On the Use of a 3-D Fundamental Solution for Axisymmetric Steady-State Dynamic Problems

The use of 3-D fundamental solution is some axisymmetric problems is straightforward. The resulting algorithms seem to work better than the usual ones (at least for static solutions) and for dynamic cases, than those presented in the previous paragraph. The robustness of the method allows the computations for very high and very low frequencies without any noticeable difficulty.

Steady-state thermal analysis of an innovative receiver for linear Fresnel reflectors

The study of the performance of an innovative receiver for linear Fresnel reflectors is carried out in this paper, and the results are analyzed with a physics perspective of the process. The receiver consists of a bundle of tubes parallel to the mirror arrays, resulting on a smaller cross section for the same receiver width as the number of tubes increases, due to the diminution of their diameter. This implies higher heat carrier fluid speeds, and thus, a more effective heat transfer process, although it conveys higher pumping power as well. Mass flow is optimized for different tubes diameters, different impinging radiation intensities and different fluid inlet temperatures. It is found that the best receiver design, namely the tubes diameter that maximizes the exergetic efficiency for given working conditions, is similar for the cases studied. There is a range of tubes diameters that imply similar efficiencies, which can drive to capital cost reduction thanks to the flexibility of design. In addition, the length of the receiver is also optimized, and it is observed that the optimal length is similar for the working conditions considered. As a result of this study, it is found that this innovative receiver provides an optimum design for the whole day, even though impinging radiation intensity varies notably. Thermal features of this type of receiver could be the base of a new generation of concentrated solar power plants with a great potential for cost reduction, because of the simplicity of the system and the lower weigh of the components, plus the flexibility of using the receiver tubes for different streams of the heat carrier fluid.

Analysis of microscopic magnitudes of radiative blast waves launched in xenon clusters with collisional-radiative steady-state simulations

Radiative shock waves play a pivotal role in the transport energy into the stellar medium. This fact has led to many efforts to scale the astrophysical phenomena to accessible laboratory conditions and their study has been highlighted as an area requiring further experimental investigations. Low density material with high atomic mass is suitable to achieve radiative regime, and, therefore, low density xenon gas is commonly used for the medium in which the radiative shocks such as radiative blast waves propagate. In this work, by means of collisional-radiative steady-state calculations, a characterization and an analysis of microscopic magnitudes of laboratory blast waves launched in xenon clusters are made. Thus, for example, the average ionization, the charge state distribution, the cooling time or photon mean free paths are studied. Furthermore, for a particular experiment, the effects of the self-absorption and self-emission in the specific intensity emitted by the shock front and that is going through the radiative precursor are investigated. Finally, for that experiment, since the electron temperature is not measured experimentally, an estimation of this magnitude is made both for the shock shell and the radiative precursor.

Steady state analysis of a storage integrated solar thermophotovoltaic (SISTPV) system

This paper presents the theoretical analysis of a storage integrated solar thermophotovoltaic (SISTPV) system operating in steady state. These systems combine thermophotovoltaic (TPV) technology and high temperature thermal storage phase-change materials (PCM) in the same unit, providing a great potential in terms of efficiency, cost reduction and storage energy density. The main attraction in the proposed system is its simplicity and modularity compared to conventional Concentrated Solar Power (CSP) technologies. This is mainly due to the absence of moving parts. In this paper we analyze the use of Silicon as the phase change material (PCM). Silicon is an excellent candidate because of its high melting point (1680 K) and its very high latent heat of fusion of 1800 kJ/kg, which is about ten times greater than the conventional PCMs like molten salts. For a simple system configuration, we have demonstrated that overall conversion efficiencies up to ?35% are approachable. Although higher efficiencies are expected by incorporating more advanced devices like multijunction TPV cells, narrow band selective emitters or adopting near-field TPV configurations as well as by enhancing the convective/conductive heat transfer within the PCM. In this paper, we also discuss about the optimum system configurations and provide the general guidelines for designing these systems. Preliminary estimates of night time operations indicate it is possible to achieve over 10 h of operation with a relatively small quantity of Silicon.

