A finite element method for neutron noise analysis in hexagonal reactors

[EN] The early detection of anomalies through the analysis of the neutron noise recorded by in-core and ex-core instrumentation gives the possibility to take proper actions before such problems lead to safety concerns or impact plant availability. The study of the neutron fluctuations permits detecting and differentiate anomalies depending on their type and possibly to characterize and localize such anomalies. This method is non-intrusive and does not require any external perturbation of the system. To effectively use the neutron noise for reactor diagnostics it is essential to accurately model the effects of the anomalies on the neutron field. This paper deals with the development and validation of a neutron noise simulator for reactors with different geometries. The neutron noise is obtained by solving the frequency-domain two-group neutron diffusion equation in the first order approximation. In order to solve this partial differential equation a code based on a high order finite element method is developed. The novelty of this simulator resides on the possibility of dealing with rectangular meshes in any kind of geometry, thus allowing for complex domains and any location of the perturbation. The finite element method also permits automatic refinements in the cell size (h-adaptability) and in its polynomial degree (p-adaptability) that lead to a fast convergence. In order to show the possibilities of the neutron noise simulator developed a perturbation in a hexagonal two-dimensional reactor is investigated in this paper.This project has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 754316. Also, this work has been partially supported by Spanish Ministerio de Economía y Competitividad under project BES-2015-072901 and financed with the help of a Primeros Proyectos de Investigacin (PAID-06-18), Vicerrectorado de Investigación, Innovación y Transferencia of the Universitat Politecnica de València (UPV).Vidal-Ferràndiz, A.; Ginestar Peiro, D.; Carreño, A.; Verdú Martín, GJ.; Demazière, C. (2021). A finite element method for neutron noise analysis in hexagonal reactors. EPJ Web of Conferences (Online). 247:1-8. https://doi.org/10.1051/epjconf/202124721007S1824

Pin-wise homogenization for SPN neutron transport approximation using the finite element method

[EN] The neutron transport equation describes the distribution of neutrons inside a nuclear reactor core. Homogenization strategies have been used for decades to reduce the spatial and angular domain complexity of a nuclear reactor by replacing previously calculated heterogeneous subdomains by homogeneous ones and using a low order transport approximation to solve the new problem. The generalized equivalence theory for homogenization looks for discontinuous solutions through the introduction of discontinuity factors at the boundaries of the homogenized subdomains. In this work, the generalized equivalence theory is extended to the Simplified P-N equations using the finite element method. This extension proposes pin discontinuity factors instead of the usual assembly discontinuity factors and the use of the simplified spherical harmonics approximation rather than diffusion theory. An interior penalty finite element method is used to discretize and solve the problem using discontinuity factors. One dimensional numerical results show that the proposed pin discontinuity factors produce more accurate results than the usual assembly discontinuity factors. The proposed pin discontinuity factors produce precise results for both pin and assembly averaged values without using advanced reconstruction methods. Also, the homogenization methodology is verified against the calculation performed with reference discontinuity factors. (C) 2017 Elsevier B.V. All rights reserved.The work has been partially supported by the spanish Ministerio de Economía y Competitividad under projects ENE 2014-59442-P and MTM2014-58159-P, the Generalitat Valenciana under the project PROMETEO II/2014/008 and the Universitat Politècnica de València under the project FPI-2013. The work has also been supported partially by the Swedish Research Council (VR-Vetenskapsrådet) within a framework grant called DREAM4SAFER, research contract C0467701Vidal-Ferràndiz, A.; Gonzalez-Pintor, S.; Ginestar Peiro, D.; Demaziere, C.; Verdú Martín, GJ. (2018). Pin-wise homogenization for SPN neutron transport approximation using the finite element method. Journal of Computational and Applied Mathematics. 330:806-821. https://doi.org/10.1016/j.cam.2017.06.023S80682133

