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

Discrete Feynman-Kac formulas for branching random walks

Branching random walks are key to the description of several physical and biological systems, such as neutron multiplication, genetics and population dynamics. For a broad class of such processes, in this Letter we derive the discrete Feynman-Kac equations for the probability and the moments of the number of visits $n_V$ of the walker to a given region $V$ in the phase space. Feynman-Kac formulas for the residence times of Markovian processes are recovered in the diffusion limit.Comment: 4 pages, 3 figure

Gamma Multiplicities in a Multiplying Sample for the Assay of Nuclear Materials

The multiplicities, or factorial moments, of the distribution of the number of neutrons emerging from a fissile sample can be used to identify and quantify fissile isotopes, in particular even-N isotopes of transuranic elements. In fact, the spontaneously emitted source neutrons can induce further fissions in the sample, thereby changing the number distributions of the neutrons leaving the sample, and therefore their multiplicities. The multiplicities increase monotonically with sample mass, hence the measurement of the multiplicities can be used to quantify the sample mass. Analytical expressions for multiplicities that include induced fission effects have been derived for neutrons in the past. These expressions are given as functions of the probability of induced fission per neutron, and have been investigated both by Monte Carlo methods and in experiments using thermal neutron detectors. The object of this paper is to derive analytical formulae for the multiplicities of the gamma photons emitted by both spontaneous and induced fissions, and to perform a quantitative analysis. In addition, neutron and gamma multiplicities are calculated by Monte Carlo simulation using a modified version of the MCNP-PoliMi code. Good agreement is found between the analytical formulae and the Monte Carlo results. The results show the potential advantage of using gamma multiplicities when compared to neutron multiplicities: their higher quantitative values may, in principle, have the effect of leading to a larger sensitivity on the sample mass when compared to the analysis based on neutrons alone

Calculation of higher moments of the neutron multiplication process in a time-varying medium

The zero-power reactor noise theory in a steady neutron multiplying medium was extended recently to a medium randomly varying in time to bridge the fields of the zero-power and the power reactor noise. For a time-varying medium in which the transition probability randomly fluctuates, only the use of the probability generating function technique based on the forward master equation approach is practical. However, with the forward master equation approach, the treatment of the joint moments of the neutron number and the medium state leads to a closure problem. Recently, the capability of the moment calculation technique for such cases was extended such that the closure problem could be solved exactly. The present paper describes and demonstrates this closure-free moment calculation technique in a time-varying binary multiplying medium, in which the medium state has two possible realizations. In addition to the first two moments of the neutron number N alone (irrespective of the medium state η), the joint moments of Nn and ηm, i.e., <Nnηm>, were also obtained in a compact form for n = 1, 2 and arbitrary values of m, without a closure assumption. It was found that, for even m values, the asymptotic values of Nn and ηm are uncorrelated, whereas, for odd m values, they are negatively correlated, namely, their covariance is less than zero. The first two moments of the neutron number theoretically obtained were verified by the Monte Carlo technique. A perfect agreement was found between the Monte Carlo and the theoretical solutions. The closure-free moment calculation technique demonstrated in the present paper is expected to be applicable to various other problems related to the birth-and-death process with fluctuations of the transition probability, in which a closure problem occurs

Monte Carlo and analytical models of neutron detection with organic scintillation detectors

This paper presents a new technique for the analysis of neutron pulse height distributions generated in an organic scintillation detector. The methodology presented can be applied to techniques such as neutron spectrum unfolding, which have a variety of applications, including nuclear nonproliferation and homeland security. The technique is based on two independent approaches: (i) the use of the MCNP-PoliMi code to simulate neutron detection on an event-by-event basis with the Monte Carlo method and (ii) an analytical approach for neutron slowing down and detection processes. We show that the total neutron pulse height response measured by the organic scintillators is given by the sum of a large number of different neutron histories, each composed of a certain number of neutron scatterings on hydrogen and/or carbon. The relative contributions of each of these histories are described for a cylindrical liquid scintillator BC-501A. Simulations and measurements of neutron pulse height distributions are essential for neutron spectrum unfolding procedures. (c) 2007 Elsevier B.V. All rights reserved

Derivation of pulsed Feynman- and Rossi-alpha formulae including delayed neutrons

In previous works, the authors have developed an effective solution technique for calculating the pulsed Feynman- and Rossi-alpha formulae. Through derivation of these formulae, it was shown that the technique can easily handle various pulse shapes of the pulsed neutron source. Furthermore, it was also shown that both the deterministic (i.e.{} synchronizing with the pulsing of neutron source) and stochastic (non-synchronizing) Feynman-alpha formulae can be obtained with this solution technique. However, for mathematical simplicity and the sake of insight, the formal derivation was performed in a model without delayed neutrons. In this paper, to demonstrate the robustness of the technique, the pulsed Feynman- and Rossi-alpha formulae were re-derived by taking one group of delayed neutrons into account. The results show that the advantages of this technique are retained even by inclusion of the delayed neutrons. Compact explicit formulae are derived for the Feynman- and Rossi-alpha methods for various pulse shapes and pulsing methods