis. As part of the PhD work, we have compiled an inventory of the radio-echo sounded glaciers in Svalbard, and we have performed the volume calculations for more than 80 glacier basins in Svalbard from GPR data. These volumes have been used to calibrate the volume-area relationships derived in this dissertation. Such GPR data have been obtained during fieldwork campaigns carried out by international teams, often lead by the Group of Numerical Simulation in Science and Engineering of the Technical University of Madrid, to which the PhD candidate and her supervisors belong. Furthermore, we have developed a methodology to estimate the error in the volume calculation, which includes a novel technique to calculate the interpolation error for data sets of the type produced by GPR profiling, which show very characteristic data distribution patterns but with very irregular data density. We have derived in this dissertation scaling relationships specific for Svalbard glaciers, exploring the sensitivity of the scaling parameters to different glacier morphologies and adding new variables. In particular, we did experiments aimed to verify whether scaling relationships obtained through characterization of individual glacier shape, slope and size imply significant differences in the estimated volume of the total population of Svalbard glaciers, and whether this partitioning implies any noticeable pattern in the scaling relationship parameters. Our results indicate that, for a fixed value of the factor in the scaling relationship, the exponent of the area in the volume-area relationship decreases as slope and shape increase, whereas size-based classifications do not reveal any clear trend. This means that steep slopes and cirque-type glaciers are less sensitive to changes in glacier area. Moreover, the volumes of the total population of Svalbard glaciers calculated according to partitioning in subgroups by size and slope are smaller (by 1-4%) than that obtained considering all glaciers without partitioning into subgroups, whereas the volumes calculated according to partitioning in subgroups by shape are 3-5% larger. We also did multivariate experiments attempting to optimally predict the volume of Svalbard glaciers from a combination of different predictors. Our results show that a simple power-type V-A model explains 98.6% of the variance. Only the predictor glacier length provides statistical significance when used in addition to the predictor glacier area, though the coefficient of determination decreases as compared with the simpler V-A model. The predictor elevation range did not provide any additional information when used in addition to glacier area. Our estimates of the volume of the entire population of Svalbard glaciers using the different scaling relationships that we have derived along this thesis range within 6890-8106 km3, with estimated relative errors in total volume of the order of 6.6-8.1% The average value of all of our estimates, which could be used as a best estimate for the volume, is 7,504 km3. In terms of sea-level equivalent (SLE), our volume estimates correspond to a potential contribution to sea-level rise within 17-20 mm SLE, averaging 19 _ 2 mm SLE, where the quoted error corresponds to our estimated relative error in volume. For comparison, the estimates using the V-A scaling relations found in the literature range within 13-26 mm SLE, averaging 20 _ 2 mm SLE, where the quoted error represents the standard deviation of the different estimates.

Development of a method of assessment of the problem-solving competence at the technical University of Madrid.

The competence evaluation promoted by the European High Education Area entails a very important methodological change that requires guiding support to help lecturers carry out this new and complex task. In this regard, the Technical University of Madrid (UPM, by its Spanish acronym) has financed a series of coordinated projects with the objective of developing a model for teaching and evaluating core competences and providing support to lecturers. This paper deals with the problem-solving competence. The first step has been to elaborate a guide for teachers to provide a homogeneous way to asses this competence. This guide considers several levels of acquisition of the competence and provides the rubrics to be applied for each one. The guide has been subsequently validated with several pilot experiences. In this paper we will explain the problem-solving assessment guide for teachers and will show the pilot experiences that has been carried out. We will finally justify the validity of the method to assess the problem-solving competence.

Effect of control method on impedance-based interactions in a buck converter

All the interconnected regulated systems are prone to impedance-based interactions making them sensitive to instability and transient-performance degradation. The applied control method affects significantly the characteristics of the converter in terms of sensitivity to different impedance interactions. This paper provides for the first time the whole set of impedance-type internal parameters and the formulas according to which the interaction sensitivity can be fully explained and analyzed. The formulation given in this paper can be utilized equally either based on measured frequency responses or on predicted analytic transfer functions. Usually, the distributed dc-dc systems are constructed by using ready-made power modules without having thorough knowledge on the actual power-stage and control-system designs. As a consequence, the interaction characterization has to be based on the frequency responses measureable via the input and output terminals. A buck converter with four different control methods is experimentally characterized in frequency domain to demonstrate the effect of control method on the interaction sensitivity. The presented analytical models are used to explain the phenomena behind the changes in the interaction sensitivity.

Development of a method of assessment of the problem-solving competency at the Technical University of Madrid

The competence evaluation promoted by the European High Education Area entails a very important methodological change that requires guiding support to help lecturers carry out this new and complex task. In this regard, the Technical University of Madrid (UPM, by its Spanish acronym) has financed a series of coordinated projects with the objective of developing a model for teaching and evaluating core competences and providing support to lecturers. This paper deals with the problem solving competence. The first step has been to elaborate a guide for teachers to provide an homogeneous way to asses this competence. This guide considers several levels of acquisition of the competence and provided the rubrics to be applied for each one. The guide has been subsequently validated with several pilot experiences. In this paper we will explain the problem-solving assessment guide for teachers and will show the pilot experiences that has been carried out. We will finally justify the validity of the method to assess the problem solving competence.

Numerical issues in Lagrangian tracking and topological evolution of fluid particles in wallbounded turbulent flows

The determination of the local Lagrangian evolution of the flow topology in wall-bounded turbulence, and of the Lagrangian evolution associated with entrainment across the turbulent / non-turbulent interface into a turbulent boundary layer, require accurate tracking of a fluid particle and its local velocity gradients. This paper addresses the implementation of fluid-particle tracking in both a turbulent boundary layer direct numerical simulation and in a fully developed channel flow simulation. Determination of the sub-grid particle velocity is performed using both cubic B-spline, four-point Hermite spline and higher-order Hermite spline interpolation. Both wall-bounded flows show similar oscillations in the Lagrangian tracers of both velocity and velocity gradients, corresponding to the movement of particles across the boundaries of computational cells. While these oscillation in the particle velocity are relatively small and have negligible effect on the particle trajectories for time-steps of the order of CFL = 0.1, they appear to be the cause of significant oscillations in the evolution of the invariants of the velocity gradient tensor.

