| 1. |
- Dufek, Jan, 1978-
(författare)
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Development of New Monte Carlo Methods in Reactor Physics : Criticality, Non-Linear Steady-State and Burnup Problems
- 2009
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The Monte Carlo method is, practically, the only approach capable of giving detail insight into complex neutron transport problems. In reactor physics, the method has been used mainly for determining the keff in criticality calculations. In the last decade, the continuously growing computer performance has allowed to apply the Monte Carlo method also on simple burnup simulations of nuclear systems. Nevertheless, due to its extensive computational demands the Monte Carlo method is still not used as commonly as deterministic methods. One of the reasons for the large computational demands of Monte Carlo criticality calculations is the necessity to carry out a number of inactive cycles to converge the fission source. This thesis presents a new concept of fission matrix based Monte Carlo criticality calculations where inactive cycles are not required. It is shown that the fission matrix is not sensitive to the errors in the fission source, and can be thus calculated by a Monte Carlo calculation without inactive cycles. All required results, including keff, are then derived via the final fission matrix. The confidence interval for the estimated keff can be conservatively derived from the variance in the fission matrix. This was confirmed by numerical test calculations of Whitesides's ``keff of the world problem'' model where other Monte Carlo methods fail to estimate the confidence interval correctly unless a large number of inactive cycles is simulated. Another problem is that the existing Monte Carlo criticality codes are not well shaped for parallel computations; they cannot fully utilise the processing power of modern multi-processor computers and computer clusters. This thesis presents a new parallel computing scheme for Monte Carlo criticality calculations based on the fission matrix. The fission matrix is combined over a number of independent parallel simulations, and the final results are derived by means of the fission matrix. This scheme allows for a practically ideal parallel scaling since no communication among the parallel simulations is required, and no inactive cycles need to be simulated. When the Monte Carlo criticality calculations are sufficiently fast, they will be more commonly applied on complex reactor physics problems, like non-linear steady-state calculations and fuel cycle calculations. This thesis develops an efficient method that introduces thermal-hydraulic and other feedbacks into the numerical model of a power reactor, allowing to carry out a non-linear Monte Carlo analysis of the reactor with steady-state core conditions. The thesis also shows that the major existing Monte Carlo burnup codes use unstable algorithms for coupling the neutronic and burnup calculations; therefore, they cannot be used for fuel cycle calculations. Nevertheless, stable coupling algorithms are known and can be implemented into the future Monte Carlo burnup codes.
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| 2. |
- Chan, Yi Meng, et al.
(författare)
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A deep-learning representation of multi-group cross sections in lattice calculations
- 2024
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Ingår i: Annals of Nuclear Energy. - : Elsevier BV. - 0306-4549 .- 1873-2100. ; 195
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Tidskriftsartikel (refereegranskat)abstract
- To compute few-group nodal cross sections, lattice codes must first generate multi-group cross sections using continuous energy cross-section libraries for each material in each fuel cell. Since the processing cost is significant, we propose representing the multi-group cross sections during lattice calculations using a pre-trained deep-learning-based model. The model utilizes a combination of Principal Component Analysis (PCA) and fully connected Neural Networks (NN). The model is specifically designed to manage extensive multi-group cross-section data sets, which contain data for several dozen nuclides and encompass more than 50 energy groups. Our testing of the trained model on a PWR assembly with a realistic boron letdown curve revealed an average relative error of around 0.1% for both fission and total macroscopic cross sections. The average time required for the model to generate the cross sections was approximately 0.01% of the time needed to execute the cross-section processing module.
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| 3. |
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| 4. |
- Dufek, Jan, et al.
(författare)
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An efficient parallel computing scheme for Monte Carlo criticality calculations
- 2009
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Ingår i: Annals of Nuclear Energy. - : Elsevier BV. - 0306-4549 .- 1873-2100. ; 36:8, s. 1276-1279
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Tidskriftsartikel (refereegranskat)abstract
- The existing parallel computing schemes for Monte Carlo criticality calculations suffer from a low efficiency when applied on many processors. We suggest a new fission matrix based scheme for efficient parallel computing. The results are derived from the fission matrix that is combined from all parallel simulations. The scheme allows for a practically ideal parallel scaling as no communication among the parallel simulations is required, and inactive cycles are not needed. (C) 2009 Elsevier Ltd. All rights reserved.
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| 5. |
- Dufek, Jan, 1978
(författare)
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Building the nodal nuclear data dependences in a many-dimensional state-variable space
- 2011
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Ingår i: Annals of Nuclear Energy. - : Elsevier BV. - 0306-4549 .- 1873-2100. ; 38:7, s. 1569-1577
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Tidskriftsartikel (refereegranskat)abstract
- We present new methods for building the polynomial-regression based nodal nuclear data models. Thedata models can reflect dependences on a large number of state variables, and they can consider varioushistory effects. Suitable multivariate polynomials that approximate the nodal data dependences are identifiedefficiently in an iterative manner. The history effects are analysed using a new sampling scheme forlattice calculations where the traditional base burnup and branch calculations are replaced by a largenumber of diverse burnup histories. The total number of lattice calculations is controlled so that the datamodels are built to a required accuracy.
