Ion charge number and flux saturation effects in the corona of a laser-irradiated pellet

The quasisteady structure of the corona of a laser-irradiated pellet is completely determined for arbitrary Z, (ion charge number} and re/ra (ratio of critical and ablation radii), and for heat-flux saturation factor/above approximately 0.04. The ion-to-electron temperature ratio at rc grows sensibly with Z,; all other quantities depend weakly and nonmonotonically on Z,. For rc /ra close to unity, and all Z, of interest (Z, < 47}, the flow is subsonic at rc. For a given laser power W, flux saturation may decrease (low/) or increase (high/) the ablation pressure Pa relative to the value obtained when saturation is not considered; in some cases a decrease in/with W fixed increases Pa. For intermediate^ ~0.1), Pa cc (W/r* )2/3 p\n\pc = critical density), independently of rc/ra; for/~0.6, Pa «s larger by a factor of about [rc/raf13. For rjra > 1.2 roughly, the mass ablation rate is C{Z,) [{m/kZ.f^Kr^Pl) l,\ independent of pc and/, and barely dependent on Z,(m, is ion mass; k, Boltzmann's constant; K, conductivity coefficient; and C, a tabulated function).

Electron temperature versus laser intensity times wavelength squared: a comparison of theory and experiments

The peak temperature in the corona of plasma ejected by a laser-irradiated slab is discussed in terms of a one-electron-temperature model. Both heat-flux saturation and pulse rise-time effects are considered;the intensity in the rising half of the pulse is approximated by a linear function of time, I(t) = Iot/r. The temperature is found to be proportional to (IQX2)273 and a function of I0X4/r. Above a certain value of I0X4/T, the plasma presents two characteristic temperatures (at saturation and at the critical surface) which can be identified with experimentally observed cold- and hot-electron temperatures. The results are compared with extensive experimental data available for both nd and CO2 lasers, I0(W'cnf2) X2 (/um) starting around 1012. The agreement is good if substantial flux inhibition is assumed (flux-limit factor f = 0.03), and fails for I0X2 above 1O1S. Results for both ablation pressure and mass ablation rate are also given.

Coronal fluid-dynamics in laser fusion

The fluid-dynamics of the corona ejected by laser-fusion targets in the direct-drive approach (thermal radiation and atomic physics unimportant) is discussed. A two-fluid model involves inverse bremsstrahlung absorption, refraction, different ion and electron temperatures with energy exchange, different ion and electron velocities and magnetic field generation, and their effect on ion-electron friction and heat flux. Four dimensionless parameters determine coronal regimes for one-dimensional flows under uniform irradiation. One additional parameter is involved in two-dimensional problems,including the stability of one-dimensional flows, and the smoothing of nonuniform driving.

Nonlocal electron heat relaxation in a plasma shock at arbitrary ionization number

A recently obtained nonlocal expression for the electron heat flux valid for arbitrary ionization numbers Z is used to study the structure of a plane shock wave in a fully ionized plasma. Nonlocal effects are only important in the foot of the electronic preheating region, where the electron temperature gradient is the steepest. The results are quantified as a function of a characteristic Knudsen number of that region. This work also generalizes to arbitrary values of Z previous results on plasma shock wave structure.

High power beam dump project for the accelerator prototype LIPAc: Cooling design and analysis