Neutronic Simulation of Fuel Assembly Vibrations in a Nuclear Reactor

This is an Accepted Manuscript of an article published by Taylor & Francis in Nuclear Science and Engineering on 2020, available online: http://www.tandfonline.com/10.1080/00295639.2020.1756617[EN] The mechanical vibrations of core internals such as fuel assemblies (FAs) cause oscillations in the neutron flux that require in some circumstances nuclear power plants to operate at a reduced power level. This work simulates and analyzes the changes of the neutron flux throughout a nuclear core due to the oscillation of a single FA without considering thermal-hydraulic feedback. The amplitude of the FA vibration is bounded to a few millimeters, and this implies the use of fine meshes and accurate numerical solvers due to the different scales of the problem. The results of the simulations show a main oscillation of the neutron flux with the same frequency as the FA vibration along with other harmonics at multiples of the vibration frequency much smaller in amplitude. Also, this work compares time domain analysis and frequency domain analysis of the mechanical vibrations. Numerical results show a close match between these two approaches for the fundamental frequency.This project has received funding from the Euratom research and training programme 2014-2018 under grant agreement number 754316. Also, this work has been partially supported by Spanish Ministerio de Economia y Competitividad under project BES-2015-072901 and financed with the help of Primeros Proyectos de Investigacion (PAID-06-18), Vicerrectorado de Investigacion, Innovacion y Transferencia of the Universitat Politecnica de Valencia (UPV).Vidal-Ferràndiz, A.; Carreño, A.; Ginestar Peiro, D.; Demazière, C.; Verdú Martín, GJ. (2020). Neutronic Simulation of Fuel Assembly Vibrations in a Nuclear Reactor. Nuclear Science and Engineering. 194(11):1067-1078. https://doi.org/10.1080/00295639.2020.1756617S106710781941

Viscoelastic Effects on the Response of Electroelastic Materials

[EN] Electroelastic materials, as for example, 3M VHB 4910, are attracting attention as actuators or generators in some developments and applications. This is due to their capacity of being deformed when submitted to an electric field. Some models of their actuation are available, but recently, viscoelastic models have been proposed to give an account of the dissipative behaviour of these materials. Their response to an external mechanical or electrical force field implies a relaxation process towards a new state of thermodynamic equilibrium, which can be described by a relaxation time. However, it is well known that viscoelastic and dielectric materials, as for example, polymers, exhibit a distribution of relaxation times instead of a single relaxation time. In the present approach, a continuous distribution of relaxation times is proposed via the introduction of fractional derivatives of the stress and strain, which gives a better account of the material behaviour. The application of fractional derivatives is described and a comparison with former results is made. Then, a double generalisation is carried out: the first one is referred to the viscoelastic or dielectric models and is addressed to obtain a nonsymmetric spectrum of relaxation times, and the second one is the adoption of the more realistic Mooney-Rivlin equation for the stress-strain relationship of the elastomeric material. A modified Mooney-Rivlin model for the free energy density of a hyperelastic material, VHB 4910 has been used based on experimental results of previous authors. This last proposal ensures the appearance of the bifurcation phenomena which is analysed for equibiaxial dead loads; time-dependent bifurcation phenomena are predicted by the extended Mooney-Rivlin equations.Díaz-Calleja, R.; Ginestar Peiro, D.; Compañ Moreno, V.; Llovera Segovia, P.; Burgos-Simon, C.; Cortés, J.; Quijano-Lopez, A.... (2021). Viscoelastic Effects on the Response of Electroelastic Materials. Polymers. 13(13):1-28. https://doi.org/10.3390/polym13132198S128131

A time and frequency domain analysis of the effect of vibrating fuel assemblies on the neutron noise