Deviations of cup anemometer rotational speed measurements due to steady state harmonic accelerations of the rotor

The measurement deviations of cup anemometers are studied by analyzing the rotational speed of the rotor at steady state (constant wind speed). The differences of the measured rotational speed with respect to the averaged one based on complete turns of the rotor are produced by the harmonic terms of the rotational speed. Cup anemometer sampling periods include a certain number of complete turns of the rotor, plus one incomplete turn, the residuals from the harmonic terms integration within that incomplete turn (as part of the averaging process) being responsible for the mentioned deviations. The errors on the rotational speed due to the harmonic terms are studied analytically and then experimentally, with data from more than 500 calibrations performed on commercial anemometers.

The Boundary Element Method in elastodynamics

As is well known B.E.M. is obtained as a mixture of the integral representation formula of classical elasticity and the discretization philosophy of the finite element method (F.E.M.). The paper presents the application of B.E.M. to elastodynamic problems. Both the transient and steady state solutions are presented as well as some techniques to simplify problems with a free-stress boundary.

Quasi-a priori truncation error estimation in the DGSEM

In this paper we show how to accurately perform a quasi-a priori estimation of the truncation error of steady-state solutions computed by a discontinuous Galerkin spectral element method. We estimate the spatial truncation error using the ?-estimation procedure. While most works in the literature rely on fully time-converged solutions on grids with different spacing to perform the estimation, we use non time-converged solutions on one grid with different polynomial orders. The quasi-a priori approach estimates the error while the residual of the time-iterative method is not negligible. Furthermore, the method permits one to decouple the surface and the volume contributions of the truncation error, and provides information about the anisotropy of the solution as well as its rate of convergence in polynomial order. First, we focus on the analysis of one dimensional scalar conservation laws to examine the accuracy of the estimate. Then, we extend the analysis to two dimensional problems. We demonstrate that this quasi-a priori approach yields a spectrally accurate estimate of the truncation error.

Steps Ahead in the Few-Group CRoss-Section Library Generation at the Pin Level

There exists an interest in performing pin-by-pin calculations coupled with thermal hydraulics so as to improve the accuracy of nuclear reactor analysis. In the framework of the EU NURISP project, INRNE and UPM have generated an experimental version of a few group diffusion cross sections library with discontinuity factors intended for VVER analysis at the pin level with the COBAYA3 code. The transport code APOLLO2 was used to perform the branching calculations. As a first proof of principle the library was created for fresh fuel and covers almost the full parameter space of steady state and transient conditions. The main objective is to test the calculation schemes and post-processing procedures, including multi-pin branching calculations. Two library options are being studied: one based on linear table interpolation and another one using a functional fitting of the cross sections. The libraries generated with APOLLO2 have been tested with the pin-by-pin diffusion model in COBAYA3 including discontinuity factors; first comparing 2D results against the APOLLO2 reference solutions and afterwards using the libraries to compute a 3D assembly problem coupled with a simplified thermal-hydraulic model.

Estudio Hidrogeológico de la Llanura Manchega mediante simulación numérica

El objetivo del presente estudio es el análisis de un sistema complejo, el Acuífero de la Mancha Occidental, mediante un modelo numérico de simulación que represente de la manera más rigurosa posible la evolución del Sistema Acuífero 23. Este modelo se realiza en régimen permanente con una rigurosa configuración del sistema desde el punto de vista geológico y geométrico. De esta forma se deja iniciado y planeado un modelo y su estructura que será una base real de futuras formulaciones transitorias, base de los sucesivos análisis de explotación y predicción. . Las distintas situaciones que en las últimas décadas ha experimentado el Sistema 23, soluciones que se han dado para las mismas, y los posibles planes de actuación que se podrían llevar a cabo en un futuro frente a condiciones cambiantes de clima y explotación se podrán estudiar a partir del presente modelo de simulación numérica. ABSTRACT The main purpose of this study is to analyses a complex system such as Western La Mancha Aquifer by the use of a numeric model that simulates as accurately as possible the evolution of Aquifer 23. This model is made in steady state with a thorough configuration of the system from both the geological and geometric point of view. Therefore, it is left initiated with a planned model and its structure which will be used as a real base for following transient flow simulations that also will be the foundation of subsequent prediction and exploitation analysis. The different situations that Aquifer 23 has experienced during the last decades; the solutions that have been given for them; and the possible plans that would be implemented in the future in order to deal with the changing environmental and exploitation conditions will be able to be studied using this model.

