Effects of cross sections tables generation and optimization on rod ejection transient analyses

Best estimate analysis of rod ejection transients requires 3D kinetics core simulators. If they use cross sections libraries compiled in multidimensional tables,interpolation errors – originated when the core simulator computes the cross sections from the table values – are a source of uncertainty in k-effective calculations that should be accounted for. Those errors depend on the grid covering the domain of state variables and can be easily reduced, in contrast with other sources of uncertainties such as the ones due to nuclear data, by choosing an optimized grid distribution. The present paper assesses the impact of the grid structure on a PWR rod ejection transient analysis using the coupled neutron-kinetics/thermal-hydraulicsCOBAYA3/COBRA-TF system. Forthispurpose, the OECD/NEA PWR MOX/UO2 core transient benchmark has been chosen, as material compositions and geometries are available, allowing the use of lattice codes to generate libraries with different grid structures. Since a complete nodal cross-section library is also provided as part of the benchmark specifications, the effects of the library generation on transient behavior are also analyzed.Results showed large discrepancies when using the benchmark library and own-generated libraries when compared with benchmark participants’ solutions. The origin of the discrepancies was found to lie in the nodal cross sections provided in the benchmark.

Application of the Boundary Method to the determination of the properties of the beam cross-sections

Using the 3-D equations of linear elasticity and the asylllptotic expansion methods in terms of powers of the beam cross-section area as small parameter different beam theories can be obtained, according to the last term kept in the expansion. If it is used only the first two terms of the asymptotic expansion the classical beam theories can be recovered without resort to any "a priori" additional hypotheses. Moreover, some small corrections and extensions of the classical beam theories can be found and also there exists the possibility to use the asymptotic general beam theory as a basis procedure for a straightforward derivation of the stiffness matrix and the equivalent nodal forces of the beam. In order to obtain the above results a set of functions and constants only dependent on the cross-section of the beam it has to be computed them as solutions of different 2-D laplacian boundary value problems over the beam cross section domain. In this paper two main numerical procedures to solve these boundary value pf'oblems have been discussed, namely the Boundary Element Method (BEM) and the Finite Element Method (FEM). Results for some regular and geometrically simple cross-sections are presented and compared with ones computed analytically. Extensions to other arbitrary cross-sections are illustrated.

Shear stress distribution on beam cross-sections under shear loading

In this work, some results obtained by Trabucho and Viaño for the shear stress distribution in beam cross sections using asymptotic expansions of the three-dimensional elasticity equations are compared with those calculated by the classical formulae of the Strength of Materials. We use beams with rectangular and circular cross section to compare the degree of accuracy reached by each method.

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.

Análisis comparativo de procedimientos para la medición de las gemas y evaluación de su influencia en la determinación de las propiedades mecánicas de la madera de Pinus sylvestris L. de gran escuadría. Comparison of wanes measurement systems to evaluate their influence on the mechanical properties of large cross section timber of Pinus sylvestris L.

Las gemas se evalúan mediante la norma de clasificación visual (UNE 56544), pero su aplicación en estructuras existentes y grandes escuadrías resulta poco eficaz y conduce a estimaciones demasiado conservadoras. Este trabajo analiza la influencia de las gemas comparando la resistencia de piezas con gemas y piezas correctamente escuadradas. Se han analizado 218 piezas de pino silvestre con dimensiones nominales 150 x 200 x 4.200 mm, de las que 102 presentaban una gema completa a lo largo de toda su longitud y el resto estaban correctamente escuadradas. En las piezas con gema se ha medido la altura de la sección cada 30 cm (altura en cada cara y altura máxima). Para determinar la resistencia se han ensayado todas las piezas de acuerdo a la norma EN 408. Se ha comparado la resistencia obtenida para las piezas con gema, diferenciando si la gema se encuentra en el borde comprimido o en el borde traccionado, con las piezas escuadradas. Puede concluirse que la presencia de gemas disminuye la resistencia excepto si la gema se encuentra en el borde traccionado, en cuyo caso los resultados obtenidos han sido similares a los de las piezas escuadradas. The wanes on structural timber are evaluated according to the visual grading standard (UNE 56544), but its application on existing structures and large cross sections is ineffective and leads to conservative estimations. This paper analyzes the influence of the wanes by comparing the resistance of pieces with wanes and square pieces. 218 pieces of Scotch pine with nominal dimensions 150 x 200 x 4200 mm have been analyzed, 102 of them had a complete wane along its length and the rest were properly squared. The height of the cross section was measured every 30 cm (the height on each side and the maximum height) for the pieces with wane. The bending strength of all the pieces was obtained according to the EN 408 standard. The bending strength of the pieces with wane has been compared with the strength of the squared pieces, taking into account if the wane is positioned on the compressed edge or on the tensioned edge. It can be concluded that the bending strength of the pieces with wanes is lower than the one of squared pieces, except if the wanes are on the tensioned edge of the beam.

