• Nuclear Engineering and Technology
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• v.49 no.5
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• pp.920-927
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• 2017

With ever-advancing computer technology, the Monte Carlo (MC) neutron transport calculation is expanding its application area to nuclear reactor transient analysis. Dynamic MC (DMC) neutron tracking for transient analysis requires efficient algorithms for delayed neutron generation, neutron population control, and initial condition modeling. In this paper, a new MC steady-state simulation method based on time-dependent MC neutron tracking is proposed for steady-state initial condition modeling; during this process, prompt neutron sources and delayed neutron precursors for the DMC transient simulation can easily be sampled. The DMC method, including the proposed time-dependent DMC steady-state simulation method, has been implemented in McCARD and applied for two-dimensional core kinetics problems in the time-dependent neutron transport benchmark C5G7-TD. The McCARD DMC calculation results show good agreement with results of a deterministic transport analysis code, nTRACER.

• Nuclear Engineering and Technology
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• v.55 no.7
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• pp.2712-2722
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• 2023

For an accurate and efficient time-dependent Monte Carlo (TDMC) neutron transport analysis, several advanced methods are newly developed and implemented in the Seoul National University Monte Carlo code, McCARD. For an efficient control of the neutron population, a dynamic weight window method is devised to adjust the weight bounds of the implicit capture in the time bin-by-bin TDMC simulations. A moving geometry module is developed to model a continuous insertion or withdrawal of a control rod. Especially, the history-based batch method for the TDMC calculations is developed to predict the unbiased variance of a bin-wise mean estimate. The developed methods are verified for three-dimensional problems in the C5G7-TD benchmark, showing good agreements with results from a deterministic neutron transport analysis code, nTRACER, within the statistical uncertainty bounds. In addition, the TDMC analysis capability implemented in McCARD is demonstrated to search the optimum detector positions for the pulsed-neutron-source experiments in the Kyoto University Critical Assembly and AGN201K.

• Nuclear Engineering and Technology
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• v.53 no.12
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• pp.3861-3878
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• 2021

The steady-state simplified spherical harmonics equations (SP_N equations) are a higher order approximation to the neutron transport equations than the neutron diffusion equation that also have reasonable computational demands. This work extends these results for the analysis of transients by comparing of two formulations of time-dependent SP_N equations considering different treatments for the time derivatives of the field moments. The first is the full system of equations and the second is a diffusive approximation of these equations that neglects the time derivatives of the odd moments. The spatial discretization of these methodologies is made by using a high order finite element method. For the time discretization, a semi-implicit Euler method is used. Numerical results show that the diffusive formulation for the time-dependent simplified spherical harmonics equations does not present a relevant loss of accuracy while being more computationally efficient than the full system.

• Nuclear Engineering and Technology
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• v.56 no.3
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• pp.916-921
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• 2024

The control rod worth sensitivity to the neutron detector position in the rod drop experiment is studied by the time-dependent Monte Carlo (TDMC) neutron transport calculations for AGN-201K educational reactor and the Kyoto University Critical Assembly. The TDMC simulations of the rod drop experiments are conducted by the Seoul National University Monte Carlo (MC) code, McCARD, yielding time-dependent neutron densities at detector positions. The detector-position-dependent results of the total control rod worth calculated by the extrapolation, the integral counting, and the inverse methods are compared with the numerical reference using the MC eigenvalue calculations and the experimental results. From these comparisons, it is observed that the total control rod worth can be estimated with a considerable difference depending on the detector position through the rod drop experiment. The proposed TDMC simulation of the rod drop experiment can be applied for searching a better detector position or quantifying a bias for the control rod worth measurement.