En el campo de la fusión nuclear y desarrollándose en paralelo a ITER (International Thermonuclear Experimental Reactor), el proyecto IFMIF (International Fusion Material Irradiation Facility) se enmarca dentro de las actividades complementarias encaminadas a solucionar las barreras tecnológicas que aún plantea la fusión. En concreto IFMIF es una instalación de irradiación cuya misión es caracterizar materiales resistentes a condiciones extremas como las esperadas en los futuros reactores de fusión como DEMO (DEMOnstration power plant). Consiste de dos aceleradores de deuterones que proporcionan un haz de 125 mA y 40 MeV cada uno, que al colisionar con un blanco de litio producen un flujo neutrónico intenso (1017 neutrones/s) con un espectro similar al de los neutrones de fusión [1], [2]. Dicho flujo neutrónico es empleado para irradiar los diferentes materiales candidatos a ser empleados en reactores de fusión, y las muestras son posteriormente examinadas en la llamada instalación de post-irradiación. Como primer paso en tan ambicioso proyecto, una fase de validación y diseño llamada IFMIFEVEDA (Engineering Validation and Engineering Design Activities) se encuentra actualmente en desarrollo. Una de las actividades contempladas en esta fase es la construcción y operación de una acelarador prototipo llamado LIPAc (Linear IFMIF Prototype Accelerator). Se trata de un acelerador de deuterones de alta intensidad idéntico a la parte de baja energía de los aceleradores de IFMIF. Los componentes del LIPAc, que será instalado en Japón, son suministrados por diferentes países europeos. El acelerador proporcionará un haz continuo de deuterones de 9 MeV con una potencia de 1.125 MW que tras ser caracterizado con diversos instrumentos deberá pararse de forma segura. Para ello se requiere un sistema denominado bloque de parada (Beam Dump en inglés) que absorba la energía del haz y la transfiera a un sumidero de calor. España tiene el compromiso de suministrar este componente y CIEMAT (Centro de Investigaciones Energéticas Medioambientales y Tecnológicas) es responsable de dicha tarea. La pieza central del bloque de parada, donde se para el haz de iones, es un cono de cobre con un ángulo de 3.5o, 2.5 m de longitud y 5 mm de espesor. Dicha pieza está refrigerada por agua que fluye en su superficie externa por el canal que se forma entre el cono de cobre y otra pieza concéntrica con éste. Este es el marco en que se desarrolla la presente tesis, cuyo objeto es el diseño del sistema de refrigeración del bloque de parada del LIPAc. El diseño se ha realizado utilizando un modelo simplificado unidimensional. Se han obtenido los parámetros del agua (presión, caudal, pérdida de carga) y la geometría requerida en el canal de refrigeración (anchura, rugosidad) para garantizar la correcta refrigeración del bloque de parada. Se ha comprobado que el diseño permite variaciones del haz respecto a la situación nominal siendo el flujo crítico calorífico al menos 2 veces superior al nominal. Se han realizado asimismo simulaciones fluidodinámicas 3D con ANSYS-CFX en aquellas zonas del canal de refrigeración que lo requieren. El bloque de parada se activará como consecuencia de la interacción del haz de partículas lo que impide cualquier cambio o reparación una vez comenzada la operación del acelerador. Por ello el diseño ha de ser muy robusto y todas las hipótesis utilizadas en la realización de éste deben ser cuidadosamente comprobadas. Gran parte del esfuerzo de la tesis se centra en la estimación del coeficiente de transferencia de calor que es determinante en los resultados obtenidos, y que se emplea además como condición de contorno en los cálculos mecánicos. Para ello por un lado se han buscado correlaciones cuyo rango de aplicabilidad sea adecuado para las condiciones del bloque de parada (canal anular, diferencias de temperatura agua-pared de decenas de grados). En un segundo paso se han comparado los coeficientes de película obtenidos a partir de la correlación seleccionada (Petukhov-Gnielinski) con los que se deducen de simulaciones fluidodinámicas, obteniendo resultados satisfactorios. Por último se ha realizado una validación experimental utilizando un prototipo y un circuito hidráulico que proporciona un flujo de agua con los parámetros requeridos en el bloque de parada. Tras varios intentos y mejoras en el experimento se han obtenido los coeficientes de película para distintos caudales y potencias de calentamiento. Teniendo en cuenta la incertidumbre de las medidas, los valores experimentales concuerdan razonablemente bien (en el rango de 15%) con los deducidos de las correlaciones. Por motivos radiológicos es necesario controlar la calidad del agua de refrigeración y minimizar la corrosión del cobre. Tras un estudio bibliográfico se identificaron los parámetros del agua más adecuados (conductividad, pH y concentración de oxígeno disuelto). Como parte de la tesis se ha realizado asimismo un estudio de la corrosión del circuito de refrigeración del bloque de parada con el doble fin de determinar si puede poner en riesgo la integridad del componente, y de obtener una estimación de la velocidad de corrosión para dimensionar el sistema de purificación del agua. Se ha utilizado el código TRACT (TRansport and ACTivation code) adaptándalo al caso del bloque de parada, para lo cual se trabajó con el responsable (Panos Karditsas) del código en Culham (UKAEA). Los resultados confirman que la corrosión del cobre en las condiciones seleccionadas no supone un problema. La Tesis se encuentra estructurada de la siguiente manera: En el primer capítulo se realiza una introducción de los proyectos IFMIF y LIPAc dentro de los cuales se enmarca esta Tesis. Además se describe el bloque de parada, siendo el diseño del sistema de rerigeración de éste el principal objetivo de la Tesis. En el segundo y tercer capítulo se realiza un resumen de la base teórica así como de las diferentes herramientas empleadas en el diseño del sistema de refrigeración. El capítulo cuarto presenta los resultados del relativos al sistema de refrigeración. Tanto los obtenidos del estudio unidimensional, como los obtenidos de las