A MOC-based neutron kinetics model for noise analysis (original) (raw)

2019, Annals of Nuclear Energy

A 2-D noise model is implemented in the deterministic reactor code APOLLO3 R to simulate a periodic oscillation of a structural component. The Two/Three Dimensional Transport (TDT) solver, using the Method of Characteristics, is adopted for the calculation of the case studies, constituted by a moving detector and control-rod bundle. The periodic movement is built by properly linking the geometries corresponding to the temporal positions. The calculation is entirely performed in the real time domain, without resorting to the traditional frequency approach. A specifically defined dynamic eigenvalue is used to renormalize in average the reactivity over a period. The algorithm is accelerated by the DP N synthetic method. For each cell of the domain, the time values of fission rates are analysed to determine the noise extent. Moreover we propose a systematic approach to the definition of the macroscopic cross sections to be used in dynamical calculations starting from library data. As an aside of our work we have found that even in static calculation this approach can produce significant changes.

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Development of dynamic models for neutron transport calculations

Il Nuovo Cimento C, 2009

A quasi-static approach within the framework of neutron transport theory is used to develop a computational tool for the time-dependent analysis of nuclear systems. The determination of the shape function needed for the quasistatic scheme is obtained by the steady-state transport code DRAGON. The kinetic model solves the system of ordinary differential equations for the amplitude function on a fast scale. The kinetic parameters are calculated by a coupling module that retrieves the shape from the output of the transport code and performs the required adjoint-weighted quadratures. When the update of the shape has to be carried out, the coupling module generates an appropriate input file for the transport code. Both the standard Improved Quasi-Static scheme and an innovative Predictor-Corrector algorithm are implemented. The results show the feasibility of both procedures and their effectiveness in terms of computational times and accuracy.

Linear reactor kinetics and neutron noise in systems with fluctuating boundaries

Annals of Nuclear Energy, 2000

The general theory of linear reactor kinetics and that of the induced neutron noise is developed for systems with varying size, i.e. in which the position of the boundary fluctuates around a stationary value. The point kinetic and adiabatic approximations are defined by a generalisation of the flux factorisation, and the full solution of the general problem with an arbitrarily fluctuating boundary is given by the Green's function technique. The correctness of the general solution is proven both generally and also by considering the simple case of a 2-D cylindrical reactor with a fluctuating radius, in which case a direct compact solution is possible.

Modelling of a vibrating reactor boundary and calculation of the induced neutron noise

Annals of Nuclear Energy, 1996

Three different models of a moving (vibrating) reactor boundary in time-dependent diffusion theory are investigated. The models are: (a) a localized absorber of variable strength at the boundary (equivalent to a perturbational treatment); (b) a time-varying extrapolation length; (c) explicit treatment of the moving boundary with a new transformation technique. The induced neutron noise was calculated in first order of the perturbation parameter both exactly and in the adiabatic approximation. All three models lead to equivalent results, confirming the applicability of perturbation techniques in treating moving perturbations (e.g. vibrating control rods). Application of the adiabatic approximation in model (c) required the extension of the Henry formalism, i.e. the use of orthogonality relations expressed as integrals over the system, to cases with non-constant system volume. The incentives for investigating a time-varying boundary arose from problems related to vibrating control rods; however, the results have some general relevance for systems with a varying volume such as gaseous core or liquid fuel reactors.

Local correlated sampling Monte Carlo calculations in the TFM neutronics approach for spatial and point kinetics applications

EPJ Nuclear Sciences & Technologies, 2017

These studies are performed in the general framework of transient coupled calculations with accurate neutron kinetics models. This kind of application requires a modeling of the influence on the neutronics of the macroscopic cross-section evolution. Depending on the targeted accuracy, this feedback can be limited to the reactivity for point kinetics, or can take into account the redistribution of the power in the core for spatial kinetics. The local correlated sampling technique for Monte Carlo calculation presented in this paper has been developed for this purpose, i.e. estimating the influence on the neutron transport of a local variation of different parameters such as sodium density or fuel Doppler effect. This method is associated to an innovative spatial kinetics model named Transient Fission Matrix, which condenses the time-dependent Monte Carlo neutronic response in Green functions. Finally, an accurate estimation of the feedback effects on these Green functions provides an on-the-fly prediction of the flux redistribution in the core, whatever the actual perturbation shape is during the transient. This approach is also used to estimate local feedback effects for point kinetics resolution.

Comparison of neutron noise solvers based on numerical benchmarks in a 2-D simplified UOX fuel assembly

2021

In the CORTEX project, several solvers are developed and applied to analyze neutron noise problems. They are based on Monte Carlo and deterministic (higher-order transport and diffusion) methods. For the study of their validity and limitations, an extensive verification and validation work has been undertaken and includes the simulation of numerical exercises and experiments. In the current paper the solvers are compared over two neutron noise benchmarks defined in a 2-D simplified UOX fuel assembly, with Monte Carlo used as a reference. In the two exercises, a global neutron noise source and a combination of stationary perturbations of the various cross sections are respectively prescribed. The higher-order neutron transport methods provide consistent results with respect to Monte Carlo. The calculations obtained from the diffusion-based solvers show discrepancies that can be significant, in particular close to the neutron noise source.

Calculation of the Parameters of Stochastic Neutron Kinetics in Zero Power Nuclear Reactors

PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. SERIES: NUCLEAR AND REACTOR CONSTANTS, 2019

The majority of neutron-physical problems of nuclear power plants design can be solved on the basis of various approximations to the Boltzmann transport equation in terms of the averaged characteristics of the reactor: the effective multiplication factor, neutron flux, average neutron lifetime, etc. However, the neutron chain reaction itself is always stochastic. There are situations in which the stochastic nature of the chain reaction cannot be ignored. This is the so-called “blind” start-up problem with a weak external neutron source, the work of physical assemblies of “zero” power, the analysis of the reactivity noise of such assemblies, etc. Despite the well-developed theoretical basis for the stochastic description of the behavior of neutrons in a nuclear reactor, there are still not enough calculation algorithms and programs for stochastic kinetics analysis. The paper presents two computational algorithms for point reactor model, which are developed on the basis of the theory ...

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

Annals of Nuclear Energy, 2019

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.

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