Identification of the method to quantify soluble fibre and the effect of the source of fibre on the ileal and faecal digestibility of soluble and insoluble fibre in rabbits = Identificación del método para cuantificar la fibra soluble y el efecto de la fuente de fibra en la digestibilidad ileal y fecal de la fibra soluble e insoluble en conejos

La presente tesis constituye un avance en el estudio de los métodos para cuantificar la fibra soluble y los efectos de las fracciones de fibra y las fuentes de fibra sobre la digestión de las diferentes fracciones de fibra (soluble e insoluble) en el conejo. Hay un efecto positivo de la fibra soluble sobre la salud intestinal de los conejos y, por ende, una reducción de la mortalidad en animales destetados. Pese a esto, no está claro si estos efectos se deben específicamente a la fracción soluble. Por lo que los objetivos generales de esta tesis fueron: 1) comparar diferentes metodologías químicas e in vitro para cuantificar la fibra soluble y estudiar las posibles interferencias en la cuantificación de la fibra soluble por las mucinas, y viceversa, 2) determinar los efectos de la fibra, el lugar de fermentación, el método para valorar la fibra soluble e insoluble, y la corrección de la fibra soluble por el contenido intestinal de mucinas sobre la digestibilidad de las distintas fracciones de la fibra y 3) evaluar los efectos individuales de las fracciones soluble e insoluble de la fibra de pulpa de remolacha y de manzana, sobre la digestibilidad de la fibra soluble e insoluble y los parámetros digestivos. Para ello se llevaron a cabo 4 estudios. En el primer estudio se compararon diferentes metodologías químicas e in vitro para valorar la fibra soluble de diferentes alimentos y se estudió la posible interferencia en la determinación de la fibra soluble y mucinas. Para ello se utilizaron seis ingredientes (pulpa de remolacha, pectinas de pulpa de remolacha, pulpa de remolacha lavada, paja de cereal, cascarilla de girasol y lignocelulosa) y siete piensos de conejos con diferentes niveles de fibra soluble. En un primer experimento se analizó la fibra dietética total (FDT), la fibra dietética insoluble (FDI), la fibra dietética soluble (FDS), la fibra neutro detergente corregida por cenizas y proteínas (aFNDmo-pb), y la digestibilidad in vitro 2 pasos pepsina/pancreatina (residuo corregido por cenizas y proteína, ivMSi2) de los ingredientes y piensos. Además la fibra soluble se calculó mediante la diferencia entre FDT-FDI (FDSFDI), FDT- ivMSi2 (FDSivMSi2), y FDT - aFNDmo-pb (FDSaFNDmo-pb). Cuando la fibra soluble se determinó directamente como FDS o se calculó como FDT-FDI no se observaron diferencias (109 g/kg MS, en promedio). Sin embargo, cuando la fibra soluble se calculó como FDT - aFNDmo-pb su valor fue un 40% menor (153 g/kg MS. P < 0,05), mientras que la FDSFDI (124 g/kg MS) no fue diferente a ninguna de las otras metodologías. La correlación entre los tres métodos fue elevada (r > 0,96. P < 0,001. n = 13), pero disminuyó o incluso desapareció cuando la pulpa o las pectinas de la remolacha fueron excluidas del análisis. En un segundo experimento, se comparó el método ivDMi2 usando crisoles (método de referencia) con una modificación del mismo usando bolsas ANKOM digeridas individualmente o en colectivo para simplificar la determinación de la FDSivMSi2. La FDSivMSi2 no difirió entre los métodos comparados. En un tercer experimento, se analizó la posible interferencia entre la determinación de la fibra soluble y las mucinas intestinales. Se observó un contenido de FDT y de mucinas elevado en las muestras de pectinas de remolacha (994 y 709 g/kg MS), así como en el moco intestinal de conejo (571 y 739 g/kg MS) cuando se aplicó el método de mucinas por precipitación con etanol. Sin embargo, después de aplicar una pectinasa en el material precipitado, la cantidad de mucinas recuperadas en las muestras de pectinas de remolacha fue cercana a cero, mientras que en el moco intestinal fue similar a los resultados previos al uso de la enzima. Con los resultados de este ensayo se estimaron los carbohidratos de mucinas retenidos en los contenidos digestivos y se propuso una corrección para la determinación de la digestibilidad de la FDT y fibra soluble. En conclusión, la contaminación de las mucinas de la digesta con fibra soluble se soluciona usando pectinasas. El segundo estudio se centró en estudiar: 1) el efecto del tipo de fibra, 2) el sitio de fermentación, 3) el método para cuantificar fibra y 4) la corrección por mucinas sobre la digestibilidad de la fibra. Para ello se formularon tres piensos con diferentes niveles de fibra soluble (FDT-aFNDmo-pb). Un pienso bajo en fibra soluble (LSF. 85 g/kg DM), un pienso medio en fibra soluble (MSF. 102 g/kg DM), y un pienso alto en fibra soluble (HSF. 145 g/kg DM). Estos piensos se obtuvieron reemplazando un 50% del heno del alfalfa en el pienso MSF por una mezcla de pulpa de manzana y remolacha (HSF) o por una mezcla de cascarilla de avena y proteína de soja (LSF). Se utilizaron 30 conejas canuladas para determinar la digestibilidad ileal y fecal. La digestibilidad cecal se calculó mediante diferencia entre la digestibilidad fecal e ileal. La fibra insoluble se determinó como aFNDmo-pb, IDF, e ivMSi2, mientras que la fibra soluble se calculó como FDSFDI, FDSaFNDmo-pb, y FDSivMSi2. La digestibilidad de la FDT y la fibra soluble se corrigieron por las mucinas. La concentración de mucinas en la digesta ileal y fecal, aumento desde el grupo LSF hasta el grupo con el pienso HSF (P < 0,01). La corrección por mucinas aumentó las digestibilidades de la FDT y la fibra soluble a nivel ileal, mientras que a nivel cecal las redujo. (P < 0.01). El coeficiente de digestibilidad ileal de FDT aumentó desde el grupo LSF al grupo HSF (0,12 vs. 0,281. P < 0,01), sin diferencias en el coeficiente