The topic of this paper is the development of sensitivity and uncertainty analysis capability to the CASMO-4/CASMO-4E - SIMULATE-3 code sequence in the context of the OECD/NEA benchmark 'Uncertainty Analysis in Best-Estimate Modelling for Design, Operation and Safety Analysis of LWRs' (UAM). The developed capability uses a two-step approach. In the first step, Uncertainties in nuclear data are propagated to two-group cross sections, diffusion coefficients, and assembly discontinuity factors. This is carried out using deterministic, perturbation-theory-based uncertainty analysis methodology. In the second step, a global covariance matrix, characterizing the uncertainties of the group constants, is formed, and the uncertainties are propagated through a full core SIMULATE calculation using a stochastic approach. This system enables the analysis of nuclear data related uncertainties in assembly homogenized group constants, assembly discontinuity factors, and pin powers, as well as full core results such as multiplication factor and power distribution. The mathematical background of the deterministic uncertainty analysis methodology is reviewed and the main conclusions related to the implementation are summarized. Numerical results are presented for the full core Three Mile Island model in exercise 1-3 of the UAM benchmark at hot zero power with all rods out and inserted. The computational efficiency of the calculations is discussed. (C) 2017 Elsevier Ltd. All rights reserved.

Abstract The burnup equations can, in principle, be solved by computing the exponential of the burnup matrix. However, the problem is extremely stiff, and the matrix exponential solution was long considered infeasible for entire burnup systems containing short-lived nuclides. After discovering that the eigenvalues of burnup matrices are confined to the vicinity of the negative real axis, the Chebyshev rational approximation method (CRAM) was introduced for solving the burnup equations and it was shown to be capable of providing accurate and efficient solutions without the need to exclude the short-lived nuclides. The main difficulty in using CRAM is determining the coefficients of the rational approximant for a given approximation order, with the previously published coefficients enabling only approximations up to order 16 for computing the matrix exponential. In this paper, a Remez-type method is presented for the computation of higher-order CRAM approximations. The optimal form of CRAM for the solution of burnup equations is discussed, and the method of incomplete partial fractions is proposed for this purpose. The CRAM coefficients based on this factorization are provided for approximation orders 4, 8, 12, …, 48. The accuracy of the method is demonstrated by applying it to large burnup and decay systems. It is shown that higher-order CRAM can be used to solve the burnup equations accurately for time steps of the order of 1 million years.

This paper describes the methods used in the Serpent 2 Monte Carlo code for producing homogenized group constants for nodal diffusion and other deterministic reactor simulator calculations. The methodology covers few-group reaction cross sections, scattering matrices, diffusion coefficients and poison cross sections condensed in infinite and B-1 leakage-corrected critical spectra, as well as the calculation of discontinuity factors, pin-power form factors, delayed neutron parameters and total and partial albedos. Also included is a description of an automated burnup sequence, which was recently implemented for the handling of restart calculations with branch variations. This capability enables covering the full range of local operating conditions required for the parameterization of group constants within a single run. The purpose of this paper is to bring the methodological description provided in earlier publications up to date, and provide insight into the developed methods and capabilities, including their limitations and known flaws. (C) 2016 Elsevier Ltd. All rights reserved.

The Chebyshev rational approximation method (CRAM) for solving the decay and depletion of nuclides is shown to have a remarkable decrease in error when advancing the system with the same time step and microscopic reaction rates as the previous step. This property is exploited here to achieve high accuracy in any end-of-step solution by dividing a step into equidistant substeps. The computational cost of identical substeps can be reduced significantly below that of an equal number of regular steps, as the lower-upper decompositions for the linear solutions required in CRAM need to be formed only on the first substep. The improved accuracy provided by substeps is most relevant in decay calculations, where there have previously been concerns about the accuracy and generality of CRAM. With substeps, CRAM can solve any decay or depletion problem with constant microscopic reaction rates to an extremely high accuracy for all nuclides with concentrations above an arbitrary limit.

