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This study presents collaborative work performed between GRS and PSI on benchmarking and application of the state-of-the-art uncertainty analysis methods XSUSA and SHARK-X. Applied to a PWR pin cell depletion calculation, both methods propagate input uncertainty from nuclear data to output uncertainty. The uncertainty of the multiplication factors, nuclide densities, and fuel temperature coefficients derived by both methods are compared at various burnup steps. Comparisons of these quantities are furthermore performed with the SAMPLER module of SCALE 6.2. The perturbation theory based TSUNAMI module of both SCALE 6.1 and SCALE 6.2 is additionally applied for comparisons of the reactivity coefficient.

The paper presents different methods for evaluating sensitivities and uncertainties of the effective delayed neutron fraction (βeff) with respect to microscopic nuclear data in the framework of the SCALE 6.2 code system. The prompt k ratio method is used to calculate βeff approximately. Sensitivities of βeff to microscopic reaction data are calculated with deterministic linear perturbation theory from sensitivities of the multiplication factor, and by performing linear regression analysis on results obtained from random sampling. The latter approach is also applied for estimating sensitivities of kinetic parameters in six delayed neutron groups, as obtained by adjoint flux weighting in lattice calculations, to nuclear reactions. Finally, it is demonstrated that the uncertainties of βeff strongly depend on the choice of the covariance data set; in particular, the use of SCALE 6.2 covariance data for the average number of delayed neutrons per fission in some cases leads to very high βeff uncertainties.

The paper presents solutions for the neutron transport sub-exercises regarding pin cells, fuel assemblies, and supercells of the OECD/NEA UAM-SFR Benchmark. For this, the GRS XSUSA methodology is applied with a recently introduced approach performing linear regression analysis on the output samples, denoted as XSUSA(LR). The main purpose for this is to calculate sensitivity profiles and the main contributions to the total output uncertainties via the first-order uncertainty propagation formula, i.e. by multiplying the corresponding total/partial nuclear data covariance matrices with the total/partial sensitivity vectors. Confidence intervals were estimated by applying Jackknife resampling. Implicit effects are considered. All output uncertainties are compared to the corresponding values calculated with deterministic linear perturbation theory using TSUNAMI from SCALE 6.2.3. Various optimizations were applied with respect to nuclear data and problem geometry. The output uncertainties are significant – around 1.5% for multiplication factors and 5% for Doppler and sodium void reactivity effects.

The impact of nuclear data uncertainties is studied for the reactor power and the reactivity during control rod withdrawal transients with reactivity insertions of 0.5$ and 0.97$, respectively, for a PWR mini-core model. Multi-group cross sections, the multiplicities of both prompt and delayed neutrons, and fission spectra are varied by the application of the random sampling-based method XSUSA with covariance data of SCALE 6.1 supplemented by JENDL-4.0. The varied multi-group data are used by TRITON/NEWT to generate varied 2-group cross sections, which are then applied in neutron-kinetic/thermal-hydraulic calculations with DYN3D-ATHLET. A significant impact on both the reactivity uncertainty and the power uncertainty is observed. Since the distributional properties of the output time series vary across the problem time, the distribution-free Wilks tolerance limit is applied as a robust uncertainty measure to complex time series patterns. The most contributing nuclide reactions to the power uncertainty are identified via sensitivity analysis. (C) 2019 Elsevier Ltd. All rights reserved.

International audience; The impact of the current nuclear data library covariances such as in ENDF/B-VII.1, JEFF-3.2, JENDL-4.0, SCALE and TENDL, for relevant current reactors is presented in this work. The uncertainties due to nuclear data are calculated for existing PWR and BWR fuel assemblies (with burn-up up to 40 GWd/tHM, followed by 10 years of cooling time) and for a simplified PWR full core model (without burn-up) for quantities such as k∞ , macroscopic cross sections, pin power or isotope inventory. In this work, the method of propagation of uncertainties is based on random sampling of nuclear data, either from covariance files or directly from basic parameters. Additionally, possible biases on calculated quantities are investigated such as the self-shielding treatment. Different calculation schemes are used, based on CASMO, SCALE, DRAGON, MCNP or FISPACT-II, thus simulating real-life assignments for technical-support organizations. The outcome of such a study is a comparison of uncertainties with two consequences. One: although this study is not expected to lead to similar results between the involved calculation schemes, it provides an insight on what can happen when calculating uncertainties and allows to give some perspectives on the range of validity on these uncertainties. Two: it allows to dress a picture of the state of the knowledge as of today, using existing nuclear data library covariances and current methods.

