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[en] Emergency spray cooling injection is a safety feature implemented in many boiling water reactor designs to reflood a reactor during an accident. Significant experimental work has qualified the efficacy of spray cooling, and ongoing computational modeling efforts strive to more accurately portray the phenomena involved. This work examines the physical phenomena pertaining to emergency spray cooling injection over SVEA-type fuel assemblies. BWR emergency core cooling system (ECCS) designs commonly incorporate a Low-Pressure Core Spray (LPCS) system that introduces coolant through spray nozzles directed to the top of the core, and are located in the upper plenum region. This design is effective for LOCA response, particularly during the initial refill and reflood stages of accident response where the goal is limiting the peak cladding temperature rise in the core. The U.S. NRC thermal-hydraulics code TRACE version 5.0 Patch 4 has been chosen to simulate the separate-effect tests performed by ASEA-ATOM. The computational model was evaluated by performing forward uncertainty quantification using Dakota as the analysis tool and code driver on 31 identified parameters from the input model and TRACE physical constitutive models. This paper discusses the sensitivity of the investigated parameters with respect to spray cooling simulation. (authors)
[en] Highlights: • Wilks’ method of uncertainty quantification was confirmed with a realistic problem. • Thermal-hydraulics modeling of a BWR spray cooling licensing experiment was used. • Critical points of the method (input distribution, sidedness, order) were assessed. - Abstract: Wilks’ formula has been frequently used to quantify the minimum amount of computational work required to meaningfully assess a model’s uncertainty, due to its nonparametric statistical nature that does not require knowledge of the distribution of the qualifying parameters of interest. Additionally, this method allows for any number of input uncertain parameters in the simulation model. This is favorable due to considerable computational expense of typical nuclear safety simulations, providing a quantifiable number of code executions that can statistically verify a desired level of safety. However, there are various existing definitions and uses of Wilks’ theorem in such scenarios, which the present study aims to investigate and quantify for a real thermal-hydraulics experiment used for reactor safety licensing. In this work, the U.S. NRC TRACE thermal-hydraulics code was chosen to simulate the separate-effect spray cooling tests performed by ASEA-ATOM for licensing of BWR SVEA-64 fuel. The computational model was evaluated by performing forward uncertainty quantification (UQ) using Dakota as the analysis tool and code driver on 31 identified sensitive parameters. Using this validated model, the TRACE model was sampled 1000 times with four different input parameter probability distributions to produce four model data sets to assess the applicability of Wilks’ theorem within a realistic nuclear safety analysis scenario. The obtained results compared various Wilks-defined ‘sample sizes’ according to one-sided confidence intervals for the 1st, 2nd and 3rd-order statistics, and with the two-sided confidence interval for the 1st-order statistics. The comparison demonstrated that Wilks’ method satisfies the reactor safety modeling requirements at the 95%/95% tolerance/confidence level as determined by the U.S. NRC.
[en] Highlights: • Inverse Uncertainty Quantification is performed for TRACE physical model parameters to replace expert judgment. • Bayesian analysis is used to formulate the inverse UQ problem. • Global sensitivity analysis is done using Sobol’ indices and correlation coefficients. • Sparse Grid Stochastic Collocation surrogate model is used for MCMC sampling. • Different adaptive MCMC sampling algorithms are investigated. - Abstract: Within the BEPU (Best Estimate plus Uncertainty) methodology uncertainties must be quantified in order to prove that the investigated design remains within acceptance criteria. For best-estimate system thermal-hydraulics codes like TRACE and RELAP5, significant uncertainties come from the closure laws which are used to describe transfer terms in the balance equations. The accuracy and uncertainty information of these correlations are usually unknown to the code users, which results in the user simply ignoring or describing them using expert opinion or personal judgment during uncertainty and sensitivity analysis. The purpose of this paper is to replace such ad-hoc expert judgment of the uncertainty information of TRACE physical model parameters with inverse Uncertainty Quantification (UQ) based on OECD/NRC BWR Full-size Fine-Mesh Bundle Tests (BFBT) benchmark steady-state void fraction data. Inverse UQ seeks statistical descriptions of the physical model random input parameters that are consistent with the experimental data. Inverse UQ always captures the uncertainty of its estimates rather than merely determining point estimates of the best-fit input parameters. Bayesian analysis is used to establish the inverse UQ problems based on experimental data, with systematic and rigorously derived surrogate models based on Sparse Gird Stochastic Collocation (SGSC). Global sensitivity analysis including Sobol' indices and correlation coefficients are used to identify the important TRACE input parameters. Several adaptive Markov Chain Monte Carlo (MCMC) sampling techniques are investigated and implemented to explore the posterior probability density functions. This research solves the problem of lack of uncertainty information for TRACE physical model parameters for the closure relations. The quantified uncertainties are necessary for future uncertainty and sensitivity study of TRACE code in nuclear reactor system design and safety analysis.