[EN] The mechanical vibrations of fuel assemblies have been shown to give rise to high levels of neutron noise, triggering in some circumstances the necessity to operate nuclear reactors at a reduced power level. This work analyses the effect in the neutron field of the oscillation of one single fuel assembly. Results show two different effects in the neutron field caused by the fuel assembly vibration. First, a global slow variation of the total reactor power due to a change in the criticality of the system. Second, an oscillation in the neutron flux in-phase with the assembly vibration. This second effect has a strong spatial dependence that can be used to localize the oscillating assembly. This paper shows a comparison between a time-domain and a frequency-domain analysis of the phenomena to calculate the spatial response of the neutron noise. Numerical results show a really close agreement between these two approaches.This project has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 754316. Also, this work has been partially supported by Spanish Ministerio de Economia y Competitividad under project BES-2015-072901 and financed with the help of a Primeros Proyectos de Investigation (PAID-06-18), Vicerrectorado de Investigacitin, Innovation y Transferencia of the Universitat Politecnica de Valencia (UPV).Vidal-Ferràndiz, A.; Carreño, A.; Ginestar Peiro, D.; Demazière, C.; Verdú Martín, GJ. (2020). A time and frequency domain analysis of the effect of vibrating fuel assemblies on the neutron noise. Annals of Nuclear Energy. 137:1-12. https://doi.org/10.1016/j.anucene.2019.107076S112137Akcasu, Z. (1958). General Solution of the Reactor Kinetic Equations without Feedback. Nuclear Science and Engineering, 3(4), 456-467. doi:10.13182/nse58-a25482Antonopoulos-Domis, M. (1976). Reactivity and neutron density noise excited by random rod vibration. Annals of Nuclear Energy, 3(9-10), 451-459. doi:10.1016/0306-4549(76)90030-xDemaziere, C. (2006). Analysis methods for the determination of possible unseated fuel assemblies in BWRs. International Journal of Nuclear Energy Science and Technology, 2(3), 167. doi:10.1504/ijnest.2006.010713Demazière, C. (2011). CORE SIM: A multi-purpose neutronic tool for research and education. Annals of Nuclear Energy, 38(12), 2698-2718. doi:10.1016/j.anucene.2011.06.010Demazière, C., & Andhill, G. (2005). Identification and localization of absorbers of variable strength in nuclear reactors. Annals of Nuclear Energy, 32(8), 812-842. doi:10.1016/j.anucene.2004.12.011Demazière, C., Dykin, V., & Jareteg, K. (2017). Development of a point-kinetic verification scheme for nuclear reactor applications. Journal of Computational Physics, 339, 396-411. doi:10.1016/j.jcp.2017.03.020Demazière, C., & Pázsit, I. (2009). Numerical tools applied to power reactor noise analysis. Progress in Nuclear Energy, 51(1), 67-81. doi:10.1016/j.pnucene.2008.01.010Ginestar, D., Verdú, G., Vidal, V., Bru, R., Marín, J., & Muñoz-Cobo, J. L. (1998). High order backward discretization of the neutron diffusion equation. Annals of Nuclear Energy, 25(1-3), 47-64. doi:10.1016/s0306-4549(97)00046-7Hébert, A. (1985). Application of the Hermite Method for Finite Element Reactor Calculations. Nuclear Science and Engineering, 91(1), 34-58. doi:10.13182/nse85-a17127Jonsson, A., Tran, H. N., Dykin, V., & Pázsit, I. (2012). Analytical investigation of the properties of the neutron noise induced by vibrating absorber and fuel rods. Kerntechnik, 77(5), 371-380. doi:10.3139/124.110258Kronbichler, M., & Kormann, K. (2012). A generic interface for parallel cell-based finite element operator application. Computers & Fluids, 63, 135-147. doi:10.1016/j.compfluid.2012.04.012Larsson, V., & Demazière, C. (2009). Comparative study of 2-group and diffusion theories for the calculation of the neutron noise in 1D 2-region systems. Annals of Nuclear Energy, 36(10), 1574-1587. doi:10.1016/j.anucene.2009.07.009Olmo-Juan, N., Demazière, C., Barrachina, T., Miró, R., & Verdú, G. (2019). PARCS vs CORE SIM neutron noise simulations. Progress in Nuclear Energy, 115, 169-180. doi:10.1016/j.pnucene.2019.03.041Park, J., Lee, J. H., Kim, T.-R., Park, J.-B., Lee, S. K., & Koo, I.-S. (2003). Identification of reactor internals’ vibration modes of a Korean standard PWR using structural modeling and neutron noise analysis. Progress in Nuclear Energy, 43(1-4), 177-186. doi:10.1016/s0149-1970(03)00021-0Pázsit, I. (1988). Control-rod models and vibration induced noise. Annals of Nuclear Energy, 15(7), 333-346. doi:10.1016/0306-4549(88)90081-3Pázsit, I., & Th.Analytis, G. (1980). Theoretical investigation of the neutron noise diagnostics of two-dimensional control rod vibrations in a PWR. Annals of Nuclear Energy, 7(3), 171-183. doi:10.1016/0306-4549(80)90082-1Pázsit, I., & Glöckler, O. (1983). On the Neutron Noise Diagnostics of Pressurized Water Reactor Control Rod Vibrations. I. Periodic Vibrations. Nuclear Science and Engineering, 85(2), 167-177. doi:10.13182/nse83-a27424Ravetto, P. (1997). Reactivity oscillations in a point reactor. Annals of Nuclear Energy, 24(4), 303-314. doi:10.1016/s0306-4549(96)00066-7Sunde, C., Demazière, C., & Pázsit, I. (2006). Calculation of the Neutron Noise Induced by Shell-Mode Core-Barrel Vibrations in a 1-D, Two-Group, Two-Region Slab Reactor Model. Nuclear Technology, 154(2), 129-141. doi:10.13182/nt06-1Tran, H.-N., Pázsit, I., & Nylén, H. (2015). Investigation of the ex-core noise induced by fuel assembly vibrations in the Ringhals-3 PWR. Annals of Nuclear Energy, 80, 434-446. doi:10.1016/j.anucene.2015.01.045Vidal-Ferràndiz, A., Carreño, A., Ginestar, D., & Verdú, G. (2019). A Block Arnoldi Method for the SPN Equations. International Journal of Computer Mathematics, 1-22. doi:10.1080/00207160.2019.1602768Vidal-Ferrandiz, A., Fayez, R., Ginestar, D., & Verdú, G. (2014). Solution of the Lambda modes problem of a nuclear power reactor using an h–p finite element method. Annals of Nuclear Energy, 72, 338-349. doi:10.1016/j.anucene.2014.05.026Vidal-Ferràndiz, A., Fayez, R., Ginestar, D., & Verdú, G. (2016). Moving meshes to solve the time-dependent neutron diffusion equation in hexagonal geometry. Journal of Computational and Applied Mathematics, 291, 197-208. doi:10.1016/j.cam.2015.03.040Viebach, M., Bernt, N., Lange, C., Hennig, D., & Hurtado, A. (2018). On the influence of dynamical fuel assembly deflections on the neutron noise level. Progress in Nuclear Energy, 104, 32-46. doi:10.1016/j.pnucene.2017.08.010Weinberg, A. M., & Schweinler, H. C. (1948). Theory of Oscillating Absorber in a Chain Reactor. Physical Review, 74(8), 851-863. doi:10.1103/physrev.74.85