de digestibilidad cecal (0,264), por lo que la tendencia a nivel fecal entre los grupos se mantuvo. El coeficiente de digestibilidad ileal de la fibra insoluble aumento desde el grupo con el pienso LSF al grupo con el pienso HSF (0,113 vs. 0,210. P < 0,01), sin diferencias a nivel cecal (0,139) y sin efecto del método usado, resultando en una digestibilidad elevada a nivel fecal, con tendencias similares a las observadas a nivel ileal. El coeficiente de digestibilidad de la FND fue elevada en comparación con la FDI o la ivMSi2 (P > 0.01). El coeficiente de la digestibilidad ileal de la fibra soluble fue mayor en el grupo LSF respecto al grupo LSF (0,436 vs. 0,145. P < 0,01) y el método no afectó a esta determinación. El coeficiente de la digestibilidad cecal de la fibra soluble se redujo desde el grupo LSF hasta el grupo HSF (0,721 vs. 0,492. P < 0,05). El valor más bajo de digestibilidad cecal y fecal de fibra soluble fue medido con el método FDSaFNDmo-pb (P < 0,01). Se observó una alta correlación entre las digestibilidades de la fibra soluble determinada como FDSFDI, FDSaFNDmo-pb, y FDSivMSi2, por lo tanto la información proporcionada por una u otra metodología fueron similares. Sin embargo, cuando se compararon con efectos fisiológicos (producción de mucinas y peso del ciego y pH del ciego de un trabajo previo), la FDSaFNDmo-pb globalmente mostró estar mejor correlacionado con estos parámetros fisiológicos. En conclusión, la corrección por mucinas es necesaria para determinar la digestibilidad ileal de la FDT y fibra soluble, mientras que la elección de uno u otro método es menos relevante. La inclusión de pulpa de manzana y remolacha incrementa la cantidad de FDT que desaparece antes de llegar al ciego. En el tercer estudio se estudió el efecto de la fracción fibrosa soluble e insoluble de la pulpa de remolacha y el método de cuantificación de la fibra soluble e insoluble sobre la digestibilidad de la fibra y algunos parámetros digestivos. Para ello se formularon cuatro piensos con niveles similares de fibra insoluble (315g aFNDmo-pb/kg MS) y proteína (167 g/kg MS). El pienso control contuvo el nivel más bajo de fibra soluble (30,3 g/kg, con cascarilla de girasol y paja como fuente de fibra). Un segundo pienso se obtuvo mediante la sustitución de 60 g de almidón/kg del pienso control por pectinas de remolacha (82,9 g fibra soluble/kg MS). Los otras dos piensos resultaron de la sustitución parcial de las fuentes de fibra del pienso control por la fracción insoluble de la pulpa de remolacha y la pulpa de remolacha entera (42.2 y 82.3 g fibra soluble/kg MS, respectivamente). Cincuenta y seis conejos en cebo (14/pienso), de 2,4  0.21 kg de peso, fueron usados para determinar la digestibilidad ileal y fecal de la FDT, FDI, aFNDmo-pb, FDSFDI, y FDSaFNDmo-pb. La concentración de mucinas en el íleon y heces se utilizaron para corregir la digestibilidad de la FDT y fibra soluble. También se midió el peso de diferentes segmentos del tracto digestivo y el pH del contenido digestivo. Los conejos alimentados con el pienso de fibra insoluble de pulpa de remolacha mostraron los consumos más bajos con respecto a los demás grupos (124 vs. 139 g/d, respectivamente. P < 0,05). El flujo de mucinas ileales fue más alto (P < 0.05) en el grupo alimentado con el pienso de pectinas de remolacha (9,0 g/d en promedio) que los del grupo control (4,79 g/d), mostrando los otros dos grupos valores intermedios, sin detectarse diferencias a nivel fecal. La digestibilidad ileal de la FDT (corregida por mucinas) y la fibra insoluble no se vieron afectadas por el tipo de pienso. El método usado para determinar la fibra insoluble afectó su digestibilidad ileal (0,123 para FDI vs. 0,108 para aFNDmo-pb. P < 0.01). De todas formas, los métodos no afectaron al cálculo de la fibra fermentada antes del ciego (4,9 g/d en promedio). Los conejos alimentados con el pienso de pulpa de remolacha y con el pienso con la fracción insoluble de la pulpa de remolacha mostraron las digestibilidades fecales más altas de la fibra insoluble (0,266 en promedio vs. 0,106 del grupo control), mientras que en los animales del pienso con pectinas esta digestibilidad fue un 47% mayor respecto al pienso control (P < 0,001). La digestibilidad fecal de la fibra insoluble fue un 20% más alta cuando se usó la FND en lugar de FDI para determinarla (P < 0.001). Esto hizo variar la cantidad de fibra insoluble fermentada a lo largo del tracto digestivo (9,5 ó 7,5 g/d cuando fue calculada como FDI o aFNDmo-pb, respectivamente. P < 0,001). Las digestibilidades ileales de la fibra soluble fueron positivas cuando los análisis de fibra soluble de los contenidos ileales fueron corregidos por mucinas, (P < 0,001) excepto para la digestibilidad ileal de la FDSIDF del grupo control. Una vez corregidas por mucinas, los conejos alimentados con los piensos que contuvieron la fracción soluble de la pulpa de remolacha (pienso de pectina y pulpa de remolacha) mostraron una mayor digestibilidad ileal de la fibra soluble, respecto al grupo control (0,483 vs. -0,010. P = 0.002), mientras que el grupo del pienso de fibra insoluble de pulpa de remolacha mostró un valor intermedio (0,274). La digestibilidad total de la fibra soluble fue similar entre todos los grupos (0.93). Los conejos alimentados con pulpa de remolacha y su fracción insoluble mostraron los pesos relativos más altos del estómago respecto a los del pienso control y de pectinas (11 y 56 % respectivamente; P < 0,05). Por otra parte, el peso relativo del ciego aumentó en los animales que consumieron tanto la fracción soluble como insoluble de la pulpa de remolacha, siendo un 16% más pesados (P < 0,001) que el grupo control. El pH del contenido cecal fue más bajo en los animales del grupo de pulpa de remolacha que en los del grupo control (5,64 vs. 6,03; P < 0,001), mientras que