simulaciones fluidodinámicas 3D mediante el empleo del código ANSYS-CFX. En el quinto capítulo se presentan los resultados referentes al análisis de corrosión del circuito de refrigeración del bloque de parada. El capítulo seis se centra en la descripción del montaje experimental para la obtención de los valores de pérdida de carga y coeficiente de transferencia del calor. Asimismo se presentan los resultados obtenidos en dichos experimentos. Finalmente encontramos un capítulo de apéndices en el que se describen una serie de experimentos llevados a cabo como pasos intermedios en la obtención del resultado experimental del coeficiente de película. También se presenta el código informático empleado para el análisis unidimensional del sistema de refrigeración del bloque de parada llamado CHICA (Cooling and Heating Interaction and Corrosion Analysis). ABSTRACT In the nuclear fusion field running in parallel to ITER (International Thermonuclear Experimental Reactor) as one of the complementary activities headed towards solving the technological barriers, IFMIF (International Fusion Material Irradiation Facility) project aims to provide an irradiation facility to qualify advanced materials resistant to extreme conditions like the ones expected in future fusion reactors like DEMO (DEMOnstration Power Plant). IFMIF consists of two constant wave deuteron accelerators delivering a 125 mA and 40 MeV beam each that will collide on a lithium target producing an intense neutron fluence (1017 neutrons/s) with a similar spectra to that of fusion neutrons [1], [2]. This neutron flux is employed to irradiate the different material candidates to be employed in the future fusion reactors, and the samples examined after irradiation at the so called post-irradiative facilities. As a first step in such an ambitious project, an engineering validation and engineering design activity phase called IFMIF-EVEDA (Engineering Validation and Engineering Design Activities) is presently going on. One of the activities consists on the construction and operation of an accelerator prototype named LIPAc (Linear IFMIF Prototype Accelerator). It is a high intensity deuteron accelerator identical to the low energy part of the IFMIF accelerators. The LIPAc components, which will be installed in Japan, are delivered by different european countries. The accelerator supplies a 9 MeV constant wave beam of deuterons with a power of 1.125 MW, which after being characterized by different instruments has to be stopped safely. For such task a beam dump to absorb the beam energy and take it to a heat sink is needed. Spain has the compromise of delivering such device and CIEMAT (Centro de Investigaciones Energéticas Medioambientales y Tecnológicas) is responsible for such task. The central piece of the beam dump, where the ion beam is stopped, is a copper cone with an angle of 3.5o, 2.5 m long and 5 mm width. This part is cooled by water flowing on its external surface through the channel formed between the copper cone and a concentric piece with the latter. The thesis is developed in this realm, and its objective is designing the LIPAc beam dump cooling system. The design has been performed employing a simplified one dimensional model. The water parameters (pressure, flow, pressure loss) and the required annular channel geometry (width, rugoisty) have been obtained guaranteeing the correct cooling of the beam dump. It has been checked that the cooling design allows variations of the the beam with respect to the nominal position, being the CHF (Critical Heat Flux) at least twice times higher than the nominal deposited heat flux. 3D fluid dynamic simulations employing ANSYS-CFX code in the beam dump cooling channel sections which require a more thorough study have also been performed. The beam dump will activateasaconsequenceofthe deuteron beam interaction, making impossible any change or maintenance task once the accelerator operation has started. Hence the design has to be very robust and all the hypotheses employed in the design mustbecarefully checked. Most of the work in the thesis is concentrated in estimating the heat transfer coefficient which is decisive in the obtained results, and is also employed as boundary condition in the mechanical analysis. For such task, correlations which applicability range is the adequate for the beam dump conditions (annular channel, water-surface temperature differences of tens of degrees) have been compiled. In a second step the heat transfer coefficients obtained from the selected correlation (Petukhov- Gnielinski) have been compared with the ones deduced from the 3D fluid dynamic simulations, obtaining satisfactory results. Finally an experimental validation has been performed employing a prototype and a hydraulic circuit that supplies a flow with the requested parameters in the beam dump. After several tries and improvements in the experiment, the heat transfer coefficients for different flows and heating powers have been obtained. Considering the uncertainty in the measurements the experimental values agree reasonably well (in the order of 15%) with the ones obtained from the correlations. Due to radiological reasons the quality of the cooling water must be controlled, hence minimizing the copper corrosion. After performing a bibligraphic study the most adequate water parameters were identified (conductivity, pH and dissolved oxygen concentration). As part of this thesis a corrosion study of the beam dump cooling circuit has been performed with the double aim of determining if corrosion can pose a risk for the copper beam dump , and obtaining an estimation of the corrosion velocitytodimension the water purification system. TRACT code(TRansport and ACTivation) has been employed for such study adapting the code for the beam dump case. For such study a collaboration with the code responsible (Panos Karditsas) at Culham (UKAEA) was established. The work developed in this thesis has supposed the publication of three articles in JCR journals (”Journal of Nuclear Materials” y ”Fusion Engineering and Design”), as well as presentations in more than four conferences and relevant meetings.