Schwarz type preconditioners for the neutron diffusion equation

[EN] Domain decomposition is a mature methodology that has been used to accelerate the convergence of partial differential equations. Even if it was devised as a solver by itself, it is usually employed together with Krylov iterative methods improving its rate of convergence, and providing scalability with respect to the size of the problem. In this work, a high order finite element discretization of the neutron diffusion equation is considered. In this problem the preconditioning of large and sparse linear systems arising from a source driven formulation becomes necessary due to the complexity of the problem. On the other hand, preconditioners based on an incomplete factorization are very expensive from the point of view of memory requirements. The acceleration of the neutron diffusion equation is thus studied here by using alternative preconditioners based on domain decomposition techniques inside Schur complement methodology. The study considers substructuring preconditioners, which do not involve overlapping, and additive Schwarz preconditioners, where some overlapping between the subdomains is taken into account. The performance of the different approaches is studied numerically using two-dimensional and three-dimensional problems. It is shown that some of the proposed methodologies outperform incomplete LU factorization for preconditioning as long as the linear system to be solved is large enough, as it occurs for three-dimensional problems. They also outperform classical diagonal Jacobi preconditioners, as long as the number of systems to be solved is large enough in such a way that the overhead of building the pre-conditioner is less than the improvement in the convergence rate. (C) 2016 Elsevier B.V. All rights reserved.The work has been partially supported by the spanish Ministerio de Economía y Competitividad under projects ENE 2014-59442-P and MTM2014-58159-P, the Generalitat Valenciana under the project PROMETEO II/2014/008 and the Universitat Politècnica de València under the project FPI-2013. The work has also been supported partially by the Swedish Research Council (VR-Vetenskapsrådet) within a framework grant called DREAM4SAFER, research contract C0467701.Vidal-Ferràndiz, A.; González Pintor, S.; Ginestar Peiro, D.; Verdú Martín, GJ.; Demazière, C. (2017). Schwarz type preconditioners for the neutron diffusion equation. Journal of Computational and Applied Mathematics. 309:563-574. https://doi.org/10.1016/j.cam.2016.02.056S56357430

