ALBERT

Description: Tremendous work has been done in the Light Water Reactor (LWR) Modelling and Simulation (M&S) uncertainty quantification (UQ) within the framework of the Organization for Economic Cooperation and Development (OECD)/Nuclear Energy Agency (NEA) LWR Uncertainty Analysis in Modelling (UAM) benchmark, which aims to investigate the uncertainty propagation in all M&S stages of the LWRs and to guide uncertainty and sensitivity analysis methodology development. The Best-Estimate Plus Uncertainty (BEPU) methodologies have been developed and implemented within the framework of the LWR UAM benchmark to provide a realistic predictive simulation capability without compromising the safety margins. This paper describes the current status of the methodological development, assessment, and integration of the BEPU methodology to facilitate the multiscale, multiphysics LWR core analysis. The comparative analysis of the results in the stand-alone multiscale neutronics phase (Phase I) is first reported for understanding the general trend of the uncertainty of core parameters due to the nuclear data uncertainty. It was found that the predicted uncertainty of the system eigenvalue is highly dependent on the choice of the covariance libraries used in the UQ process and is less sensitive to the solution method, nuclear data library, and UQ method. High-to-Low (Hi2Lo) model information approaches for multiscale M&S are introduced for the core single physics phase (Phase II). In this phase, the other physics (fuel and moderator), providing feedback to neutronics M&S in a LWR core, and time-dependent phenomena are considered. Phase II is focused on uncertainty propagation in single physics models which are components of the LWR core coupled multiphysics calculations. The paper discusses the link and interactions between Phase II to the multiphysics core and system phase (Phase III), that is, the link between uncertainty propagation in single physics on local scale and multiphysics uncertainty propagation on the core scale. Particularly, the consistency in uncertainty assessment between higher-fidelity models implemented in fuel performance codes and the rather simplified models implemented in thermal-hydraulics codes, to be used for coupling with neutronics in Phase III is presented. Similarly, the uncertainty quantification on thermal-hydraulic models is established on a relatively small scale, while these results will be used in Phase III at the core scale, sometimes with different codes or models. Lastly, the up-to-date UQ method for the coupled multiphysics core calculation in Phase III is presented, focusing on the core equilibrium cycle depletion calculation with associated uncertainties.

Description: In this study, the Best Estimate Plus Uncertainty (BEPU) approach is developed for the systematic quantification and propagation of uncertainties in the modelling and simulation of lead-cooled fast reactors (LFRs) and applied to the demonstration LFR (DLFR) initially investigated by Westinghouse. The impact of nuclear data uncertainties based on ENDF/B-VII.0 covariances is quantified on lattice level using the generalized perturbation theory implemented with the Monte Carlo code Serpent and the deterministic code PERSENT of the Argonne Reactor Computational (ARC) suite. The quantities of interest are the main eigenvalue and selected reactivity coefficients such as Doppler, radial expansion, and fuel/clad/coolant density coefficients. These uncertainties are then propagated through safety analysis, carried out using the MiniSAS code, following the stochastic sampling approach in DAKOTA. An unprotected transient overpower (UTOP) scenario is considered to assess the effect of input uncertainties on safety parameters such as peak fuel and clad temperatures. It is found that in steady state, the multiplication factor shows the most sensitivity to perturbations in 235U fission, 235U ν, and 238U capture cross sections. The uncertainties of 239Pu and 238U capture cross sections become more significant as the fuel is irradiated. The covariance of various reactivity feedback coefficients is constructed by tracing back to common uncertainty contributors (i.e., nuclide-reaction pairs), including 238U inelastic, 238U capture, and 239Pu capture cross sections. It is also observed that nuclear data uncertainty propagates to uncertainty on peak clad and fuel temperatures of 28.5 K and 70.0 K, respectively. Such uncertainties do not impose per se threat to the integrity of the fuel rod; however, they sum to other sources of uncertainties in verifying the compliance of the assumed safety margins, suggesting the developed BEPU method necessary to provide one of the required insights on the impact of uncertainties on core safety characteristics.

Description: This paper provides a review of current and upcoming innovations in development, validation, and uncertainty quantification of nuclear reactor multi-physics simulation methods. Multi-physics modelling and simulations (M&S) provide more accurate and realistic predictions of the nuclear reactors behavior including local safety parameters. Multi-physics M&S tools can be subdivided in two groups: traditional multi-physics M&S on assembly/channel spatial scale (currently used in industry and regulation), and novel high-fidelity multi-physics M&S on pin (sub-pin)/sub-channel spatial scale. The current trends in reactor design and safety analysis are towards further development, verification, and validation of multi-physics multi-scale M&S combined with uncertainty quantification and propagation. Approaches currently applied for validation of the traditional multi-physics M&S are summarized and illustrated using established Nuclear Energy Agency/Organization for Economic Cooperation and Development (NEA/OECD) multi-physics benchmarks. Novel high-fidelity multi-physics M&S allow for insights crucial to resolve industry challenge and high impact problems previously impossible with the traditional tools. Challenges in validation of novel multi-physics M&S are discussed along with the needs for developing validation benchmarks based on experimental data. Due to their complexity, the novel multi-physics codes are still computationally expensive for routine applications. This fact motivates the use of high-fidelity novel models and codes to inform the low-fidelity traditional models and codes, leading to improved traditional multi-physics M&S. The uncertainty quantification and propagation across different scales (multi-scale) and multi-physics phenomena are demonstrated using the OECD/NEA Light Water Reactor Uncertainty Analysis in Modelling benchmark framework. Finally, the increasing role of data science and analytics techniques in development and validation of multi-physics M&S is summarized.

Description: The Simplified Spherical Harmonic (SPN) approximation was first introduced as a three-dimensional (3D) extension of the plane-geometry Spherical Harmonic (PN) equations. A third order SPN (SP3) solver, recently implemented in the Nodal Expansion Method (NEM), has shown promising performance in the reactor core neutronics simulations. This work is focused on the development and implementation of the transport-corrected interface and boundary conditions in an NEM SP3 solver, following recent published work on the rigorous SPN theory for piecewise homogeneous regions. A streamlined procedure has been developed to generate the flux zero and second order/moment discontinuity factors (DFs) of the generalized equivalence theory to minimize the error introduced by pin-wise homogenization. Moreover, several colorset models with varying sizes and configurations are later explored for their capability of generating DFs that can produce results equivalent to that using the whole-core homogenization model for more practical implementations. The new developments are tested and demonstrated on the C5G7 benchmark. The results show that the transport-corrected SP3 solver shows general improvements to power distribution prediction compared to the basic SP3 solver with no DFs or with only the zeroth moment DF. The complete equivalent calculations using the DFs can almost reproduce transport solutions with high accuracy. The use of equivalent parameters from larger size colorset models show a slightly reduced prediction error than that using smaller colorset models in the whole-core calculations.