This study presents uncertainty and sensitivity analyses of the delayed neutron fraction of light water reactor and sodium-cooled fast reactor fuel assemblies. For these analyses, the sampling-based XSUSA methodology is used to propagate cross section uncertainties in neutron transport and depletion calculations. Cross section data is varied according to the SCALE 6.1 covariance library. Since this library includes nu-bar uncertainties only for the total values, it has been supplemented by delayed nu-bar uncertainties from the covariance data of the JENDL-4.0 nuclear data library. The neutron transport and depletion calculations are performed with the TRITON/NEWT sequence of the SCALE 6.1 package. The evolution of the delayed neutron fraction uncertainty over burn-up is analysed without and with the consideration of delayed nu-bar uncertainties. Moreover, the main contributors to the result uncertainty are determined. In all cases, the delayed nu-bar uncertainties increase the delayed neutron fraction uncertainty. Depending on the fuel composition, the delayed nu-bar values of uranium and plutonium in fact give the main contributions to the delayed neutron fraction uncertainty for the LWR fuel assemblies. For the SFR case, the uncertainty of the scattering cross section of U-238 is the main contributor.

In the present work, PSI and GRS sensitivity analysis (SA) and uncertainty quantification (UQ) methods, SHARK-X and XSUSA respectively, are compared for reactivity coefficient calculation; for reference the results of the TSUNAMI and SAMPLER modules of the SCALE code package are also provided. The main objective of paper is to assess the impact of the implicit effect, e.g., considering the effect of cross section perturbation on the self-shielding calculation, on the Doppler coefficient SA and UQ. Analyses are done for a Light Water Reactor (LWR) pin cell based on Phase I of the UAM LWR benchmark. The negligence of implicit effects in XSUSA and TSUNAMI leads to deviations of a few percent between the sensitivity profiles compared to SAMPLER and TSUNAMI (incl. implicit effects) except for 238 U elastic scattering. The implicit effect is much larger for the SHARK-X calculations because of its coarser energy group structure between 10 eV and 10 keV compared to the applied SCALE libraries. It is concluded that the influence of the implicit effect strongly depends on the energy mesh of the nuclear data library of the neutron transport solver involved in the UQ calculations and may be magnified by the response considered.

Neutron transport and depletion calculations are performed in combination with various nuclear data libraries in order to assess the impact of nuclear data on safety-relevant parameters of sodium-cooled fast reactors. These calculations are supplemented by systematic uncertainty analyses with respect to nuclear data. Analysed quantities are the multiplication factor and nuclide densities as a function of burn-up and the Doppler and Na-void reactivity coefficients at begin of cycle. While ENDF/B-VII.0 / -VII.1 yield rather consistent results, larger discrepancies are observed between the JEFF libraries. While the newest evaluation, JEFF-3.2, agrees with the ENDF/B-VII libraries, the JEFF-3.1.2 library yields significant larger multiplication factors.

The paper demonstrates the influence of uncertainties in microscopic nuclear data on the results of reactor simulations, both for stationary and transient states. It gives an overview on the methods in use for uncertainty and sensitivity analyses with respect to nuclear data, and discusses the pros and cons. For full-scale reactor simulations, in particular with coupled neutron transport and thermo-hydraulics, random sampling provides a powerful means to propagate nuclear data uncertainties through the complete calculation sequence. Results of uncertainty analyses performed with the GRS XSUSA – “cross section (XS) Uncertainty and Sensitivity Analysis” methodology are shown for radial power distributions from steady-state PWR calculations and for the time evolution of the reactor power in the course of a control rod withdrawal from a PWR mini-core. In all cases, the output uncertainties are considerable. For the radial power distributions, relative 1σ uncertainties of up to 10% are observed, and for the power peak during the transient, the relative 1σ uncertainty reaches 20%. These large uncertainties strongly suggest to routinely accompany best-estimate simulations by uncertainty analyses with respect to nuclear data, in particular for systems beyond LWR for which much less operation experience is available.