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| 6. |
- Dufek, Jan, 1978-
(författare)
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Complex models of nodal nuclear data
- 2011
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Ingår i: International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Engineering (M&C 2011). - 9788563688002
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Konferensbidrag (refereegranskat)abstract
- During the core simulations, nuclear data are required at various nodal thermal-hydraulic and fuel burnup conditions. The nodal data are also partially affected by thermal-hydraulic and fuel burnup conditions in surrounding nodes as these change the neutron energy spectrum in the node. Therefore, the nodal data are functions of many parameters (state variables), and the more state variables are considered by the nodal data models the more accurate and flexible the models get. The existing table and polynomial regressionmodels, however, cannot reflect the data dependences on many state variables. As for the table models, the number of mesh points (and necessary lattice calculations) grows exponentially with the number of variables. As for the polynomial regression models, the number of possible multivariate polynomials exceeds the limits of existing selection algorithms that should identify a few dozens of the most important polynomials. Also, the standard scheme of lattice calculations is not convenient for modelling the data dependences on various burnup conditions since it performs only a single or few burnup calculations at fixed nominal conditions. We suggest a new efficient algorithm for selecting the most important multivariate polynomials for the polynomial regression models so that dependences on many state variables can be considered. We also present a new scheme for lattice calculations where a large number of burnup histories are accomplished at varied nodal conditions. The number of lattice calculations being performed and the number of polynomials being analysed are controlled and minimised while building the nodal data models of a required accuracy.
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| 7. |
- Dufek, Jan, et al.
(författare)
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Correlation of errors in the Monte Carlo fission source and the fission matrix fundamental-mode eigenvector
- 2016
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Ingår i: Annals of Nuclear Energy. - : Elsevier. - 0306-4549 .- 1873-2100. ; 94, s. 415-421
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Tidskriftsartikel (refereegranskat)abstract
- Previous studies raised a question about the level of a possible correlation of errors in the cumulative Monte Carlo fission source and the fundamental-mode eigenvector of the fission matrix. A number of new methods tally the fission matrix during the actual Monte Carlo criticality calculation, and use its fundamental-mode eigenvector for various tasks. The methods assume the fission matrix eigenvector is a better representation of the fission source distribution than the actual Monte Carlo fission source, although the fission matrix and its eigenvectors do contain statistical and other errors. A recent study showed that the eigenvector could be used for an unbiased estimation of errors in the cumulative fission source if the errors in the eigenvector and the cumulative fission source were not correlated. Here we present new numerical study results that answer the question about the level of the possible error correlation. The results may be of importance to all methods that use the fission matrix. New numerical tests show that the error correlation is present at a level which strongly depends on properties of the spatial mesh used for tallying the fission matrix. The error correlation is relatively strong when the mesh is coarse, while the correlation weakens as the mesh gets finer. We suggest that the coarseness of the mesh is measured in terms of the value of the largest element in the tallied fission matrix as that way accounts for the mesh as well as system properties. In our test simulations, we observe only negligible error correlations when the value of the largest element in the fission matrix is about 0.1. Relatively strong error correlations appear when the value of the largest element in the fission matrix raises above about 0.5. We also study the effect of the error correlations on accuracy of the eigenvector-based error estimator. The numerical tests show that the eigenvector-based estimator consistently underestimates the errors in the cumulative fission source when a strong correlation is present between the errors in the fission matrix eigenvector and the cumulative fission source (i.e., when the mesh is too coarse). The error estimates are distributed around the real error value when the mesh is sufficiently fine.
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| 8. |
- Dufek, Jan, et al.
(författare)
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Derivation of a stable coupling scheme for Monte Carlo burnup calculations with the thermal-hydraulic feedback
- 2013
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Ingår i: Annals of Nuclear Energy. - : Elsevier BV. - 0306-4549 .- 1873-2100. ; 62, s. 260-263
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Tidskriftsartikel (refereegranskat)abstract
- Numerically stable Monte Carlo burnup calculations of nuclear fuel cycles are now possible with the previously derived Stochastic Implicit Euler method based coupling scheme. In this paper, we show that this scheme can be easily extended to include the thermal-hydraulic feedback during the Monte Carlo burnup simulations, while preserving its unconditional stability property. At each time step, the implicit solution (for the end-of-step neutron flux, fuel nuclide densities and thermal-hydraulic conditions) is calculated iteratively by the stochastic approximation; the fuel nuclide densities and thermal-hydraulic conditions are iterated simultaneously. This coupling scheme is derived as stable in theory; i.e.; its stability is not conditioned by the choice of time steps.
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| 9. |
- Dufek, Jan, et al.
(författare)
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Description of a stable scheme for steady-state coupled Monte Carlo-thermal-hydraulic calculations
- 2014
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Ingår i: Annals of Nuclear Energy. - : Elsevier BV. - 0306-4549 .- 1873-2100. ; 68, s. 1-3
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Tidskriftsartikel (refereegranskat)abstract
- We provide a detailed description of a numerically stable and efficient coupling scheme for steady-state Monte Carlo neutronic calculations with thermal-hydraulic feedback. While we have previously derived and published the stochastic approximation based method for coupling the Monte Carlo criticality and thermal-hydraulic calculations, its possible implementation has not been described in a step-by-step manner. As the simple description of the coupling scheme was repeatedly requested from us, we have decided to make it available via this note.
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| 10. |
- Dufek, Jan, et al.
(författare)
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Fission matrix based Monte Carlo criticality calculations
- 2009
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Ingår i: Annals of Nuclear Energy. - : Elsevier BV. - 0306-4549 .- 1873-2100. ; 36:8, s. 1270-1275
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Tidskriftsartikel (refereegranskat)abstract
- We have described a fission matrix based method that allows to cancel the inactive cycles in Monte Carlo criticality calculations. The fission matrix must be sampled in the course of the Monte Carlo calculation using a space mesh with sufficiently small zones as it causes the fission matrix be insensitive to errors in the initial fission source. The k(eff) and other quantities can be derived by means of the final fission matrix. The confidence interval for the k(eff) estimate can be conservatively determined via the variance in the fission matrix.
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