Search

Electrically charged particles of air pollutants show the degree of atmospheric pollution they being consistent with some chemical indicators of air pollution. This study analyses these indicators of atmospheric pollution (EIAP) present in various zones around the cities of Iasi, Bacau and Piatra Neamt and correlate them with the incidence of some diseases amongst the population. The results show that certain values of electrical indicators of atmospheric pollution point to a higher incidence of diseases, especially to respiratory and cardiovascular diseases. Higher concentrations of electrically charged particles relate to higher degree of atmospheric air pollution and to higher incidence of disease in local population.

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 I-3 of the UAM benchmark at hot zero power with all rods out and inserted. The computational efficiency of the calculations is discussed.

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 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.

We survey prediction capabilities of ENDF/B-VII.1 , JEFF-3.2 and JENDL-4.0u nuclear data libraries (NDLs) for the application of generating two-group homogenized assembly constants for a steady state diffusion model in the context of UAM-LWR (Uncertainty Analysis in Best-Estimate Modeling for Design, Operation and Safety Analysis of LWRs) Benchmark. We consider two different fuel assembly test cases representing a PWR. State of uncertainty quantification in each NDLs is presented for the application. We expect small differences between the NDLs due to the use of expert judgment in the evaluation processes, and identify several order-of-magnitude differences between the NDLs for significant contributors to uncertainty. We also quantify the contribution from cross-material correlations to the uncertainties.

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 the computation of the matrix exponential in the context of burnup equations. The established matrix exponential methods are introduced briefly. The eigenvalues of the burnup matrix are important in choosing the matrix exponential method, and their characterization is considered. Based on the characteristics of the burnup matrix, the Chebyshev rational approximation method (CRAM) and its interpretation as a numeric contour integral are discussed in detail. The introduced matrix exponential methods are applied to two test cases representing an infinite pressurized water reactor pin-cell lattice, and the numerical results are presented. The results suggest that CRAM is capable of providing a robust and accurate solution to the burnup equations with a very short computation time.

The four-year Numerical Multi-Physics (NUMPS) project funded by the Academy of Finland was initiated at VTT 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 VTT, 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.

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.

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 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 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.

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 demonstrated by computing the CRAM approximations for a large test case with over 1600 nuclides