METODOLOGÍA DE CALIBRACIÓN DE DOS MODELOS DE SIMULACIÓN DEL TRANSPORTE DE AGUA EN EL SUELO EN CULTIVOS HORTÍCOLAS

[ES] El uso de modelos de simulación de la dinámica del agua en el suelo requiere del conocimiento de un gran número de parámetros, algunos de los cuales son difíciles de medir y es necesaria su calibración a partir de medidas experimentales. Por ello, es conveniente elegir aquellos parámetros que mayor incidencia tienen en los procesos a estudiar, simplificando con ello el proceso de calibración del modelo. En este trabajo se propone la utilización de métodos de análisis de sensibilidad global para determinar los parámetros más influyentes en los errores de la predicción del contenido de humedad del suelo de dos modelos de simulación con diferente grado de complejidad, LEACHM y EU-Rotate_N. Se ha hecho uso de los valores medidos de la humedad del suelo en dos ensayos de cultivo de coliflor en dos años consecutivos, utilizando los datos del primer ensayo para la calibración de ambos modelos y los datos del segundo ensayo para evaluar la capacidad predictiva de los mismos una vez calibrados. Los resultados muestran que es posible obtener buenas predicciones calibrando solo un número reducido de parámetros.Este trabajo ha sido subvencionado parcialmente por el Ministerio de Economía y Competitividad mediante el proyecto INIA-RTA 2011–00136-C04-01.Sánchez De Oleo, C.; Jaramillo Gonzalez, CX.; Illera Gómez, I.; Lidón Cerezuela, AL.; Ramos Mompó, C.; Ginestar Peiro, D. (2015). METODOLOGÍA DE CALIBRACIÓN DE DOS MODELOS DE SIMULACIÓN DEL TRANSPORTE DE AGUA EN EL SUELO EN CULTIVOS HORTÍCOLAS. En XXXIII CONGRESO NACIONAL DE RIEGOS. Valencia 16-18 junio de 2015. Editorial Universitat Politècnica de València. https://doi.org/10.4995/CNRiegos.2015.1424OC

Does the development of new medicinal products in the European Union address global and regional health concerns?

<p>Abstract</p> <p>Background</p> <p>Since 1995, approval for many new medicinal products has been obtained through a centralized procedure in the European Union. In recent years, the use of summary measures of population health has become widespread. We investigated whether efforts to develop innovative medicines are focusing on the most relevant conditions from a global public health perspective.</p> <p>Methods</p> <p>We reviewed the information on new medicinal products approved by centralized procedure from 1995 to 2009, information that is available to the public in the European Commission Register of medicinal products and the European Public Assessment Reports from the European Medicines Agency. Morbidity and mortality data were included for each disease group, according to the Global Burden of Disease project. We evaluated the association between authorized medicinal products and burden of disease measures based on disability-adjusted life years (DALYs) in the European Union and worldwide.</p> <p>Results</p> <p>We considered 520 marketing authorizations for medicinal products and 338 active ingredients. New authorizations were seen to increase over the period analyzed. There was a positive, high correlation between DALYs and new medicinal product development (ρ = 0.619, p = 0.005) in the European Union, and a moderate correlation for middle-low-income countries (ρ = 0.497, p = 0.030) and worldwide (ρ = 0.490, p = 0.033). The most neglected conditions at the European level (based on their attributable health losses) were neuropsychiatric diseases, cardiovascular diseases, respiratory diseases, sense organ conditions, and digestive diseases, while globally, they were perinatal conditions, respiratory infections, sense organ conditions, respiratory diseases, and digestive diseases.</p> <p>Conclusions</p> <p>We find that the development of new medicinal products is higher for some diseases than others. Pharmaceutical industry leaders and policymakers are invited to consider the implications of this imbalance by establishing work plans that allow for the setting of future priorities from a public health perspective.</p

Leaf water potential and sap flow as indicators of water stress in Crimson ‘seedless’ grapevines under different irrigation strategies

Vitis vinifera L. cv. Crimson Seedless is a late season red table grape developed in 1989, with a high market value and increasingly cultivated under protected environments to extend the availability of seedless table grapes into the late fall. The purpose of this work was to evaluate leaf water potential and sap flow as indicators of water stress in Crimson Seedless vines under standard and reduced irrigation strategy, consisting of 70 % of the standard irrigation depth. Additionally, two sub-treatments were applied, consisting of normal irrigation throughout the growing season and a short irrigation induced stress period between veraison and harvest. Leaf water potential measurements coherently signaled crop-available water variations caused by different irrigation treatments, suggesting that this plant-based method can be reliably used to identify water-stress conditions. The use of sap flow density data to establish a ratio based on a reference ‘well irrigated vine’ and less irrigated vines can potentially be used to signal differences in the transpiration rates, which may be suitable for improving irrigation management strategies while preventing undesirable levels of water stress. Although all four irrigation strategies resulted in the production of quality table grapes, significant differences (p ≤ 0.05) were found in both berry weight and sugar content between the standard irrigation and reduced irrigation treatments. Reduced irrigation increased slightly the average berry size as well as sugar content and technical maturity index. The 2-week irrigation stress period had a negative effect on these parameters