Core physics and safety analysis of Generation-IV Sodium Fast Reactors using existing and newly developed computational tools

El futuro de la energía nuclear de fisión dependerá, entre otros factores, de la capacidad que las nuevas tecnologías demuestren para solventar los principales retos a largo plazo que se plantean. Los principales retos se pueden resumir en los siguientes aspectos: la capacidad de proporcionar una solución final, segura y fiable a los residuos radiactivos; así como dar solución a la limitación de recursos naturales necesarios para alimentar los reactores nucleares; y por último, una mejora robusta en la seguridad de las centrales que en definitiva evite cualquier daño potencial tanto en la población como en el medio ambiente como consecuencia de cualquier escenario imaginable o más allá de lo imaginable. Siguiendo estas motivaciones, la Generación IV de reactores nucleares surge con el compromiso de proporcionar electricidad de forma sostenible, segura, económica y evitando la proliferación de material fisible. Entre los sistemas conceptuales que se consideran para la Gen IV, los reactores rápidos destacan por su capacidad potencial de transmutar actínidos a la vez que permiten una utilización óptima de los recursos naturales. Entre los refrigerantes que se plantean, el sodio parece una de las soluciones más prometedoras. Como consecuencia, esta tesis surgió dentro del marco del proyecto europeo CP-ESFR con el principal objetivo de evaluar la física de núcleo y seguridad de los reactores rápidos refrigerados por sodio, al tiempo que se desarrollaron herramientas apropiadas para dichos análisis. Efectivamente, en una primera parte de la tesis, se abarca el estudio de la física del núcleo de un reactor rápido representativo, incluyendo el análisis detallado de la capacidad de transmutar actínidos minoritarios. Como resultado de dichos análisis, se publicó un artículo en la revista Annals of Nuclear Energy [96]. Por otra parte, a través de un análisis de un hipotético escenario nuclear español, se evalúo la disponibilidad de recursos naturales necesarios en el caso particular de España para alimentar una flota específica de reactores rápidos, siguiendo varios escenarios de demanda, y teniendo en cuenta la capacidad de reproducción de plutonio que tienen estos sistemas. Como resultado de este trabajo también surgió una publicación en otra revista científica de prestigio internacional como es Energy Conversion and Management [97]. Con objeto de realizar esos y otros análisis, se desarrollaron diversos modelos del núcleo del ESFR siguiendo varias configuraciones, y para diferentes códigos. Por otro lado, con objeto de poder realizar análisis de seguridad de reactores rápidos, son necesarias herramientas multidimensionales de alta fidelidad específicas para reactores rápidos. Dichas herramientas deben integrar fenómenos relacionados con la neutrónica y con la termo-hidráulica, entre otros, mediante una aproximación multi-física. Siguiendo este objetivo, se evalúo el código de difusión neutrónica ANDES para su aplicación a reactores rápidos. ANDES es un código de resolución nodal que se encuentra implementado dentro del sistema COBAYA3 y está basado en el método ACMFD. Por lo tanto, el método ACMFD fue sometido a una revisión en profundidad para evaluar su aptitud para la aplicación a reactores rápidos. Durante ese proceso, se identificaron determinadas limitaciones que se discutirán a lo largo de este trabajo, junto con los desarrollos que se han elaborado e implementado para la resolución de dichas dificultades. Por otra parte, se desarrolló satisfactoriamente el acomplamiento del código neutrónico ANDES con un código termo-hidráulico de subcanales llamado SUBCHANFLOW, desarrollado recientemente en el KIT. Como conclusión de esta parte, todos los desarrollos implementados son evaluados y verificados. En paralelo con esos desarrollos, se calcularon para el núcleo del ESFR las secciones eficaces en multigrupos homogeneizadas a nivel nodal, así como otros parámetros neutrónicos, mediante los códigos ERANOS, primero, y SERPENT, después. Dichos parámetros se utilizaron más adelante para realizar cálculos estacionarios con ANDES. Además, como consecuencia de la contribución de la UPM al paquete de seguridad del proyecto CP-ESFR, se calcularon mediante el código SERPENT los parámetros de cinética puntual que se necesitan introducir en los típicos códigos termo-hidráulicos de planta, para estudios de