| 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, 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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| 5. |
- 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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| 6. |
- Dufek, Jan, 1978-, et al.
(författare)
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Monte Carlo criticality calculations accelerated by a growing neutron population
- 2016
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Ingår i: Annals of Nuclear Energy. - : Elsevier. - 0306-4549 .- 1873-2100. ; 94, s. 16-21
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Tidskriftsartikel (refereegranskat)abstract
- We propose a fission source convergence acceleration method for Monte Carlo criticality simulation. As the efficiency of Monte Carlo criticality simulations is sensitive to the selected neutron population size, the method attempts to achieve the acceleration via on-the-fly control of the neutron population size. The neutron population size is gradually increased over successive criticality cycles so that the fission source bias amounts to a specific fraction of the total error in the cumulative fission source. An optimal setting then gives a reasonably small neutron population size, allowing for an efficient source iteration; at the same time the neutron population size is chosen large enough to ensure a sufficiently small source bias, such that does not limit accuracy of the simulation.
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| 7. |
- Dufek, Jan, 1978-, et al.
(författare)
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Optimal time step length and statistics in Monte Carlo burnup simulations
- 2020
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Ingår i: Annals of Nuclear Energy. - : Elsevier. - 0306-4549 .- 1873-2100. ; 139
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Tidskriftsartikel (refereegranskat)abstract
- Monte Carlo burnup simulations continue to be seen as computationally very expensive numerical routines despite recent developments of associated methods. Here, we suggest a way of improving the computing efficiency via optimisation of the length of the time steps and the number of neutron histories that are simulated at each Monte Carlo criticality run. So far, users of Monte Carlo burnup codes have been required to set these parameters at will; however, an inadequate choice of these free parameters can severely worsen the computing efficiency. We have tested a large number of combinations of the free parameters on a simplified and fast solver, and we have observed that the computing efficiency was maximized when the computing cost of all Monte Carlo neutron transport calculations (summed over all time steps) was approximately comparable to costs of other procedures (all depletion simulations, the loading and processing of neutron cross sections, etc.). In this technical note, we demonstrate these results, and we also derive a simple theoretical model of the convergence of Monte Carlo burnup simulations that conforms to these numerical results. Here, we also suggest a straightforward way to automatise the selection of the optimal values of the free parameters for Monte Carlo burnup simulations.
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| 8. |
- Dufek, Jan, 1978-, et al.
(författare)
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Optimisation of Monte Carlo burnup simulations
- 2020
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Ingår i: International Conference on Physics of Reactors. - : EDP Sciences. ; , s. 804-810
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Konferensbidrag (refereegranskat)abstract
- We show here that computing efficiency of Monte Carlo burnup simulations depends on chosen values of certain free parameters, such as the length of the time steps and the number of neutron histories simulated at each Monte Carlo criticality run. The efficiency can thus be improved by optimising these parameters. We have set up a simple numerical model that made it possible for us to test a large number of combinations of the free parameters, and suggest a way to optimise their selection.
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| 9. |
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| 10. |
- Hoogenboom, J. Eduard, et al.
(författare)
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Optimised Iteration in Coupled Monte Carlo - Thermal-Hydraulics Calculations
- 2016
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Ingår i: SNA + MC 2013 - JOINT INTERNATIONAL CONFERENCE ON SUPERCOMPUTING IN NUCLEAR APPLICATIONS + MONTE CARLO. - Les Ulis, France : E D P SCIENCES.
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Konferensbidrag (refereegranskat)abstract
- This paper describes an optimised iteration scheme for the number of neutron histories and the relaxation factor in successive iterations of coupled Monte Carlo and thermal-hydraulic reactor calculations based on the stochastic iteration method. The scheme results in an increasing number of neutron histories for the Monte Carlo calculation in successive iteration steps and a decreasing relaxation factor for the spatial power distribution to be used as input to the thermal-hydraulics calculation. The theoretical basis is discussed in detail and practical consequences of the scheme are shown, among which a nearly linear increase per iteration of the number of cycles in the Monte Carlo calculation. The scheme is demonstrated for a full PWR type fuel assembly. Results are shown for the axial power distribution during several iteration steps. A few alternative iteration method are also tested and it is concluded that the presented iteration method is near optimal.
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