Review of the C-nat(n,gamma) cross section and criticality calculations of the graphite moderated reactor BR1

A review of the experimental data for natC(n,c) and 12C(n,c) was made to identify the origin of the natC capture cross sections included in evaluated data libraries and to clarify differences observed in neutronic calculations for graphite moderated reactors using different libraries. The performance of the JEFF-3.1.2 and ENDF/B-VII.1 libraries was verified by comparing results of criticality calculations with experimental results obtained for the BR1 reactor. This reactor is an air-cooled reactor with graphite as moderator and is located at the Belgian Nuclear Research Centre SCK-CEN in Mol (Belgium). The results of this study confirm conclusions drawn from neutronic calculations of the High Temperature Engineering Test Reactor (HTTR) in Japan. Furthermore, both BR1 and HTTR calculations support the capture cross section of 12C at thermal energy which is recommended by Firestone and Révay. Additional criticality calculations were carried out in order to illustrate that the natC thermal capture cross section is important for systems with a large amount of graphite. The present study shows that only the evaluation carried out for JENDL-4.0 reflects the current status of the experimental data.

Propagation of Cross-Section Uncertainties in Criticality Calculations in the Framework of UAM-Phase I Using MCNPX-2.7e and SCALE-6.1

In the framework of the OECD/NEA project on Benchmark for Uncertainty Analysis in Modeling (UAM) for Design, Operation, and Safety Analysis of LWRs, several approaches and codes are being used to deal with the exercises proposed in Phase I, “Specifications and Support Data for Neutronics Cases.” At UPM, our research group treats these exercises with sensitivity calculations and the “sandwich formula” to propagate cross-section uncertainties. Two different codes are employed to calculate the sensitivity coefficients of to cross sections in criticality calculations: MCNPX-2.7e and SCALE-6.1. The former uses the Differential Operator Technique and the latter uses the Adjoint-Weighted Technique. In this paper, the main results for exercise I-2 “Lattice Physics” are presented for the criticality calculations of PWR. These criticality calculations are done for a TMI fuel assembly at four different states: HZP-Unrodded, HZP-Rodded, HFP-Unrodded, and HFP-Rodded. The results of the two different codes above are presented and compared. The comparison proves a good agreement between SCALE-6.1 and MCNPX-2.7e in uncertainty that comes from the sensitivity coefficients calculated by both codes. Differences are found when the sensitivity profiles are analysed, but they do not lead to differences in the uncertainty.

Validation of the burn-up code EVOLCODE 2.0 with PWR experimental data and with a Sensitivity/Uncertainty analysis

A validation of the burn-up simulation system EVOLCODE 2.0 is presented here, involving the experimental measurement of U and Pu isotopes and some fission fragments production ratios after a burn-up of around 30 GWd/tU in a Pressurized Light Water Reactor (PWR). This work provides an in-depth analysis of the validation results, including the possible sources of the uncertainties. An uncertainty analysis based on the sensitivity methodology has been also performed, providing the uncertainties in the isotopic content propagated from the cross sections uncertainties. An improvement of the classical Sensitivity/ Uncertainty (S/U) model has been developed to take into account the implicit dependence of the neutron flux normalization, that is, the effect of the constant power of the reactor. The improved S/U methodology, neglected in this kind of studies, has proven to be an important contribution to the explanation of some simulation-experiment discrepancies for which, in general, the cross section uncertainties are, for the most relevant actinides, an important contributor to the simulation uncertainties, of the same order of magnitude and sometimes even larger than the experimental uncertainties and the experiment- simulation differences. Additionally, some hints for the improvement of the JEFF3.1.1 fission yield library and for the correction of some errata in the experimental data are presented.

A computer formulation for the analysis on continuous non prismatic folded plate structures of arbitrary cross-section

A computer solution to analyze nonprismatic folded plate structures is shown. Arbitrary cross-sections (simple and multiple), continuity over intermediate supports and general loading and longitudinal boundary conditions are dealt with. The folded plates are assumed to be straight and long (beam like structures) and some simplifications are introduced in order to reduce the computational effort. The formulation here presented may be very suitable to be used in the bridge deck analysis.