The four-year Numerical Multi-Physics (NUMPS) project funded by the Academy of Finland was initiated at VU Technical Research Centre of Finland in September 2012, for the purpose of studying and developing high-fidelity computational methods for nuclear reactor analysis. The project is built around calculation codes developed at VU, and it aims at the coupled three-dimensional modeling of neutronics, thermal hydraulics and fuel behavior of nuclear reactors. The work involves the continuous-energy Monte Carlo code Serpent and CFD code PORFLO, together with two light-weight solvers, COSY and FINIX, coupled to Serpent at source code level. This paper is a review on the current status and development activities, reflecting the status of the NUMPS project at the beginning of its second complete year. (c) 2014 Elsevier Ltd. All rights reserved.

The Serpent Monte Carlo reactor physics burnup calculation code has been developed at VTT Technical Research Centre of Finland since 2004, and is currently used in 100 universities and research organizations around the world. This paper presents the brief history of the project, together with the currently available methods and capabilities and plans for future work. Typical user applications are introduced in the form of a summary review on Serpent-related publications over the past few years.

The Serpent-ARES code sequence, applying Monte Carlo based group constants in a full-core nodal diffusion calculation, is currently being validated for PWR fuel cycle simulations. The test case chosen for the task is the MIT BEAVRS benchmark, which provides a detailed description of a commercial PWR core, including operating data and results of experimental measurements. This paper summarizes the first stage of the validation study, which is focused on the neutronics solution at the hot zero-power state of the initial core. The results show a good agreement between the ARES simulation and a reference full-scale Monte Carlo calculation at both assembly- and pin-level. At core mid-plane, the reconstructed pin-powers are off by less than 1% in 82% of all fuel pins. (C) 2014 Elsevier Ltd. All rights reserved.

The Chebyshev Rational Approximation Method (CRAM) has recently been introduced by the authors to solve burnup equations, and the results have been excellent. This method has been shown to be capable of simultaneously solving an entire burnup system with thousands of nuclides both accurately and efficiently. The method was prompted by an analysis of the spectral properties of burnup matrices, and it can be characterized as the best rational approximation on the negative real axis. The coefficients of the rational approximation are fixed and have been reported for various approximation orders. In addition to these coefficients, implementing the method requires only a linear solver. This paper describes an efficient method for solving the linear systems associated with the CRAM approximation. The introduced direct method is based on sparse Gaussian elimination, where the sparsity pattern of the resulting upper triangular matrix is determined before the numerical elimination phase. The stability of the proposed Gaussian elimination method is discussed based on consideration of the numerical properties of burnup matrices. Suitable algorithms are presented for computing the symbolic factorization and numerical elimination in order to facilitate the implementation of CRAM and its adoption into routine use. The accuracy and efficiency of the described technique are demonstrated by computing the CRAM approximations for a large test case with 1606 nuclides.

The Chebyshev Rational Approximation Method (CRAM) has been recently introduced by the authors for solving the burnup equations with excellent results. This method has been shown to be capable of simultaneously solving an entire burnup system with thousands of nuclides both accurately and efficiently. The method was prompted by an analysis of the spectral properties of burnup matrices and it can be characterized as the best rational approximation on the negative real axis. The coefficients of the rational approximation are fixed and have been reported for various approximation orders. In addition to these coefficients, implementing the method only requires a linear solver. This paper describes an efficient method for solving the linear systems associated with the CRAM approximation. The introduced direct method is based on sparse Gaussian elimination where the sparsity pattern of the resulting upper triangular matrix is determined before the numerical elimination phase. The stability of the proposed Gaussian elimination method is discussed based on considering the numerical properties of burnup matrices. Suitable algorithms are presented for computing the symbolic factorization and numerical elimination in order to facilitate the implementation of CRAM and its adoption into routine use. The accuracy and efficiency of the described technique are demonstratedmore » by computing the CRAM approximations for a large test case with over 1600 nuclides. (authors)« less

The topic of this paper is the development of sensitivity and uncertainty analysis capability to the reactor physics code CASMO-4 in the context of the UAM (Uncertainty Analysis in Best-Estimate Modelling for Design, Operation, and Safety Analysis of LWRs) benchmark. The sensitivity analysis implementation is based on generalized perturbation theory, which enables computing the sensitivity profiles of reaction rate ratios efficiently by solving one generalized adjoint system for each response. Both the theoretical background and the practical guidelines for modifying a deterministic transport code to compute the generalized adjoint solutions and sensitivity coefficients are reviewed. The implementation to CASMO-4 is described in detail. The developed uncertainty analysis methodology is deterministic, meaning that the uncertainties are computed based on the sensitivity profiles and covariance matrices for the uncertain nuclear data parameters. The main conclusions related to the approach used for creating a covariance library compatible with the cross-section libraries of CASMO-4 are presented. Numerical results are given for a lattice physics test problem representing a BWR, and the results are compared to the TSUNAMI-2D sequence in SCALE 6.1.