• Nuclear Engineering and Technology
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• v.43 no.3
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• pp.243-256
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• 2011

This paper considers the concept of analog computing based on a cellular neural network (CNN) paradigm to simulate nuclear reactor dynamics using a time-dependent second order form of the neutron transport equation. Instead of solving nuclear reactor dynamic equations numerically, which is time-consuming and suffers from such weaknesses as vulnerability to transient phenomena, accumulation of round-off errors and floating-point overflows, use is made of a new method based on a cellular neural network. The state-of-the-art shows the CNN as being an alternative solution to the conventional numerical computation method. Indeed CNN is an analog computing paradigm that performs ultra-fast calculations and provides accurate results. In this study use is made of the CNN model to simulate the space-time response of scalar flux distribution in steady state and transient conditions. The CNN model also is used to simulate step perturbation in the core. The accuracy and capability of the CNN model are examined in 2D Cartesian geometry for two fixed source problems, a mini-BWR assembly, and a TWIGL Seed/Blanket problem. We also use the CNN model concurrently for a typical small PWR assembly to simulate the effect of temperature feedback, poisons, and control rods on the scalar flux distribution.

• Nuclear Engineering and Technology
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• v.4 no.2
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• pp.102-108
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• 1972

Time-dependent neutron transport equation with delayed neutrons is analytic-ally solved in the case of isotropic scattering with constant cross sections. The equations in the two divided time regions are obtained from the original equation by the asymptotic method. It is shown that the approximate solutions in each time region are uniformly valid in time to the order of the inverse magnitude of the velocity.

• Nuclear Engineering and Technology
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• v.2 no.4
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• pp.263-268
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• 1970

The spectrum of continuous transfer operator arising in a time-energy dependent neutron transport equation is analyzed. Four theorems concerning on the spectrum are proved. A convolution theorem of the generalized Mellin energy transform is given. Also the completeness theorem necessary for a final solution is proved. A unique time decay constant 1 - c is found, which is dominant asymptotically.

• Journal of Energy Engineering
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• v.15 no.4 s.48
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• pp.250-255
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• 2006

In this study, the discrete ordinates method which has been widely used in the solution of neutron transport equation is applied to the solution of the time dependent radiative transfer equation. The self-adjoint form of the second order radiation intensity equation is used to enhance the stability of the solution, and a new multi-step linearization method is developed to avoid the nonlinearity in the material temperature equation. This new solution method is applied to the well known Marshak wave problem, and the numerical result is compared with that of the conventional Monte-Carlo method.

• Nuclear Engineering and Technology
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• v.2 no.4
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• pp.249-254
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• 1970

A time-energy transient characteristics of pulsed neutron transport problem with an inelastic kernel in the fast domain is solved exactly with a continuous energy transfer operator. A discrete time eigenvalue is found which is asymptotically dominant. The complete solution consists of three parts: a time-energy separable mode which is asymptotically dominant and a non-separable mode which is made up by two parts； a pure energy slowing-down transient and a mixture of time and energy transient which is negligible asymptotically.

• Nuclear Engineering and Technology
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• v.55 no.5
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• pp.1593-1603
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• 2023

In deterministic and Monte Carlo transport codes, b-delayed emission is included using a group structure where all of the precursors are grouped together in 6 groups or families, but given the increase in computational power, nowadays there is no reason to keep this structure. Furthermore, there have been recent efforts to compile and evaluate all the available b-delayed neutron emission data and to measure new and improved data on individual precursors. In order to be able to perform a transient Monte Carlo simulation, data from individual precursors needs to be implemented in a transport code. This work is the first step towards the development of a tool to explore the effect of individual precursors in a fissile system. In concrete, individual precursor data is included by expanding the capabilities of the open source Monte Carlo code OpenMC. In the modified code - named Time Dependent OpenMC or OpenMC(TD)- time dependency related to β-delayed neutron emission was handled by using forced decay of precursors and combing of the particle population. The data for continuous energy neutron cross-sections was taken from JEFF-3.1.1 library. Regarding the data needed to include the individual precursors, cumulative yields were taken from JEFF-3.1.1 and delayed neutron emission probabilities and delayed neutron spectra were taken from ENDF-B/VIII.0. OpenMC(TD) was tested in a monoenergetic system, an energy dependent unmoderated system where the precursors were taken individually or in a group structure, and in a light-water moderated energy dependent system, using 6-groups, 50 and 40 individual precursors. Neutron flux as a function of time was obtained for each of the systems studied. These results show the potential of OpenMC(TD) as a tool to study the impact of individual precursor data on fissile systems, thus motivating further research to simulate more complex fissile systems.