Optimization of multidimensional cross-section tables for few-group core calculations

Multigroup diffusion codes for three dimensional LWR core analysis use as input data pre-generated homogenized few group cross sections and discontinuity factors for certain combinations of state variables, such as temperatures or densities. The simplest way of compiling those data are tabulated libraries, where a grid covering the domain of state variables is defined and the homogenized cross sections are computed at the grid points. Then, during the core calculation, an interpolation algorithm is used to compute the cross sections from the table values. Since interpolation errors depend on the distance between the grid points, a determined refinement of the mesh is required to reach a target accuracy, which could lead to large data storage volume and a large number of lattice transport calculations. In this paper, a simple and effective procedure to optimize the distribution of grid points for tabulated libraries is presented. Optimality is considered in the sense of building a non-uniform point distribution with the minimum number of grid points for each state variable satisfying a given target accuracy in k-effective. The procedure consists of determining the sensitivity coefficients of k-effective to cross sections using perturbation theory; and estimating the interpolation errors committed with different mesh steps for each state variable. These results allow evaluating the influence of interpolation errors of each cross section on k-effective for any combination of state variables, and estimating the optimal distance between grid points.

Vortex-induced vibrations on bridges : the interaction mechanism in complex sections and a new proposed semi-empirical model

El presente trabajo de investigación se ocupa del estudio de las vibraciones verticales inducidas por vórtices (VIV) en aquellos puentes que, por sus características geométricas y propiedades dinámicas, muestran cierta sensibilidad este tipo de fenómeno aeroelástico. El objeto principal es el análisis del mecanismo de interacción viento-estructura sobre secciones no fuseladas de geometría simple, con objeto de realizar una adecuada caracterización del problema y poder abordar posteriormente el análisis de otras secciones de geometría más compleja, representativas de los principales elementos estructurales de los puentes, como arcos, tableros, torres y pilas. Este aspecto es fundamental durante la fase de diseño del puente, donde deberán tenerse en cuenta también una serie de detalles que pueden influir significativamente su sensibilidad ante problemas aerodinámicos, como la morfología y dimensiones principales de la sección transversal del tablero, la disposición de barreras de seguridad y barreras cortaviento, o las riostras que unen diferentes elementos estructurales. La configuración de dos elementos en tándem o la construcción de un puente en las inmediaciones de otro existente son otros aspectos a considerar respecto a la sensibilidad frente a efectos aeroelásticos. El estudio se ha llevado a cabo principalmente mediante la implementación de simulaciones numéricas que reproducen la interacción entre la corriente de aire y secciones representativas de modelos estructurales, a partir de un código CFD basado en el método de las partículas de vórtices (VPM), siguiendo por tanto un esquema Lagrangiano. Los resultados han sido validados con datos experimentales existentes, valores procedentes de ensayos en túnel de viento y registros reales a partir de diferentes casos de estudio: Alconétar (2006), Niterói (1980), Trans- Tokyo Bay (1995) y Volgogrado (2010). Finalmente, se propone un modelo semi-empírico para la estimación del rango de velocidades críticas y amplitudes de oscilación basado en la utilización de las derivadas de flameo de Scanlan, y la densidad espectral de las fuerzas aerodinámicas en el dominio de la frecuencia. The present research work concerns the study of vertical vortex-induced vibrations (VIV) in bridges which show certain sensitivity to this type of aeroelastic phenomenon. It focuses on the analysis of the wind-structure interaction mechanism on bluff sections, with the objective of making a good characterisation of the problem and subsequently addressing the analysis of sections with a complex geometry, which are representative of the bridge structural elements, such as arches, decks, towers and piers. This issue is of relative importance during the bridge design phase, since minor details of the aforementioned elements can significantly influence its sensitivity to aerodynamic problems. The shape and main dimensions of the deck cross section, the addition of safety barriers and windshields, the presence of braces to enhance the structure mechanical properties, the utilisation of cross sections in tandem arrangement, or the erection of a new bridge in the vicinity of another existing one are some of the aspects to be considered regarding the sensitivity to the aeroelastic effects. The study has been carried out mainly through the implementation of numerical simulations that reproduces the interaction between the airflow and the representative cross section of a structural bridge model, by the use of a CFD code based on the vortex particle method (VPM), thus following a Lagrangian scheme. The results have been validated with existing experimental data, values from wind tunnel tests and full scale observations from the different case studies: Alconétar (2006), Niterói (1980), Trans-Tokyo Bay (1995) and Volgograd (2010). Finally, a new semi-empirical model is proposed for the estimation of the critical wind velocity ranges and oscillation amplitudes based on the use of the Scanlan’s flutter derivatives and the power spectral density of aerodynamic force time history in the frequency domain.