Chebyshev rational approximation can be a viable method to compute the exponential of matrices with eigenvalues in the vicinity of the negative real axis, and it was recently applied successfully to solving nuclear fuel burnup equations. Determining the partial fraction decomposition (PFD) coefficients of this approximation can be difficult and they have been provided (for approximation orders 10 and 14) by Gallopoulos and Saad in "Efficient solution of parabolic equations by Krylov approximation methods", SIAM J. Sci. Stat. Comput., 13(1992). It was recently discovered that the order 14 coefficients contain errors and result in 100 times poorer accuracy than expected by theory. The purpose of this note is to provide the correct PFD coefficients for approximation orders 14 and 16 and to briefly discuss the approximation accuracy resulting from the erroneous coefficients.

This paper describes the implementation of classical perturbation theory based sensitivity and uncertainty analysis to the reactor physics code CASMO-4 in the context of the UAM (Uncertainty Analysis in Best-Estimate Modelling for Design, Operation and Safety Analysis of LWRS) benchmark. The theoretical background as well as practical guidelines for similar work are reviewed and the developed methodology is described in detail. A technique is proposed for handling a discrepancy between the code and covariance libraries regarding the amount of reactions present in the cross-section model. Numerical results for PWR and GEN-III MOX pin-cell test problems are presented and compared to TSUNAMI-1D. The results are in accordance with theoretical considerations and reflect the characteristics of the developed methodology.

The topic of this paper is solving the burnup equations using dedicated matrix exponential methods that are based on two different types of rational approximation near the negative real axis. The previously introduced Chebyshev Rational Approximation Method (CRAM) is now analyzed in detail for its accuracy and convergence, and correct partial fraction coefficients for approximation orders 14 and 16 are given to facilitate its implementation and improve the accuracy. As a new approach, rational approximation based on quadrature formulas derived from complex contour integrals is proposed, which forms an attractive alternative to CRAM, as its coefficients are easy to compute for any order of approximation. This gives the user the option to routinely choose between computational efficiency and accuracy all the way up to the level permitted by the available arithmetic precision. The presented results for two test cases are validated against reference solutions computed using high-precision arithmetics. The observed behavior of the methods confirms the previous conclusions of CRAM's excellent suitability for burnup calculations and establishes the quadrature-based approximation as a viable and flexible alternative that, like CRAM, has its foundation in the specific eigenvalue properties of burnup matrices.

Access to sustainable, sufficient and economically viable energy sources, mitigation of climate change, and avoiding harmful environmental and health impacts are vital to growing world population. The new generation fission reactors can offer a remarkable contribution to this end by extending the availability of nuclear fuel resources to thousands of years. Nuclear energy causes negligible greenhouse gas and fine particulate emissions. However, strict control on safety of reactors and fuel cycle facilities as well as safe and timely nuclear waste disposal and improved proliferation resistance are prerequisites of a positive net contribution to the wellbeing of the whole society. In addition to electricity production, new applications: process heat for industrial use and hydrogen generation, are foreseen. Recycling of actinides, use of thorium as an additional fission fuel, and reduction of nuclear waste generation will improve the position of nuclear fission as a long term sustainable energy source. Increased international attention has recently been devoted to reactor concepts that differ essentially from the existing light water reactors. Basic processes of these new concepts, known as Gen IV reactors, are fundamentally different from those used today. Some new features may create new type safety challenges. They also aim to push nuclear reactor technology to completely new regimes of performance parameters, thus raising engineering challenges. In order to allow Finland to benefit from these new technologies and influence their development, it is necessary to join relevant international projects, develop domestic expertise on critical technologies involved, and participate in ongoing international efforts to develop safety requirements for them. The technical potential of Gen IV will be shown in a time span of 15 - 20 years as the first demonstration plants are to be built. The NETNUC project is a multidisciplinary consortium of national and international partners to carry out basic research to generate scientific knowledge needed for Gen IV reactors and to educate a new generation of