los del grupo de pectinas y de fibra insoluble de pulpa de remolacha mostraron valores intermedios. En conclusión, el efecto positivo de la pulpa de remolacha en el flujo de mucinas a nivel ileal se debe a la fracción soluble e insoluble de la pulpa de remolacha. La mitad de la fibra soluble de la pulpa de remolacha desaparece antes de llegar al ciego, independientemente si esta proviene de pectinas puras o de la pulpa de remolacha. El pH cecal esta mejor correlacionado con la cantidad de FDT que desaparece antes del ciego más que con la que se degrada en el ciego. En el último estudio se estudiaron los efectos de la fibra soluble e insoluble de la pulpa de manzana sobre la digestibilidad de la fibra y algunos parámetros digestivos. Cuatro dietas fueron formuladas con niveles similares de fibra insoluble (aFNDmo-pb 32,4%) y proteína (18,6% ambos en base seca). El pienso control contuvo el nivel más bajo de fibra soluble (46 g de fibra soluble/kg, con cascarilla de girasol y paja de cereales como la fuentes de fibra). Un segundo pienso fue obtenido mediante la sustitución de 60 g de almidón/kg del pienso control por pectinas de manzana (105 g fibra soluble/kg). Los otros dos piensos se obtuvieron por la substitución de parte de las fuentes de fibra del pienso control por pulpa de manzana o pulpa de manzana despectinizada (93 y 71 g de fibra soluble/kg, respectivamente). La digestibilidad fecal fue determinada en 23 conejos/pienso con 1.68 ± 0.23 kg de peso vivo, los cuales fueron sacrificados a los 60 d edad para recolectar su contenido digestivo para determinar digestibilidad ileal y otros parámetros digestivos. La fibra soluble de manzana (pectinas y pulpa entera) estimuló el flujo ileal de mucinas (P = 0,002), pero no asi la pulpa despectinizada. La corrección por mucinas incrementó la digestibilidad de la FDT y la fibra soluble a nivel fecal, y especialmente a nivel ileal. Cerca de la mitad de la fibra soluble proveniente de los piensos con cualquiera de las fracciones de la pulpa de manzana fue degradada a nivel ileal, sin mostrar diferencias entre los grupos (46 y 86% en promedio a nivel ileal y fecal respectivamente). La inclusión de pulpa despectinizada de manzana mejoró la digestibilidad de la FND a nivel fecal (P < 0,05) pero no a nivel ileal. El contenido cecal de los conejos alimentados con la pulpa de manzana tuvieron el pH cecal más ácido que los del pienso control (5,55 vs. 5,95. P < 0,001), mientras que los animales con el pienso de pectinas de manzana y de pulpa de manzana despectinizada mostraron valores intermedios. En conclusión los efectos positivo de la pulpa de manzana en el flujo de mucinas se debió principalmente a la fracción soluble de la pulpa de manzana. La mitad de la fibra soluble fue degradada antes del ciego independientemente de si esta provino de las pectinas o de la pulpa de manzana. El pH cecal estuvo mejor correlacionado con la cantidad de FDT fermentada en todo el tracto digestivo y antes de llegar al ciego que con la que se degradó en el ciego. Al integrar los resultados de los estudio 2, 3 y 4 se concluyó que la corrección de mucinas de los contenidos digestivos al determinar FDT y fibra soluble es necesaria para ajustar los cálculos de su digestibilidad. Esta corrección es mucho más importante a nivel ileal y en dietas bajas en fibra soluble. Por otra parte, la FDT desapareció en proporciones importantes antes de llegar al ciego, especialmente en piensos que contienen pulpa de remolacha o de manzana o alguna fracción soluble o insoluble de las mismas y estas diferencias observadas entre los piensos a nivel ileal se correlacionaron mejor con el pH cecal, lo que indicaría que la FDT se solubilizó antes de llegar al ciego y una vez en esté fermentó. Estos resultados implican que determinar la fibra soluble como FDSaFNDmo-pb es la mejor opción y que en la determinación de la digestibilidad de la FDT y fibra soluble se debe considerar la corrección por mucinas especialmente a nivel ileal y en piensos bajos en fibra soluble. ABSTRACT The present thesis constitutes a step forward in advancing the knowledge of the methods to quantify soluble fibre and the effects of the fibre fractions and source of fibre on the site the digestion of different fractions of fibre (soluble and insoluble) in the rabbit. There is a positive effect of soluble fibre on rabbit digestive health and therefore on the reduction of mortality in weaning rabbits. Nevertheless, it is no so clear that the effects of soluble fibre on rabbits are due particularly to this fraction. This thesis aims: 1) to compare the quantification of soluble fibre in feeds using different chemical and in vitro approaches, and to study the potential interference between soluble fibre and mucin determinations, 2) to identify the effects of type of fibre, site of fermentation, method to quantify insoluble and soluble fibre, and correction of the intestinal soluble fibre content for intestinal mucin on the digestibility of fibre fractions and 3) to evaluate the individual effect of soluble and insoluble fibre from sugar beet pulp and apple pulp on ileal and faecal soluble and insoluble digestibility and digestive traits. These objectives were developed in four studies: The first study compared the quantification of soluble fibre in feeds using different chemical and in vitro approaches, and studied the potential interference between soluble fibre and mucin determinations. Six ingredients, sugar beet pulp (SBP), SBP pectins, insoluble SBP, wheat straw, sunflower hulls and lignocellulose, and seven rabbit diets, differing in soluble fibre content, were evaluated. In experiment 1, ingredients and diets were analysed for total dietary fibre (TDF), insoluble dietary fibre (IDF), soluble dietary fibre (SDF), aNDFom (corrected for protein, aNDFom-cp) and 2-step pepsin/pancreatin in vitro