Análisis del comportamiento de las tuberías de poliéster reforzado con fibra de vidrio con capa de arena

Aunque las primeras fábricas de tubos de poliéster reforzado con fibra de vidrio en España datan del año 1984, no es sino hasta el año 1996 cuando se comienza su utilización masiva como un sustituto de las tuberías de fribrocemento, que ya habían sido prohibidas por la legislación, debido a los efectos cancerígenos de este material. Desde entonces se ha prodigado la utilización de todas las diferentes tipologías de esta clase de tubería, de conformidad a los procesos de fabricación empleados que se encuentran recopilados en el AWWA Manual M45 (Fiberglass Pipe Design), obteniéndose muy diversos resultados. Durante estos años, ha surgido una creciente preocupación en los usuarios de este tipo de tuberías dadas las continuas y numerosas averías en todo el ámbito geográfico. Esto ha promovido el desarrollo de la presente investigaicón, que se ha dividido en dos partes y que ha concluido con la determinación de un nuevo mecanismo específico de fractura. La primera parte se centró en la obtención y desarrollo del modelo teórico que hemos venido a denominar como "Teoría de la Caja Mecánicamente Contaminada", y que está basado en la contaminación o separación por un impacto de dos de las tres capas que forman la tubería, la capa intermedia de arena y la capa más interna o "inner layer". La consecuencia es la disminución del canto resistente, la rotura del inner layer y la entrada de fluido a la capa de arena. Para la evaluación de la magnitud de esta separación se ha desarrollado un modelo analítico que ha determinado la existencia de una relación cuadrática que la rige, y que ha sido verificado mediante ensayos de impacto sobre probetas de tuberías, alcanzando ajustes de hasta el 92%. Así, se ha determinado que impactos de muy baja intensidad, del entorno de 90 a 160 Julios en tuberías Filament Winding continuo PN 16-20 (de 800 a 1000mm) pueden comprometer seriamente la integridad estructural de la tubería sin dejar, en un principio, muesca o traza alguna que pueda alertar del problema. Los siguientes pasos en el estudio se dirigieron a determinar qué otros mecanismos, aparte del golpe, podrían contaminar la tubería y a estudiar el consiguiente avance de la fractura a las capas externas. Se trataba además de analizar la aparición en el tubo de unas misteriosas manchas en forma de "piel de leopardo" y de otros fenómenos aparecidos en las averías como que algunas de las deformaciones de la rotura por presión interna son hacia el interior del tubo y no al revés, como habría sido de esperar a priori. Se optó entonces por comenzar la que ha constituido la segunda parte de la investigación. Para ello se recurrió a realizar ensayos hidráulicos en banco de pruebas a alta presión, cuyos resultados fueron sorprendentes al descubrir que en el proceso se producía la hidrólisis de la resina de poliéster no catalizada que fluía hacia el exterior del tubo. Como consecuencia se llevaron a cabo nuevos ensayos físicos y químicos para estudiar la migración del material y la hidrólisis producida en el proceso de fractura. En este estudio, resultó muy relevante el hecho de sobrepasar o no la presión que producía el desagarro entre las capas del tubo. En definitiva, en esta investigación, que ha constado de estudios analíticos y estudios experimentales, químicos y numéricos, se ha determinado un nuevo mecanismo de fractura que explica gran parte de los fallos acontecidos en las tuberías de poliéster reforzado con fibra de vidrio. Como aplicación se exponen recomendaciones para mejorar el comportamiento mecánico de esta tipología y evitar así los sobrecostes millonarios producidos por su reposición. Numerous and continuous failures in fiberglass reinforced polyester pipes of different companies and manufacturing processes of the AWWA Manual M45 (Fiberglass Pipe Design), have prompted the development of this research, that has concluded with a specific mechanism describing pipe fractures. This research was carried out via two independent studies. The first one is the development of the hypothesis that turned into the Mechanically Contaminated Layer Theory. This theory describes the fracture mchanism which explains a significant part of massive failures due to the existence of a sand layer placed near the neutral axis in the core making the composite very sensitive to impacts in fibreglass reinforced polyester pipes. These failures create interface delamination and consequently fluid can leak into supporting sand backfill thereby iniating the fracture process. In order to assess the delimination magnitude, an analytic method is developed and a squared root law between delamination and energy applied proposed. Vertical blunt ram testts on samples extracted from complete pipes have been carried out to verify this theory, reaching a goodness of fit up to 92%. It is concluded that low energy impacts, around 90-160J in 800-1000mm diameter PN 16-20 continuous filament winding pipes, can seriously compromise their structural integraty with no external trace. The next step in the study was to determine what other mechanism, apart from the brittle hit, could contaminate the pipe and to analyse the consequente advance of the fracture to the external layers. Another aim was to analyse two phenomena occurred in real pipe failures. The first one is the appearance on the tube of "leopard fur" stains on some of the analysed failures, and the other phenomenon is the "inverse fracture", in which the deformations of the failure due to internal pressure are towards the inside of the tube and not the other way round, as it would be expected. It was then chosen to follow a new branch of the investigation by hydraulic high-pressure bench tests that study seepage and load transmission. The results were very surprising as it was discovered that in the process, hydrolysis of the non-catalysed polyester resin occured, flowing towards the outer of the pipe, which entailed the development of chemical and physical tests of the exuded material to study material migration and hydrolysis of the fracture process. In this particular study it was relevant to exceed or not the pressure that produced the rip between the layers of the tube. In conclusion, a new breakage mechanism in FRP pies with sand-filled layer has been found, which explains a high part of the failure global cases. The whole failure process is justified by the Mechanically Contaminated Layer Theory, which has been corroborated by means of analytical, numerical and experimental studies. Several recommendations are also provided in order to improve the mechanical behaviour of this typology and avoid the millionaire overruns generated by its massive failures.

Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles

In this work, a new two-dimensional optics design method is proposed that enables the coupling of three ray sets with two lens surfaces. The method is especially important for optical systems designed for wide field of view and with clearly separated optical surfaces. Fermat’s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The presented general analytic solution makes it possible to calculate the lens profiles. Ray tracing results for calculated 15th order Taylor polynomials describing the lens profiles demonstrate excellent imaging performance and the versatility of this new analytic design method.

Analytic Kramer kernels, Lagrange-type interpolation series and de Branges spaces

The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. In particular, when the involved kernel is analytic in the sampling parameter it can be stated in an abstract setting of reproducing kernel Hilbert spaces of entire functions which includes as a particular case the classical Shannon sampling theory. This abstract setting allows us to obtain a sort of converse result and to characterize when the sampling formula associated with an analytic Kramer kernel can be expressed as a Lagrange-type interpolation series. On the other hand, the de Branges spaces of entire functions satisfy orthogonal sampling formulas which can be written as Lagrange-type interpolation series. In this work some links between all these ideas are established.

On the Extension of the Analytic Nodal Diffusion Solver ANDES to Sodium Fast Reactors

Within the framework of the Collaborative Project for a European Sodium Fast Reactor, the reactor physics group at UPM is working on the extension of its in-house multi-scale advanced deterministic code COBAYA3 to Sodium Fast Reactors (SFR). COBAYA3 is a 3D multigroup neutron kinetics diffusion code that can be used either as a pin-by-pin code or as a stand-alone nodal code by using the analytic nodal diffusion solver ANDES. It is coupled with thermalhydraulics codes such as COBRA-TF and FLICA, allowing transient analysis of LWR at both fine-mesh and coarse-mesh scales. In order to enable also 3D pin-by-pin and nodal coupled NK-TH simulations of SFR, different developments are in progress. This paper presents the first steps towards the application of COBAYA3 to this type of reactors. ANDES solver, already extended to triangular-Z geometry, has been applied to fast reactor steady-state calculations. The required cross section libraries were generated with ERANOS code for several configurations. The limitations encountered in the application of the Analytic Coarse Mesh Finite Difference (ACMFD) method –implemented inside ANDES– to fast reactors are presented and the sensitivity of the method when using a high number of energy groups is studied. ANDES performance is assessed by comparison with the results provided by ERANOS, using a mini-core model in 33 energy groups. Furthermore, a benchmark from the NEA for a small 3D FBR in hexagonal-Z geometry and 4 energy groups is also employed to verify the behavior of the code with few energy groups.

Analytic free-form lens design in 3D: coupling three ray sets using two lens surfaces

The two-dimensional analytic optics design method presented in a previous paper [Opt. Express 20, 5576–5585 (2012)] is extended in this work to the three-dimensional case, enabling the coupling of three ray sets with two free-form lens surfaces. Fermat’s principle is used to deduce additional sets of functional differential equations which make it possible to calculate the lens surfaces. Ray tracing simulations demonstrate the excellent imaging performance of the resulting free-form lenses described by more than 100 coefficients.

Perfect imaging of three object points with only two analytic lens surfaces in two dimensions

In this work, a new two-dimensional analytic optics design method is presented that enables the coupling of three ray sets with two lens profiles. This method is particularly promising for optical systems designed for wide field of view and with clearly separated optical surfaces. However, this coupling can only be achieved if different ray sets will use different portions of the second lens profile. Based on a very basic example of a single thick lens, the Simultaneous Multiple Surfaces design method in two dimensions (SMS2D) will help to provide a better understanding of the practical implications on the design process by an increased lens thickness and a wider field of view. Fermat?s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The transformation of these functional differential equations into an algebraic linear system of equations allows the successive calculation of the Taylor series coefficients up to an arbitrary order. The evaluation of the solution space reveals the wide range of possible lens configurations covered by this analytic design method. Ray tracing analysis for calculated 20th order Taylor polynomials demonstrate excellent performance and the versatility of this new analytical optics design concept.

Analytic free-form lens design for imaging applications with high aspect ratio

A new three-dimensional analytic optics design method is presented that enables the coupling of three ray sets with only two free-form lens surfaces. Closely related to the Simultaneous Multiple Surface method in three dimensions (SMS3D), it is derived directly from Fermat?s principle, leading to multiple sets of functional differential equations. The general solution of these equations makes it possible to calculate more than 80 coefficients for each implicit surface function. Ray tracing simulations of these free-form lenses demonstrate superior imaging performance for applications with high aspect ratio, compared to conventional rotational symmetric systems.

Analytic free-form lens design for tracking integration in concentrating photovoltaics

In this work the concept of tracking integration in concentrating photovoltaics (CPV) is revisited and developed further. With respect to conventional CPV, tracking integration eliminates the clear separation between stationary units of optics and solar cells, and external solar trackers. This approach is capable of further increasing the concentration ratio and makes high concentrating photovoltaics (> 500x) available for single-axis tracker installations. The reduced external solar tracking effort enables possibly cheaper and more compact installations. Our proposed optical system uses two laterally moving plano-convex lenses to achieve high concentration over a wide angular range of ±24°. The lateral movement allows to combine both steering and concentration of the incident direct sun light. Given the specific symmetry conditions of the underlying optical design problem, rotational symmetric lenses are not ideal for this application. For this type of design problems, a new free-form optics design method presented in previous papers perfectly matches the symmetry. It is derived directly from Fermat's principle, leading to sets of functional differential equations allowing the successive calculation of the Taylor series coeficients of each implicit surface function up to very high orders. For optical systems designed for wide field of view and with clearly separated optical surfaces, this new analytic design method has potential application in both fields of nonimaging and imaging optics.

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.