Metodología de simulación numérica de la transferencia de calor por ebullición en película en torno a superficies esféricas refrigeradas por líquido saturado en convección libre: aplicación a reactores nucleares de lecho de bolas (PBR)

En la presente Tesis se realizó un análisis numérico, usando el código comercial Ansys-Fluent, de la refrigeración de una bola de combustible de un reactor de lecho de bolas (PBR, por sus siglas en inglés), ante un escenario de emergencia en el cual el núcleo sea desensamblado y las bolas se dejen caer en una piscina de agua, donde el mecanismo de transferencia de calor inicialmente sería la ebullición en película, implicando la convección y la radiación al fluido. Previamente se realizaron pruebas de validación, comparando los resultados numéricos con datos experimentales disponibles en la literatura para tres geometrías diferentes, lo cual permitió seleccionar los esquemas y modelos numéricos con mejor precisión y menor costo computacional. Una vez identificada la metodología numérica, todas las pruebas de validación fueron ampliamente satisfactorias, encontrándose muy buena concordancia en el flujo de calor promedio con los datos experimentales. Durante estas pruebas de validación se lograron caracterizar numéricamente algunos parámetros importantes en la ebullición en película con los cuales existen ciertos niveles de incertidumbre, como son el factor de acoplamiento entre convección y radiación, y el factor de corrección del calor latente de vaporización. El análisis térmico de la refrigeración de la bola del reactor por ebullición en película mostró que la misma se enfría, a pesar del calor de decaimiento, con una temperatura superficial de la bola que desciende de forma oscilatoria, debido al comportamiento inestable de la película de vapor. Sin embargo, la temperatura de esta superficie tiene una buena uniformidad, notándose que las áreas mejor y peor refrigeradas están localizadas en la parte superior de la bola. Se observó la formación de múltiples domos de vapor en diferentes posiciones circunferenciales, lo cual causa que el área más caliente de la superficie se localice donde se forman los domos más grandes. La separación entre los domos de vapor fue consistente con la teoría hidrodinámica, con la adición de que la separación entre domos se reduce a medida que evolucionan y crecen, debido a la curvatura de la superficie. ABSTRACT A numerical cooling analysis of a PBR fuel pebble, after an emergency scenario in which the nucleus disassembly is made and the pebbles are dropped into a water pool, transmitting heat by film boiling, involving convection and radiation to the fluid, is carried out in this Thesis. First, were performed validation tests comparing the numerical results with experimental works available for three different geometries, which allowed the selection of numerical models and schemes with better precision and lower computational cost. Once identified the numerical methodology, all validation tests were widely satisfactory, finding very good agreement with experimental works in average heat flux. During these validation tests were achieved numerically characterize some important parameters in film boiling with which there are certain levels of uncertainty, such as the coupling factor between convection and radiation, and the correction factor of the latent heat of vaporization. The thermal analysis of pebble cooling by film boiling shows that despite its decay heat, cooling occurs, with pebble surface temperature descending from an oscillatory manner, due to the instability of the vapor film. However, the temperature of this surface has a good uniformity, noting that the best and worst refrigerated area is located at the top of the pebble. The formation of multiple vapor domes at different circumferential positions is observed, which cause that the hottest area of the surface was located where biggest vapor domes were formed. The separation between vapor domes was consistent with the hydrodynamic theory, with the addition that the separation is reduced as the vapor dome evolves and grows, due to the surface curvature.