DM indigestibility (corrected for ash and protein, ivDMi2). Soluble fibre was estimated by difference using three procedures: TDF - IDF (SDFIDF), TDF - ivDMi2 (SDFivDMi2), and TDF - aNDFom-cp (SDFaNDFom-cp). Soluble fibre determined directly (SDF) or by difference, as SDFivDMi2 were not different (109 g/kg DM, on average). However, when it was calculated as SDFaNDFom-cp the value was 40% higher (153 g/kg DM, P < 0.05), whereas SDFIDF (124 g/kg DM) did not differ from any of the other methods. The correlation between the four methods was high (r ≥ 0.96. P ≤ 0.001. n = 13), but it decreased or even disappeared when SBP pectins and SBP were excluded and a lower and more narrow range of variation of soluble fibre was used. In experiment 2, the ivDMi2 using crucibles (reference method) were compared to those made using individual or collective ankom bags in order to simplify the determination of SDFivDMi2. The ivDMi2 was not different when using crucibles or individual or collective ankom bags. In experiment 3, the potential interference between soluble fibre and intestinal mucin determinations was studied using rabbit intestinal raw mucus, digesta and SBP pectins, lignocelluloses and a rabbit diet. An interference was observed between the determinations of soluble fibre and crude mucin, as the content of TDF and apparent crude mucin were high in SBP pectins (994 and 709 g/kg DM) and rabbit intestinal raw mucus (571 and 739 g/kg DM). After a pectinase treatment, the coefficient of apparent mucin recovery of SBP pectins was close to zero, whereas that of rabbit mucus was not modified. An estimation of the crude mucin carbohydrates retained in digesta TDF is proposed to correct TDF and soluble fibre digestibility. In conclusion, the values of soluble fibre depend on the methodology used. The contamination of crude mucin with soluble fibre is avoided using pectinase. The second study focused on the effect of type of fibre, site of fermentation, method for quantifying insoluble and soluble dietary fibre, and their correction for intestinal mucin on fibre digestibility. Three diets differing in soluble fibre were formulated (85 g/kg DM soluble fibre, in the low soluble fibre [LSF] diet; 102 g/kg DM in the medium soluble fibre [MSF] diet; and 145 g/kg DM in the high soluble fibre [HSF] diet). They were obtained by replacing half of the dehydrated alfalfa in the MSF diet with a mixture of beet and apple pulp (HSF diet) or with a mix of oat hulls and soybean protein (LSF diet). Thirty rabbits with ileal T-cannulas were used to determine total tract apparent digestibility (CTTAD) and ileal apparent digestibility (CIAD). Caecal digestibility was determined by difference between CTTAD and CIAD. Insoluble fibre was measured as aNDFom-cp, IDF, and ivDMi2, whereas soluble fibre was calculated as SDFaNDFom-cp, SDFIDF, SDFivDMi2. The intestinal mucin content was used to correct the TDF and soluble fibre digestibility. Ileal and faecal concentration of mucin increased from the LSF to the HSF diet group (P < 0.01). Once corrected for intestinal mucin, The CTTAD and CIAD of TDF and soluble fibre increased whereas caecal digestibility decreased (P < 0.01). The CIAD of TDF increased from the LSF to the HSF diet group (0.12 vs. 0.281. P < 0.01), with no difference in the caecal digestibility (0.264), resulting in a higher CTTAD from the LSF to the HSF diet group (P < 0.01). The CIAD of insoluble fibre increased from the LSF to the HSF diet group (0.113 vs. 0.21. P < 0.01), with no difference in the caecal digestibility (0.139) and no effect of fibre method, resulting in a higher CTTAD for rabbits fed the HSF diet compared with the MSF and LSF diets groups (P < 0.01). The CTTAD of aNDFom-cp was higher compared with IDF or ivDMi2 (P < 0.01). The CIAD of soluble fibre was higher for the HSF than for the LSF diet group (0.436 vs. 0.145. P < 0.01) and fibre method did not affect it. Caecal soluble fibre digestibility decreased from the LSF to the HSF diet group (0.721 vs. 0.492. P < 0.05). The lowest caecal and faecal soluble fibre digestibility was measured using SDFaNDFom-cp (P < 0.01). There was a high correlation among the digestibilities of soluble fibre measured as SDFaNDFom-cp, SDFIDF, and SDFivDMi2. Therefore, these methodologies provide similar information. However, the method that seems to be globally better related to the physiological traits (ileal flow of mucins, and relative weight of the caecum and caecal pH from previous work) was the SDFaNDFom-cp. In conclusion, a correction for intestinal mucin is necessary for ileal TDF and soluble fibre digestibility whereas the selection of the fibre method has a minor relevance. The inclusion of sugar beet and apple pulp increased the amount of TDF fermented in the small intestine. The third study examined the effect of fibre fractions of sugar beet pulp (SBP) and the method for quantifying soluble and insoluble fibre on soluble and insoluble fibre digestibility and digestive traits. Four diets were formulated with similar level of insoluble fibre (aNDFom-cp: 315 g/kg DM) and protein (167 g/kg DM). Control diet contained the lowest level of soluble fibre (30.3 g/kg DM, including sunflower hulls and straw as sole sources of fibre). A second diet was obtained by replacing 60 g starch/kg of control diet with SBP pectins (82.9 g soluble fibre/kg DM). Two more diets were obtained by replacing part of the fibrous sources of the control diet with either insoluble SBP fibre or SBP (42.2 and 82.3 g soluble fibre/kg DM, respectively). Fifty six (14/diet) rabbits weighing 2.40  0.213 kg were used to determine faecal and ileal digestibility of total dietary fibre (TDF), insoluble dietary fibre (IDF), neutral detergent fibre corrected for ash and CP (aNDFom-cp) and soluble fibre estimated as SDFaNDFom-cp and SDFIDF. Faecal and ileal mucin