seguridad. En concreto, dichos parámetros sirvieron para el análisis del impacto que tienen los actínidos minoritarios en el comportamiento de transitorios. Concluyendo, la tesis presenta una aproximación sistemática y multidisciplinar aplicada al análisis de seguridad y comportamiento neutrónico de los reactores rápidos de sodio de la Gen-IV, usando herramientas de cálculo existentes y recién desarrolladas ad' hoc para tal aplicación. Se ha empleado una cantidad importante de tiempo en identificar limitaciones de los métodos nodales analíticos en su aplicación en multigrupos a reactores rápidos, y se proponen interesantes soluciones para abordarlas. ABSTRACT The future of nuclear reactors will depend, among other aspects, on the capability to solve the long-term challenges linked to this technology. These are the capability to provide a definite, safe and reliable solution to the nuclear wastes; the limitation of natural resources, needed to fuel the reactors; and last but not least, the improved safety, which would avoid any potential damage on the public and or environment as a consequence of any imaginable and beyond imaginable circumstance. Following these motivations, the IV Generation of nuclear reactors arises, with the aim to provide sustainable, safe, economic and proliferationresistant electricity. Among the systems considered for the Gen IV, fast reactors have a representative role thanks to their potential capacity to transmute actinides together with the optimal usage of natural resources, being the sodium fast reactors the most promising concept. As a consequence, this thesis was born in the framework of the CP-ESFR project with the generic aim of evaluating the core physics and safety of sodium fast reactors, as well as the development of the approppriated tools to perform such analyses. Indeed, in a first part of this thesis work, the main core physics of the representative sodium fast reactor are assessed, including a detailed analysis of the capability to transmute minor actinides. A part of the results obtained have been published in Annals of Nuclear Energy [96]. Moreover, by means of the analysis of a hypothetical Spanish nuclear scenario, the availability of natural resources required to deploy an specific fleet of fast reactor is assessed, taking into account the breeding properties of such systems. This work also led to a publication in Energy Conversion and Management [97]. In order to perform those and other analyses, several models of the ESFR core were created for different codes. On the other hand, in order to perform safety studies of sodium fast reactors, high fidelity multidimensional analysis tools for sodium fast reactors are required. Such tools should integrate neutronic and thermal-hydraulic phenomena in a multi-physics approach. Following this motivation, the neutron diffusion code ANDES is assessed for sodium fast reactor applications. ANDES is the nodal solver implemented inside the multigroup pin-by-pin diffusion COBAYA3 code, and is based on the analytical method ACMFD. Thus, the ACMFD was verified for SFR applications and while doing so, some limitations were encountered, which are discussed through this work. In order to solve those, some new developments are proposed and implemented in ANDES. Moreover, the code was satisfactorily coupled with the thermal-hydraulic code SUBCHANFLOW, recently developed at KIT. Finally, the different implementations are verified. In addition to those developments, the node homogenized multigroup cross sections and other neutron parameters were obtained for the ESFR core using ERANOS and SERPENT codes, and employed afterwards by ANDES to perform steady state calculations. Moreover, as a result of the UPM contribution to the safety package of the CP-ESFR project, the point kinetic parameters required by the typical plant thermal-hydraulic codes were computed for the ESFR core using SERPENT, which final aim was the assessment of the impact of minor actinides in transient behaviour. All in all, the thesis provides a systematic and multi-purpose approach applied to the assessment of safety and performance parameters of Generation-IV SFR, using existing and newly developed analytical tools. An important amount of time was employed in identifying the limitations that the analytical nodal diffusion methods present when applied to fast reactors following a multigroup approach, and interesting solutions are proposed in order to overcome them.

