Time series analysis and Monte Carlo methods for eigenvalue separation in neutron multiplication problems

Nease, Brian R.; Ueki, Taro

doi:10.1016/j.jcp.2009.07.037

Cited by 9 publications

(16 citation statements)

References 9 publications

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“…11) This is a sufficiently large DR to be considered for reactor-core-type problems whose source distribution is slowly varying. For example, the DR of a 1,100 MWe pressurized water reactor was computed to be 0:9927 AE 0:0017 (2 ) and 0:9902 AE 0:0008 (2 ) by time series analysis, 12,13) respectively, for two-and threedimensional modeling. Also, as shown in Fig.…”

Section: Center Distance Summentioning

confidence: 99%

A Mesh-Input-Free On-The-Fly Source Convergence Indicator in Monte Carlo Power Method

Ueki

Chapman

2011

Journal of Nuclear Science and Technology

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A mesh-input-free on-the-fly source convergence indicator is proposed for Monte Carlo source iterations by the power method. This indicator consists of two step computations of source particle centers. In the first step, the geometric center of all source particles is computed. The spatial domain is then divided into eight subdomains by the xy, yz, and zx planes that intersect at the geometric center. In the second step, a new geometric center is computed for the source particles in each of the eight subdomains. Therefore, nine centers are obtained at each cycle of source iterations and the distances to the corresponding centers at the initial cycle are computed, yielding the nine center-distances sum (NCDS). NCDS was compared against entropy indicators defined on a fixed mesh. Visual inspection reveals that the overall trend of NCDS is as sound as the entropy indicators. The feasibility of NCDS is shown by the step-refined on-thefly convergence diagnosis with Wilcoxon rank sum.

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Section: Center Distance Summentioning

confidence: 99%

A Mesh-Input-Free On-The-Fly Source Convergence Indicator in Monte Carlo Power Method

Ueki

Chapman

2011

Journal of Nuclear Science and Technology

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“…Recent work 13,14) has shown, assuming only population dynamics, that Eq. (3) is valid with the nonlinear terms being the order of the inverse square root of the number of neutron histories per cycle.…”

Section: Noise Propagation and Autoregressive Moving Average Reprmentioning

confidence: 99%

“…Equation (6) can be derived with no assumption. 14) Therefore, Eqs. (3), (5), and (6) are the starting points in this work.…”

Section: Noise Propagation and Autoregressive Moving Average Reprmentioning

confidence: 99%

“…Equation (A1) is fission event distribution while fission source distribution was the starting point in previous work. 13,14) A realization of sought-after tally-event distribution is also expressed aŝ S S ðmÞ C0 ðr r; EÞ…”

Section: Appendix: Derivation Of Eq (21)mentioning

confidence: 99%

“…The derivations essentially follow the derivation steps of fission source noise propagation formula in recent work 13,14) with some additional details and special considerations concerning the fission and tally events, energy variable, and track length estimation. The starting locations of neutron histories for active cycle m þ 1 are selected based on the fission sites and collection of weights in active cycle m. The probability of choosing a fission event atr r j caused by a neutron with energy E j in order to initiate a history in cycle m þ 1 formally becomes, upon the realization ofŜ S ðmÞ F in Eq.…”

Section: Appendix: Derivation Of Eq (21)mentioning

confidence: 99%

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Standard Deviation of Local Tallies in Global Monte Carlo Calculation of Nuclear Reactor Core

Ueki

2010

Journal of Nuclear Science and Technology

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Time series methodology has been studied to assess the feasibility of statistical error estimation in the continuous space and energy Monte Carlo calculation of the three-dimensional whole reactor core. The noise propagation was examined and the fluctuation of track length tallies for local fission rate and power has been formally shown to be represented by the autoregressive moving average process of orders p and, where p is an integer larger than or equal to two. Therefore, ARMA(p,p À 1) fitting was applied to the real standard deviation estimation of the power of fuel assemblies at particular heights. Numerical results indicate that straightforward ARMA(3,2) fitting is promising, but a stability issue must be resolved toward the incorporation in the distributed version of production Monte Carlo codes. The same numerical results reveal that the average performance of ARMA(3,2) fitting is equivalent to that of the batch method with a batch size larger than 100 and smaller than 200 cycles for a 1,100 MWe pressurized water reactor.

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An algorithm for accurate modeling and simulating reactor cores with involute‐shaped fuel plates by Monte Carlo

et al. 2021

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Summary A real three‐dimensional representation of reactor core with involute fuel plates via Monte Carlo method is still lacking at the present, and usually equivalent homogeneous models of water coolants and simplified fuel plate shapes have been used. This work proposed an algorithm to simulate the reactor core composed of involute fuel plates with an explicit accurate description of its involute surfaces. The description of involute surfaces is through its governing equations. The mathematical function methods to depict the involute curves and the schemes to compute the distance between any neutron particle and an involute surface along a ray are presented and demonstrated step‐by‐step. The algorithm is realized in the Monte Carlo code and validated by the published data of a high flux isotope reactor. This study definitively provides a method to model the involute fuel plates in the Monte Carlo simulation.

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Time series analysis and Monte Carlo methods for eigenvalue separation in neutron multiplication problems

Cited by 9 publications

References 9 publications

A Mesh-Input-Free On-The-Fly Source Convergence Indicator in Monte Carlo Power Method

A Mesh-Input-Free On-The-Fly Source Convergence Indicator in Monte Carlo Power Method

Standard Deviation of Local Tallies in Global Monte Carlo Calculation of Nuclear Reactor Core

An algorithm for accurate modeling and simulating reactor cores with involute‐shaped fuel plates by Monte Carlo

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