content was used to correct TDF and soluble fibre digestibility. It was also recorded weight of digestive segments and digesta pH. Rabbits fed insoluble SBP showed the lowest feed intake with respect to the other 3 diets (124 vs. 139 g/d, respectively. P < 0.05). Ileal mucin flow was higher (P < 0.05) in animals fed pectin and SBP diets (9.0 g/d, as average) than those fed control diet (4.79 g/d), showing InsSBP group an intermediate value. No differences on mucin content were detected at faecal level. There was no diet effect on the CIAD of TDF (corrected for mucin) and insoluble fibre. Fibre methodology influenced the CIAD of insoluble fibre (0.123 for IDF vs. 0.108 for aNDFom-cp. P < 0.01). Anyway, the amount of insoluble fibre fermented before the caecum did not differ between both methods (4.9 g/d, on average). Rabbits fed insoluble SBP and SBP diets showed the highest CTTAD of insoluble fibre (0.266 on average vs. 0.106 for control group), whereas those fed pectin diet had an intermediate value (0.106. P < 0.001). The CTTAD of insoluble fibre measured with IDF was higher than that measured with aNDFom-cp (by 20%. P < 0.001). It led that the amount of insoluble fibre fermented along the digestive tract were different (9.5 or 7.5 g/d when calculated as IDF or aNDFom-cp, respectively; P < 0.001). When the CIAD of soluble fibre was corrected for mucin they became positive (P < 0.001) except for control group measured as SDFIDF. Once corrected for mucin content, rabbits fed soluble fibre from SBP (pectin and SBP groups) showed higher CIAD of soluble fibre than control group (0.483 vs. -0.019. respectively), whereas the value for insoluble SBP group was intermediate 0.274. The CTTAD of soluble fibre (mucin corrected) was similar among diets 0.93. Rabbits fed with SBP and insoluble SBP diets showed higher total digestive tract and stomach relative weight than those fed pectin and control diets (by 11 and 56 %. respectively, P < 0.05). The caecal relative weight did not differ in rabbits fed pectin, insoluble SBP, and SBP diets (62 g/kg BW, as average) and they were on average 16% higher (P < 0.001) than in control group. Caecal content of rabbits fed SBP diet was more acid than those fed control diet (5.64 vs. 6.03. P < 0.001), whereas those from pectin and insoluble SBP diets showed intermediate values. In conclusion, the positive effect of SBP fibre on ileal mucin flow was due to both its soluble and insoluble fibre fraction. Half of the soluble SBP fibre was degraded before the caecum independently it came from pectin or SBP. The caecal pH correlated better with the ileal amount of fermented TDF in the digestive tract rather than with that fermented in the caecum. The last study examined the effect of soluble and insoluble fibre of apple pulp on fibre digestibility and digestive traits. Four diets were formulated with similar level of insoluble fibre (aNDFom-cp: 324 g/kg DM) and protein (18.6 g/kg DM). Control diet contained the lowest level of soluble fibre (46 g soluble fibre/kg DM, including oat hulls and straw as sole sources of fibre). A second diet was obtained by replacing 60 g starch/kg of control diet with apple pectins (105 g soluble fibre/kg DM). Two more diets were obtained by substituting part of the fibrous sources of the control diet by either apple pulp or depectinized apple pulp (93 and 71 g soluble fibre/kg, respectively). The CTTAD was determined in 23 rabbits/diet weighing 1.68  0.23 kg BW, and 23 rabbits/diet were slaughtered at 60 d of age to collect ileal digesta to determine CIAD and record other digestive traits. Soluble fibre from apple stimulated ileal flow of mucin (P = 0.002), but depectinized apple pulp did not. The correction for mucin increased the digestibility of crude protein, total dietary fibre, and soluble fibre at faecal, but especially at ileal level, depending in this case on the diet. Around half of the soluble fibre in diets containing any fibre fraction from apple was degraded at ileal level, with no differences among these diets (0.46 vs. 0.066 for control group, P=0.046). Faecal soluble fibre digestibility was 0.86 on average for all groups). Inclusion of the apple insoluble fibre improved NDF digestibility at faecal (0.222 vs. 0.069. P < 0.05) but not at ileal level. Caecal content of rabbits fed apple pulp diet was more acid than those fed control diet (5.55 vs. 5.95. P < 0.001), whereas those from pectin and depectinised apple pulp diets showed intermediate values. In conclusion, the positive effect of apple fibre on ileal mucin flow was mainly due to its soluble fibre fraction. Half of the soluble apple fibre was degraded before the caecum independently it came from pectin or apple pulp. The caecal pH correlated better with the total and ileal amount of fermented TDF in the digestive tract rather than with that fermented in the caecum. The results obtained in the studies 2, 3 and 4 were considered together. These results showed that the mucin correction is necessary when the TDF and soluble fibre digestibility is determined, and it correction is more important at ileal level and in diets with low level of soluble fibre. On another hand, incrementing the soluble fibre using sugar beet and apple pulp increased the amount of TDF disappear before the caecum. Moreover, the caecal pH correlated better with the ileal amount of fermented TDF in the digestive tract rather than with that fermented in the caecum. This suggests that an ileal fibre solubilisation may occur rather than ileal fermentation. Therefore the implications of this work were that: the estimation of soluble fibre as SDFaNDFom-cp is an adequate method considering its correlation with the physiological effects; and the TDF and soluble fibre digestibility must be corrected with intestinal mucins, especially when the ileal digestibility is determined.