Elastodynamics

In this chapter some applications of boundary element techniques to dynamic problems are presented. First, the basic theory is briefly reviewed in order to provide the necessary background to interpret the numerical results (for a fuller account of elastodynamic theory we recommend a study of the specialized literature). The second part of the chapter is devoted to the numerical implementation of the BEM. The presentation is based on the steady-state solution because this is the area in which most experience exists. This is by no means a limitation of the BEM method, and the use of integral transformations to obtain transient solutions is a well established procedure. Finally, in the third part three examples are presented. The first example is the steady-state solution of a plate under cyclic forces with and without a crack. The second example relies on the determination of soil compliances necessary to study soil-structure interaction and the third example treats the problem of the influence of different incidence angles of incoming waves in foundations. The last two examples are relevant to earthquake engineering problems for which the BEM is very well suited.

Silica final lens performance in laser fusion facilities: HiPER and LIFE

Nowadays, the projects LIFE (Laser Inertial Fusion Energy) in USA and HiPER (High Power Laser Energy Research) in Europe are the most advanced ones to demonstrate laser fusion energy viability. One of the main points of concern to properly achieve ignition is the performance of the final optics (lenses) under the severe irradiation conditions that take place in fusion facilities. In this paper, we calculate the radiation fluxes and doses as well as the radiation-induced temperature enhancement and colour centre formation in final lenses assuming realistic geometrical configurations for HiPER and LIFE. On these bases, the mechanical stresses generated by the established temperature gradients are evaluated showing that from a mechanical point of view lenses only fulfil specifications if ions resulting from the imploding target are mitigated. The absorption coefficient of the lenses is calculated during reactor startup and steady-state operation. The obtained results reveal the necessity of new solutions to tackle ignition problems during the startup process for HiPER. Finally, we evaluate the effect of temperature gradients on focal length changes and lens surface deformations. In summary, we discuss the capabilities and weak points of silica lenses and propose alternatives to overcome predictable problems

Space-state robust control of a Buck converter with amorphous core coil and variable load

Pulse-width modulation is widely used to control electronic converters. One of the most frequently used topologies for high DC voltage/low DC voltage conversion is the Buck converter. These converters are described by a second order system with an LC filter between the switching subsystem and the load. The use of a coil with an amorphous magnetic material core rather than an air core permits the design of smaller converters. If high switching frequencies are used to obtain high quality voltage output, then the value of the auto inductance L is reduced over time. Robust controllers are thus needed if the accuracy of the converter response must be preserved under auto inductance and payload variations. This paper presents a robust controller for a Buck converter based on a state space feedback control system combined with an additional virtual space variable which minimizes the effects of the inductance and load variations when a switching frequency that is not too high is applied. The system exhibits a null steady-state average error response for the entire range of parameter variations. Simulation results and a comparison with a standard PID controller are also presented.

Asymptotic stability of a mathematical model of cell population

We consider a simplified system of a growing colony of cells described as a free boundary problem. The system consists of two hyperbolic equations of first order coupled to an ODE to describe the behavior of the boundary. The system for cell populations includes non-local terms of integral type in the coefficients. By introducing a comparison with solutions of an ODE's system, we show that there exists a unique homogeneous steady state which is globally asymptotically stable for a range of parameters under the assumption of radially symmetric initial data.

On a parabolic-elliptic chemotactic system with non-constant chemotactic sensitivity

We study a parabolic–elliptic chemotactic system describing the evolution of a population’s density “u” and a chemoattractant’s concentration “v”. The system considers a non-constant chemotactic sensitivity given by “χ(N−u)”, for N≥0, and a source term of logistic type “λu(1−u)”. The existence of global bounded classical solutions is proved for any χ>0, N≥0 and λ≥0. By using a comparison argument we analyze the stability of the constant steady state u=1, v=1, for a range of parameters. – For N>1 and Nλ>2χ, any positive and bounded solution converges to the steady state. – For N≤1 the steady state is locally asymptotically stable and for χN<λ, the steady state is globally asymptotically stable.