• Nuclear Engineering and Technology
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• v.55 no.7
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• pp.2516-2533
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• 2023

Several practical methods for accelerating the depletion calculation in a GPU-based Monte Carlo (MC) code PRAGMA are presented including the multilevel spectral collapse method and the vectorized Chebyshev rational approximation method (CRAM). Since the generation of microscopic reaction rates for each nuclide needed for the construction of the depletion matrix of the Bateman equation requires either enormous memory access or tremendous physical memory, both of which are quite burdensome on GPUs, a new method called multilevel spectral collapse is proposed which combines two types of spectra to generate microscopic reaction rates: an ultrafine spectrum for an entire fuel pin and coarser spectra for each depletion region. Errors in reaction rates introduced by this method are mitigated by a hybrid usage of direct online reaction rate tallies for several important fissile nuclides. The linear system to appear in the solution process adopting the CRAM is solved by the Gauss-Seidel method which can be easily vectorized on GPUs. With the accelerated depletion methods, only about 10% of MC calculation time is consumed for depletion, so an accurate full core cycle depletion calculation for a commercial power reactor (BEAVRS) can be done in 16 h with 24 consumer-grade GPUs.

• Nuclear Engineering and Technology
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• v.54 no.12
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• pp.4722-4730
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• 2022

This paper introduces a new point depletion-based source term calculation code named BESNA (Bateman Equation Solver for Nuclear Applications), which is aimed to estimate nuclide inventories and source terms from spent nuclear fuels. The BESNA code employs a new modified CE/CM (Constant Extrapolation - Constant Midpoint) predictor-corrector scheme in depletion calculations for improving computational efficiency. In this modified CE/CM scheme, the decay components leading to the large norm of the depletion matrix are excluded in the corrector, and hence the corrector calculation involves only the reaction components, which can be efficiently solved with the Talyor Expansion Method (TEM). The numerical test shows that the new scheme substantially reduces computing time without loss of accuracy in comparison with the conventional scheme using CRAM (Chebyshev Rational Approximation Method), especially when the substep calculations are applied. The depletion calculation and source term estimation capability of BESNA are verified and validated through several problems, where results from BESNA are compared with those calculated by other codes as well as measured data. The analysis results show the computational efficiency of the new modified scheme and the reliability of BESNA in both isotopic predictions and source term estimations.

• Nuclear Engineering and Technology
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• v.52 no.9
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• pp.1881-1895
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• 2020

The theoretical aspects behind the reactor depletion capability of the Monte Carlo code MCS developed at the Ulsan National Institute of Science and Technology (UNIST) and practical results of this depletion feature for a Material-Testing Reactor (MTR) with plate-type fuel are described in this paper. A verification of MCS results is first performed against MCNP6 to confirm the suitability of MCS for the criticality and depletion analysis of the MTR. Then, the dependence of the effective neutron multiplication factor to the number of axial and radial depletion cells adopted in the fuel plates is performed with MCS in order to determine the minimum spatial segmentation of the fuel plates. Monte Carlo depletion results with 37,800 depletion cells are provided by MCS within acceptable calculation time and memory usage. The results show that at least 7 axial meshes per fuel plate are required to reach the same precision as the reference calculation whereas no significant differences are observed when modeling 1 or 10 radial meshes per fuel plate. This study demonstrates that MCS can address the need for Monte Carlo codes capable of providing reference solutions to complex reactor depletion problems with refined meshes for fuel management and research reactor applications.

• Nuclear Engineering and Technology
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• v.55 no.6
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• pp.2230-2245
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• 2023

KANT (KAIST Advanced Nuclear Tachygraphy) is a PWR core simulator recently developed at Korea Advance Institute of Science and Technology, which solves three-dimensional steady-state and transient multigroup neutron diffusion equations under Cartesian geometries alongside the incorporation of thermal-hydraulics feedback effect for multi-physics calculation. It utilizes the standard Nodal Expansion Method (NEM) accelerated with various Coarse Mesh Finite Difference (CMFD) methods for neutronics calculation. For thermal-hydraulics (TH) calculation, a single-phase flow model and a one-dimensional cylindrical fuel rod heat conduction model are employed. The time-dependent neutronics and TH calculations are numerically solved through an implicit Euler scheme, where a detailed coupling strategy is presented in this paper alongside a description of nodal equivalence, macroscopic depletion, and pin power reconstruction. For validation of the steady, transient, and depletion calculation with pin power reconstruction capacity of KANT, solutions for various benchmark problems are presented. The IAEA 3-D PWR and 4-group KOEBERG problems were considered for the steady-state reactor benchmark problem. For transient calculations, LMW (Lagenbuch, Maurer and Werner) LWR and NEACRP 3-D PWR benchmarks were solved, where the latter problem includes thermal-hydraulics feedback. For macroscopic depletion with pin power reconstruction, a small PWR problem modified with KAIST benchmark model was solved. For validation of the multi-physics analysis capability of KANT concerning large-sized PWRs, the BEAVRS Cycle1 benchmark has been considered. It was found that KANT solutions are accurate and consistent compared to other published works.

