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[en] SSM has signed an agreement with KTH and Chalmers for a long-term commitment within the deterministic safety analysis (transient and severe accident analysis). The objective for this co-operation is to promote the national competence and to establish groups, whom can support SSM to perform safety analysis, reviews and inquiries, as well as participate in international projects and working groups within these areas. According to the agreement, the analysis groups at KTH and Chalmers have worked with RandD within the following areas: - plant analysis; - evaluation and contribution to international projects; - training and education of SSM's personnel. The first phase of the Technical Support Organization for the Deterministic Safety Analysis (TSO-DSA) agreement covered the period of 2008 - 2010. The objective of this document is to describe the work performed within the TSO-DSA and summarize the TSO-DSA achievements for the initial 3-year period
[en] Modeling and simulations are naturally augmented by extensive Uncertainty Quantification (UQ) and sensitivity analysis requirements in the nuclear reactor system design, in which uncertainties must be quantified in order to prove that the investigated design stays within acceptance criteria. Historically, expert judgment has been used to specify the nominal values, probability density functions and upper and lower bounds of the simulation code random input parameters for the forward UQ process. The purpose of this paper is to replace such ad-hoc expert judgment of the statistical properties of input model parameters with inverse UQ process. Inverse UQ seeks statistical descriptions of the model random input parameters that are consistent with the experimental data. Bayesian analysis is used to establish the inverse UQ problems based on experimental data, with systematic and rigorously derived surrogate models based on Polynomial Chaos Expansion (PCE). The methods developed here are demonstrated with the Point Reactor Kinetics Equation (PRKE) coupled with lumped parameter thermal-hydraulics feedback model. Three input parameters, external reactivity, Doppler reactivity coefficient and coolant temperature coefficient are modeled as uncertain input parameters. Their uncertainties are inversely quantified based on synthetic experimental data. Compared with the direct numerical simulation, surrogate model by PC expansion shows high efficiency and accuracy. In addition, inverse UQ with Bayesian analysis can calibrate the random input parameters such that the simulation results are in a better agreement with the experimental data.
[en] Highlights: • Derivation of methods (MLE, MAP, and MCMC) for quantifying physical model parameters. • Development of TRACE model for BFBT benchmark. • Sensitivity analysis of physical model parameters of TRACE code. • Quantifying the uncertainties of physical model parameters with BFBT experiment data. - Abstract: Forward quantification of simulation (code) response uncertainties requires knowledge of physical model parameter uncertainties. Nuclear thermal-hydraulics codes, such as RELAP5 and TRACE, do not provide any information on uncertainties of physical model parameters. A framework is developed to quantify uncertainties of physical model parameters using Maximum Likelihood Estimation (MLE), Bayesian Maximum A Priori (MAP), and Markov Chain Monte Carlo (MCMC) algorithms. The objective of the present work is to perform the sensitivity analysis of the physical model parameters in code TRACE and calculate their uncertainties using MLE, MAP, and MCMC algorithms. The OECD/NEA BWR Full-size fine-mesh Bundle Test (BFBT) data is used to quantify uncertainty of selected physical models of TRACE code. The BFBT is based on a multi-rod assembly with measured data available for single or two-phase pressure drop, axial and radial void fraction distributions, and critical power for a wide range of system conditions. In this work, the steady-state cross-sectional averaged void fraction distribution is used as the input data for inverse uncertainty quantification (IUQ) algorithms, and the selected physical model’s probability distribution function (PDF) is the desired output quantity.
[en] Highlights: • Coupling of Monte Carlo code Serpent and thermal–hydraulics code RELAP5. • A convergence criterion is developed based on the statistical uncertainty of power. • Correlation between MC statistical uncertainty and coupled error is quantified. • Both UO2 and MOX single assembly models are used in the coupled simulation. • Validation of coupling results with a multi-group transport code DeCART. - Abstract: Coupled multi-physics approach plays an important role in improving computational accuracy. Compared with deterministic neutronics codes, Monte Carlo codes have the advantage of a higher resolution level. In the present paper, a three-dimensional continuous-energy Monte Carlo reactor physics burnup calculation code, Serpent, is coupled with a thermal–hydraulics safety analysis code, RELAP5. The coupled Serpent/RELAP5 code capability is demonstrated by the improved axial power distribution of UO2 and MOX single assembly models, based on the OECD-NEA/NRC PWR MOX/UO2 Core Transient Benchmark. Comparisons of calculation results using the coupled code with those from the deterministic methods, specifically heterogeneous multi-group transport code DeCART, show that the coupling produces more precise results. A new convergence criterion for the coupled simulation is developed based on the statistical uncertainty in power distribution in the Monte Carlo code, rather than ad-hoc criteria used in previous research. The new convergence criterion is shown to be more rigorous, equally convenient to use but requiring a few more coupling steps to converge. Finally, the influence of Monte Carlo statistical uncertainty on the coupled error of power and thermal–hydraulics parameters is quantified. The results are presented such that they can be used to find the statistical uncertainty to use in Monte Carlo in order to achieve a desired precision in coupled simulation
[en] Group method of data handling (GMDH) is considered one of the earliest deep learning methods. Deep learning gained additional interest in today's applications due to its capability to handle complex and high dimensional problems. In this study, multi-layer GMDH networks are used to perform uncertainty quantification (UQ) and sensitivity analysis (SA) of nuclear reactor simulations. GMDH is utilized as a surrogate/metamodel to replace high fidelity computer models with cheap-to-evaluate surrogate models, which facilitate UQ and SA tasks (e.g. variance decomposition, uncertainty propagation, etc.). GMDH performance is validated through two UQ applications in reactor simulations: (1) low dimensional input space (two-phase flow in a reactor channel), and (2) high dimensional space (8-group homogenized cross-sections). In both applications, GMDH networks show very good performance with small mean absolute and squared errors as well as high accuracy in capturing the target variance. GMDH is utilized afterward to perform UQ tasks such as variance decomposition through Sobol indices, and GMDH-based uncertainty propagation with large number of samples. GMDH performance is also compared to other surrogates including Gaussian processes and polynomial chaos expansions. The comparison shows that GMDH has competitive performance with the other methods for the low dimensional problem, and reliable performance for the high dimensional problem.