Difference schemes for numerical solutions of lagging models of heat conduction

Non-Fourier models of heat conduction are increasingly being considered in the modeling of microscale heat transfer in engineering and biomedical heat transfer problems. The dual-phase-lagging model, incorporating time lags in the heat flux and the temperature gradient, and some of its particular cases and approximations, result in heat conduction modeling equations in the form of delayed or hyperbolic partial differential equations. In this work, the application of difference schemes for the numerical solution of lagging models of heat conduction is considered. Numerical schemes for some DPL approximations are developed, characterizing their properties of convergence and stability. Examples of numerical computations are included.

Difference schemes for time-dependent heat conduction models with delay

Different non-Fourier models of heat conduction, that incorporate time lags in the heat flux and/or the temperature gradient, have been increasingly considered in the last years to model microscale heat transfer problems in engineering. Numerical schemes to obtain approximate solutions of constant coefficients lagging models of heat conduction have already been proposed. In this work, an explicit finite difference scheme for a model with coefficients variable in time is developed, and their properties of convergence and stability are studied. Numerical computations showing examples of applications of the scheme are presented.

A compact difference scheme for numerical solutions of second order dual-phase-lagging models of microscale heat transfer

Dual-phase-lagging (DPL) models constitute a family of non-Fourier models of heat conduction that allow for the presence of time lags in the heat flux and the temperature gradient. These lags may need to be considered when modeling microscale heat transfer, and thus DPL models have found application in the last years in a wide range of theoretical and technical heat transfer problems. Consequently, analytical solutions and methods for computing numerical approximations have been proposed for particular DPL models in different settings. In this work, a compact difference scheme for second order DPL models is developed, providing higher order precision than a previously proposed method. The scheme is shown to be unconditionally stable and convergent, and its accuracy is illustrated with numerical examples.

Geochemistry of sediments of stage 5 of the Nordic seas

Stable isotope, foraminifera and ice rafted detritus (IRD) records covering the last interglacial (the Eemian) from 7 sediment cores in a transect from the Norwegian to the Greenland Sea are presented. The percentages of Neogloboquadrina pachyderma (s.) and Globigerina quinqueloba, foraminiferal content, and to some extent planktonic stable isotope records, demonstrate marked, regional changes in surface water conditions. Importantly, the variability in the abundances of subpolar foraminifera and foraminiferal content are not coherent, implying that these two types of proxies fluctuated independently of each other and most likely reflect changes in sea surface temperature and surface water carbonate productivity, respectively. Paleoceanographic reconstructions demonstrate significant movements of the oceanographic fronts. At the warmest periods, the Arctic front was located far west of the present-day location, at least within the Iceland Sea region. At 126-125 ka, this was most probably due to a stronger or more westerly located Norwegian current. Within the later warm intervals, higher heat flux to the western part of the basin reflects a combination of a stronger Irminger current and/or a weaker east Greenland current. During the main cold spell at ~124 ka, a diffuse Arctic front had a more southeasterly location than today, and intrusion of Atlantic surface waters was probably limited to a narrow corridor in the Eastern Norwegian Sea. A general correspondence between minima in sea surface temperatures and light benthic delta18O may indicate enhanced influx of freshwater to the basin within the cold events. At least in the Norwegian Sea, we find some evidence that the changes in surface water conditions are associated with changes in deep water ventilation. The majority of the fluctuations may be related to occasional breakdown or reduction of the thermohaline circulation within the Nordic seas. In the earliest Eemian, this could result from meltwater forcing. During the remaining part of the last interglacial the fine balance between temperature and salinity, which the deep water formation is depending on, may have been disturbed by periodic increases in fresh water supply or variable influx of warm Atlantic surface waters.