Minimum volume of long liquid bridges between noncoaxial, nonequal diameter circular disks under lateral acceleration

The stability limit of minimum volume and the breaking dynamics of liquid bridges between nonequal, noncoaxial, circular supporting disks subject to a lateral acceleration were experimentally analyzed by working with liquid bridges of very small dimensions. Experimental results are compared with asymptotic theoretical predictions, with the agreement between experimental results and asymptotic ones being satisfactory

Estimate of the total volume of Svalbard glaciers, and their potential contribution to sea-level rise, using new regionally based scaling relationships

We present a set of new volume scaling relationships specific to Svalbard glaciers, derived from a sample of 60 volume–area pairs. Glacier volumes are computed from ground-penetrating radar (GPR)-retrieved ice thickness measurements, which have been compiled from different sources for this study. The most precise scaling models, in terms of lowest cross-validation errors, are obtained using a multivariate approach where, in addition to glacier area, glacier length and elevation range are also used as predictors. Using this multivariate scaling approach, together with the Randolph Glacier Inventory V3.2 for Svalbard and Jan Mayen, we obtain a regional volume estimate of 6700 ± 835 km3, or 17 ± 2 mm of sea-level equivalent (SLE). This result lies in the mid- to low range of recently published estimates, which show values as varied as 13 and 24 mm SLE. We assess the sensitivity of the scaling exponents to glacier characteristics such as size, aspect ratio and average slope, and find that the volume of steep-slope and cirque-type glaciers is not very sensitive to changes in glacier area.

Hydrodynamic forces on heave plates for offshore systems oscillating close to the seabed or the free surface