• Nuclear Engineering and Technology
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• v.46 no.3
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• pp.343-352
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• 2014

Uncertainty and sensitivity analyses with respect to nuclear data are performed with depletion calculations for BWR and PWR fuel assemblies specified in the framework of the UAM-LWR Benchmark Phase II. For this, the GRS sampling based tool XSUSA is employed together with the TRITON depletion sequences from the SCALE 6.1 code system. Uncertainties for multiplication factors and nuclide inventories are determined, as well as the main contributors to these result uncertainties by calculating importance indicators. The corresponding neutron transport calculations are performed with the deterministic discrete-ordinates code NEWT. In addition, the Monte Carlo code KENO in multi-group mode is used to demonstrate a method with which the number of neutron histories per calculation run can be substantially reduced as compared to that in a calculation for the nominal case without uncertainties, while uncertainties and sensitivities are obtained with almost the same accuracy.

• Nuclear Engineering and Technology
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• v.52 no.9
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• pp.1907-1916
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• 2020

In this work, the depletion capability implemented in Monte Carlo code MCS is investigated to predict the isotopic compositions of spent nuclear fuel (SNF). By comparison of MCS calculation results to post irradiation examination (PIE) data obtained from one pressurized water reactor (PWR), the validation of this capability is conducted. The depletion analysis is performed with the ENDF/B-VII.1 library and a fuel assembly model. The transmutation equation is solved by the Chebyshev Rational Approximation Method (CRAM) with a depletion chain of 3820 isotopes. 18 actinides and 19 fission products are analyzed in 14 SNF samples. The effect of statistical uncertainties on the calculated number densities is discussed. On average, most of the actinides and fission products analyzed are predicted within ±6% of the experiment. MCS depletion results are also compared to other depletion codes based on publicly reported information in literature. The code-to-code analysis shows comparable accuracy. Overall, it is demonstrated that the depletion capability in MCS can be reliably applied in the prediction of SNF isotopic inventory.

• Nuclear Engineering and Technology
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• v.52 no.11
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• pp.2667-2677
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• 2020

A domain decomposition (DD) scheme for GPU-based Monte Carlo (MC) calculation which is essential for whole-core depletion is introduced within the framework of the modified history-based tracking algorithm. Since GPU-offloaded MC calculations suffer from limited memory capacity, employing DDMC is inevitable for the simulation of depleted cores which require large storage to save hundreds of newly generated isotopes. First, an automated domain decomposition algorithm named wheel clustering is devised such that each subdomain contains nearly the same number of fuel assemblies. Second, an innerouter iteration algorithm allowing overlapped computation and communication is introduced which enables boundary neutron transactions during the tracking of interior neutrons. Third, a bank update scheme which is to include the boundary sources in a way to be adequate to the peculiar data structures of the GPU-based neutron tracking algorithm is presented. The verification and demonstration of the DDMC method are done for 3D full-core problems: APR1400 fresh core and a mock-up depleted core. It is confirmed that the DDMC method performs comparably with the standard MC method, and that the domain decomposition scheme is essential to carry out full 3D MC depletion calculations with limited GPU memory capacities.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.34D no.12
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• pp.31-38
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• 1997

A new CAD-compatible non-quasi-static (NQS) MOS transient model is presented. A new type of weighted residual method, the collcoatin method, is adopted to obtian an approximate ordinary differntial equation from the continuity eqation. Contrasting to the conventional NQS models, the new model can directly include the variatin of the depletion charge and the derived transient current sare expressed with only physically meaningful variables. The new model predicts transient behaviors reasonably well in the calculation including cutoff regions where the depletion charge rapidly changes.

• Nuclear Engineering and Technology
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• v.44 no.2
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• pp.207-224
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• 2012

This article discusses selects of some outstanding problems in nuclear reactor analysis, with proposed approaches thereto and numerical test results, as follows: i) multi-group approximation in the transport equation, ii) homogenization based on isolated single-assembly calculation, and iii) critical spectrum in Monte Carlo depletion.

• Proceedings of the Korean Nuclear Society Conference
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• 1997.10a
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• pp.70-75
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• 1997

A CASMO/ORIGEN coupling utility program was developed to predict the composition of all the fission products in spent PWR fuels. The coupling program reads the CASMO output file, modifies the ORIGEN cross section library and reconstructs the ORIGEN input file at each depletion step. In ORIGEN, the burnup equation is solved for actinides and fission products based on the fission reaction rates and depletion flux of CASMO. A sample calculation has been performed using a 14$\times$14 PWR fuel assembly and the results are given in this paper.