Consistent multi-scale uncertainty quantification methodology for multi-physics modelling of prismatic HTGRs
As one of the Generation-IV advanced reactor types, High Temperature Gas-Cooled Reactors (HTGRs) can provide high-quality heat to industrial processes, in addition to saleable and inherently safe power operation. In the United States, several small- and micro-HTGR projects are currently underway, and the assessment of uncertainties in the modelling and simulation of HTGRs is an important aspect of the design and licensing process. The research reported in this dissertation is focussed on providing a practical example of a statistical uncertainty and sensitivity assessment (U/SA) methodology that can be used by HTGR designers, national nuclear regulators and academic institutions to assess the impact of input uncertainties, across many scales, multiple physics, and time, for several important Figures of Merit (FOMs) such as the core eigenvalue, peak spatial power and maximum fuel temperature. In addition to the quantification of uncertainty in these output parameters, the sensitivity assessment identifies the main contributors to the uncertainties and provides a rationale for future improvements in nuclear data, material property and operational condition uncertainties. The main objective of this work is the development of a consistent U/SA that can be applied from the lattice to the core spatial domain, and propagation of the non-linear coupled uncertainties that exists between reactor physics and thermal fluid phenomena. The selection of the statistical U/SA approach is motivated by several critical factors unique to HTGRs; the most important being the lack of experimental or operational validation databases and the presence of non-linear phenomena (e.g. coolant bypass flows, graphite thermal conductivity change with irradiation exposure). The scope of this work includes an assessment of uncertainties in cross-sections, operational boundary conditions and thermal fluid parameters. Two novel contributions include the impact of uncertainties in the core bypass flows on the maximum fuel temperature, and comparisons of the uncertainty and sensitivity results obtained utilizing three energy group structures (2-, 8- and 26 groups). The proposed methodology is applied to the U/SA of the prismatic modular high-temperature gas-cooled reactor (MHTGR)-350 design, and specifically within the context of the International Atomic Energy Agency (IAEA) Coordinated Research Program (CRP) on HTGR Uncertainty in Modelling (UAM). One of the main contributions of this research is the development of the HTGR UAM benchmark specifications that covers the simulation domain in a phased-approach from the generation of block-level cross-sections to the coupled neutronic/thermal fluid analysis of two important safety case transients (the Control Rod Withdrawal and Pressurised Loss of Cooling events). The statistical U/SA methodology is successfully implemented and demonstrated using the INL-developed codes PHISICS, RELAP5-3D and RAVEN for the stand-alone and coupled core steady-states and transients, based on perturbed cross-section libraries obtained from the SCALE/Sampler sequence. Uncertainties in nuclear data (cross-sections and the average number of neutrons produced per fission, 235U[𝑣 ]) lead to standard deviations (uncertainties of one σ) of approximately 0.5% in the core eigenvalues of various fresh and mixed MHTGR-350 lattice and core models. For the coupled neutronics/thermal fluid model, local power density uncertainties up to 3.6% were observed in the colder regions of the core, while the local maximum fuel temperature uncertainties reached 1.5% for the models that included thermal fluid uncertainties. The addition of thermal fluid uncertainties dominated the impacts of nuclear data uncertainties in all cases, and it was successfully demonstrated that the statistical methodology propagates the uncertainties from the lattice models to the coupled transients in a consistent manner. The main contributors to uncertainties in the power density and fuel temperatures during the two transients were uncertainties in the reactor operating conditions (total power, inlet mass flow rate and inlet gas temperature). Variations in the bypass flows did not have significant impact on any of the output variables. For the nuclear data uncertainties it was found that the 235U(𝑣 ) / 235U(𝑣 ) covariance produced the largest sensitivities in terms of its impact on the eigenvalue and peak reactor power. It was also observed that the impact of any nuclear data uncertainties on the maximum fuel temperature was much less significant that the impact on eigenvalue and power. Another important finding was that although the use of eight or more energy groups is recommended for best-estimate HTGR simulation, two-group models produced acceptable uncertainty and sensitivity results for most FOMs. Since the statistical U/SA methodology is computationally expensive, and most transient solver requirements will scale directly with the number of energy groups, two energy groups could be used by HTGR developers during the early stages of design when larger uncertainty margins can be tolerated.