La energía eólica marina es uno de los recursos energéticos con mayor proyección pudiendo contribuir a reducir el consumo de combustibles fósiles y a cubrir la demanda de energía en todo el mundo. El concepto de aerogenerador marino está basado en estructuras fijas como jackets o en plataformas flotantes, ya sea una semisumergible o una TLP. Se espera que la energía eólica offshore juegue un papel importante en el perfil de producción energética de los próximos años; por tanto, las turbinas eólicas deben hacerse más fables y rentables para ser competitivas frente a otras fuentes de energía. Las estructuras flotantes pueden experimentar movimientos resonantes en estados de la mar con largos períodos de oleaje. Estos movimientos disminuyen su operatividad y pueden causar daños en los componentes eléctricos de las turbinas y en las palas, también en los risers y moorings. La respuesta de la componente vertical del movimiento puede reducirse mediante diferentes actuaciones: (1) aumentando la amortiguación del sistema, (2) manteniendo el período del movimiento vertical fuera del rango de la energía de la ola, y (3) reduciendo las fuerzas de excitación verticales. Un ejemplo típico para llevar a cabo esta reducción son las "Heave Plates". Las heave plates son placas que se utilizan en la industria offshore debido a sus características hidrodinámicas, ya que aumentan la masa añadida y la amortiguación del sistema. En un análisis hidrodinámico convencional, se considera una estructura sometida a un oleaje con determinadas características y se evalúan las cargas lineales usando la teoría potencial. El amortiguamiento viscoso, que juega un papel crucial en la respuesta en resonancia del sistema, es un dato de entrada para el análisis. La tesis se centra principalmente en la predicción del amortiguamiento viscoso y de la masa añadida de las heave plates usadas en las turbinas eólicas flotantes. En los cálculos, las fuerzas hidrodinámicas se han obtenido con el f n de estudiar cómo los coeficientes hidrodinámicos de masa añadida5 y amortiguamiento varían con el número de KC, que caracteriza la amplitud del movimiento respecto al diámetro del disco. Por otra parte, se ha investigado la influencia de la distancia media de la ‘heave plate’ a la superficie libre o al fondo del mar, sobre los coeficientes hidrodinámicos. En este proceso, un nuevo modelo que describe el trabajo realizado por la amortiguación en función de la enstrofía, es descrito en el presente documento. Este nuevo enfoque es capaz de proporcionar una correlación directa entre el desprendimiento local de vorticidad y la fuerza de amortiguación global. El análisis también incluye el estudio de los efectos de la geometría de la heave plate, y examina la sensibilidad de los coeficientes hidrodinámicos al incluir porosidad en ésta. Un diseño novedoso de una heave plate, basado en la teoría fractal, también fue analizado experimentalmente y comparado con datos experimentales obtenidos por otros autores. Para la resolución de las ecuaciones de Navier Stokes se ha usado un solver basado en el método de volúmenes finitos. El solver usa las librerías de OpenFOAM (Open source Field Operation And Manipulation), para resolver un problema multifásico e incompresible, usando la técnica VOF (volume of fluid) que permite capturar el movimiento de la superficie libre. Los resultados numéricos han sido comparados con resultados experimentales llevados a cabo en el Canal del Ensayos Hidrodinámicos (CEHINAV) de la Universidad Politécnica de Madrid y en el Canal de Experiencias Hidrodinámicas (CEHIPAR) en Madrid, al igual que con otros experimentos realizados en la Escuela de Ingeniería Mecánica de la Universidad de Western Australia. Los principales resultados se presentan a continuación: 1. Para pequeños valores de KC, los coeficientes hidrodinámicos de masa añadida y amortiguamiento incrementan su valor a medida que el disco se aproxima al fondo marino. Para los casos cuando el disco oscila cerca de la superficie libre, la dependencia de los coeficientes hidrodinámicos es más fuerte por la influencia del movimiento de la superficie libre. 2. Los casos analizados muestran la existencia de un valor crítico de KC, donde la tendencia de los coeficientes hidrodinámicos se ve alterada. Dicho valor crítico depende de la distancia al fondo marino o a la superficie libre. 3. El comportamiento físico del flujo, para valores de KC cercanos a su valor crítico ha sido estudiado mediante el análisis del campo de vorticidad. 4. Introducir porosidad al disco, reduce la masa añadida para los valores de KC estudiados, pero se ha encontrado que la porosidad incrementa el valor del coeficiente de amortiguamiento cuando se incrementa la amplitud del movimiento, logrando un máximo de damping para un disco con 10% de porosidad. 5. Los resultados numéricos y experimentales para los discos con faldón, muestran que usar este tipo de geometrías incrementa la masa añadida cuando se compara con el disco sólido, pero reduce considerablemente el coeficiente de amortiguamiento. 6. Un diseño novedoso de heave plate basado en la teoría fractal ha sido experimentalmente estudiado a diferentes calados y comparado con datos experimentales obtenidos por otro autores. Los resultados muestran un comportamiento incierto de los coeficientes y por tanto este diseño debería ser estudiado más a fondo. ABSTRACT Offshore wind energy is one of the promising resources which can reduce the fossil fuel energy consumption and cover worldwide energy demands. Offshore wind turbine concepts are based on either a fixed structure as a jacket or a floating offshore platform like a semisubmersible, spar or tension leg platform. Floating offshore wind turbines have the potential to be an important part of the energy production profile in the coming years. In order to accomplish this wind integration, these wind turbines need to be made more reliable and cost efficient to be competitive with other sources of energy. Floating offshore artifacts, such oil rings and wind turbines, may experience resonant heave motions in sea states with long peak periods. These heave resonances may increase the system downtime and cause damage on the system components and as well as on risers and mooring systems. The heave resonant response may be reduced by different means: (1) increasing the damping of the system, (2) keeping the natural heave period outside the range of the wave energy, and (3) reducing the heave excitation forces. A typical example to accomplish this reduction are “Heave Plates”. Heave plates are used in the offshore industry due to their hydrodynamic characteristics, i.e., increased added mass and damping. Conventional offshore hydrodynamic analysis considers a structure in waves, and evaluates the linear and nonlinear loads using potential theory. Viscous damping, which is expected to play a crucial role in the resonant response, is an empirical input to the analysis, and is not explicitly calculated. The present research has been mainly focused on the prediction of viscous damping and added mass of floating offshore wind turbine heave plates. In the calculations, the hydrodynamic forces have been measured in order to compute how the hydrodynamic coefficients of added mass1 and damping vary with the KC number, which characterises the amplitude of heave motion relative to the diameter of the disc. In addition, the influence on the hydrodynamic coefficients when the heave plate is oscillating close to the free surface or the seabed has been investigated. In this process, a new model describing the work done by damping in terms of the flow enstrophy, is described herein. This new approach is able to provide a direct correlation between the local vortex shedding processes and the global damping force. The analysis also includes the study of different edges geometry, and examines the sensitivity of the damping and added mass coefficients to the porosity of the plate. A novel porous heave plate based on fractal theory has also been proposed, tested experimentally and compared with experimental data obtained by other authors for plates with similar porosity. A numerical solver of Navier Stokes equations, based on the finite volume technique has been applied. It uses the open-source libraries of OpenFOAM (Open source Field Operation And Manipulation), to solve 2 incompressible, isothermal immiscible fluids using a VOF (volume of fluid) phase-fraction based interface capturing approach, with optional mesh motion and mesh topology changes including adaptive re-meshing. Numerical results have been compared with experiments conducted at Technical University of Madrid (CEHINAV) and CEHIPAR model basins in Madrid and with others performed at School of Mechanical Engineering in The University of Western Australia. A brief summary of main results are presented below: 1. At low KC numbers, a systematic increase in added mass and damping, corresponding to an increase in the seabed proximity, is observed. Specifically, for the cases when the heave plate is oscillating closer to the free surface, the dependence of the hydrodynamic coefficients is strongly influenced by the free surface. 2. As seen in experiments, a critical KC, where the linear trend of the hydrodynamic coefficients with KC is disrupted and that depends on the seabed or free surface distance, has been found. 3. The physical behavior of the flow around the critical KC has been explained through an analysis of the flow vorticity field. 4. The porosity of the heave plates reduces the added mass for the studied porosity at all KC numbers, but the porous heave plates are found to increase the damping coefficient with increasing amplitude of oscillation, achieving a maximum damping coefficient for the heave plate with 10% porosity in the entire KC range. 5. Another concept taken into account in this work has been the heave plates with flaps. Numerical and experimental results show that using discs with flaps will increase added mass when compared to the plain plate but may also significantly reduce damping. 6. A novel heave plate design based on fractal theory has tested experimentally for different submergences and compared with experimental data obtained by other authors for porous plates. Results show an unclear behavior in the coefficients and should be studied further. Future work is necessary in order to address a series of open questions focusing on 3D effects, optimization of the heave plates shapes, etc.

Lagrangian descriptors: a method for revealing phase space structures of general time dependent dynamical systems

Lagrangian descriptors are a recent technique which reveals geometrical structures in phase space and which are valid for aperiodically time dependent dynamical systems. We discuss a general methodology for constructing them and we discuss a "heuristic argument" that explains why this method is successful. We support this argument by explicit calculations on a benchmark problem. Several other benchmark examples are considered that allow us to assess the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field ("time averages"). In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods.

One-dimensional self-similar solution of the dynamics of axisymmetric slender liquid bridges

In this paper the dynamics of axisymmetric, slender, viscous liquid bridges having volume close to the cylindrical one, and subjected to a small gravitational field parallel to the axis of the liquid bridge, is considered within the context of one-dimensional theories. Although the dynamics of liquid bridges has been treated through a numerical analysis in the inviscid case, numerical methods become inappropriate to study configurations close to the static stability limit because the evolution time, and thence the computing time, increases excessively. To avoid this difficulty, the problem of the evolution of these liquid bridges has been attacked through a nonlinear analysis based on the singular perturbation method and, whenever possible, the results obtained are compared with the numerical ones.