[en] Over the last decades, the analysis of transients and accidents in nuclear power plants has been performed by system codes. Though they will remain the analyst's tool of choice for the foreseeable future, their limitations are also well known. It has been suggested that an improvement in the simulation technology can be obtained by 'coupling' system codes with Computational Fluid Dynamics (CFD) calculations. This is usually attempted in a domain decomposition fashion: the CFD simulation is only performed in a selected sub-domain and its solution is 'matched' with the system code solution at the interface. However, another coupling strategy can be envisioned. Namely, CFD simulations can be used to provide closures to a system code. This strategy is based on the following two assumptions. The first assumption is that there are transients which cannot be simulated by system codes because of the lack of adequate closures. The second assumption is that appropriate closures can be provided by CFD simulations. In this paper, such a coupling strategy, inspired by the Heterogeneous Multi-scale Method (HMM), is presented. The philosophy underlying this strategy is discussed with the help of a computational example. (authors)
[en] Analyses of nuclear reactor safety have increasingly required coupling of full three dimensional neutron kinetics (NK) core models with system transient thermal-hydraulics (TH) codes. To produce results within a reasonable computing time, the coupled codes use different spatial description of the reactor core. The TH code uses few, typically 5 to 20 TH channels which represent the core. The NK code uses explicit node for each fuel assembly. Therefore, a spatial mapping of coarse grid TH and fine grid NK domain is necessary. However, improper mappings may result in loss of valuable information, thus causing inaccurate prediction of safety parameters. The purpose of this paper is to study the sensitivity of spatial coupling (channel refinement and spatial mapping) and develop recommendations for NK-TH mapping in simulation of safety transients. The research methodology consists of spatial coupling convergence study, as increasing number of TH channels and different mapping approach the reference case. The reference case consists of 700 TH channels, which gives one TH channel per one fuel assembly. The comparison of results has been done under steady-state and transient conditions. Obtained results and conclusions are presented in this paper. (authors)
[en] The reliability of predictions of the system codes is closely related to the validation of their physical models. For example, the accuracy of void fraction prediction in a Boiling Water Reactor (BWR) using TRACE code depends on the uncertainties of closure relations developed for the two-phase flow models. This work focus on quantifying the uncertainties of two physical models, interfacial drag model and subcooled boiling model, using Markov Chain Monte Carlo (MCMC) method and BFBT experimental benchmark data. We applied the MCMC and MLE algorithms to BFBT benchmark data and estimated the uncertainty distribution of two model parameters: subcooled boiling heat transfer coefficient and interfacial drag (bubbly/slug rod bundle) coefficient. These algorithms tend to give various estimation results. Despite the differences in these algorithms, we find that the estimation results are consistent. After obtaining the uncertainty estimates, we validated the uncertainty estimates by applying the estimated distributions of model parameters to TRACE prediction. The new predictions succeed in reducing the void fraction prediction error, but it is not possible to eliminate all prediction error. We are only adjusting two model parameters, and there exists uncertainties in all model parameters. Application of the algorithms to other physical models and experimental data will be helpful for future work. (authors)
[en] This paper explores the concept of instability suppression system and its performance in a BWR plant. The key idea adopted from the work of Aleksakov et al. (1980) is to utilize information provided by the in-core power monitoring detectors to guide movement of control rods in a way that suppress the global, regional and local instability. In the paper, effectiveness of a simplified suppression algorithm is characterized by implementing it on a real BWR model, using the RELAP5/PARCS coupled thermal-hydraulics and neutron kinetics code. Both forced power oscillations and realistic reactor transients (feedwater temperature transients, control rod drop) were analyzed. The results suggest that, without requiring any modifications for the in-reactor diagnostics and equipment, the proposed suppression system is capable of significantly mitigating the impact of core instability events on plant performance by maintaining the core parameters within the safe operational range. (authors)
[en] The DIMPLE benchmark problem has been analyzed using both a two-step approach with SERPENT/PARCS and direct Monte Carlo modeling with SERPENT and MCNP. Detailed computational models are developed in this paper and the calculation results of SERPENT/PARCS are compared against those of Monte Carlo codes SERPENT and MCNP. The SERPENT 1.1.19 code was employed to homogenize the fuel assembly and reflector domains for nodal calculation. Then, the PARCS 3.0 code was used to solve two group neutron diffusion equations, and the results were compared to the full-core heterogeneous solution calculated with SERPENT 1.1.19 and MCNP6. The results show that the reflector with baffle requires the use of assembly discontinuity factors (ADF). It is presumed that the homogeneous results would have been improved if ADFs were used