Uncertainty quantification in steady state simulations of a molten salt system using polynomial chaos expansion analysis

Uncertainty Quantification (UQ) of numerical simulations is highly relevant in the study and design of complex systems. Among the various approaches available, Polynomial Chaos Expansion (PCE) analysis has recently attracted great interest. It belongs to nonintrusive spectral projection methods and consists of constructing system responses as polynomial functions of the stochastic inputs. The limited number of required model evaluations and the possibility to apply it to codes without any modification make this technique extremely attractive. In this work, we propose the use of PCE to perform UQ of complex, multi-physics models for liquid fueled reactors, addressing key design aspects of neutronics and thermal fluid dynamics. Our PCE approach uses Smolyak sparse grids designed to estimate the PCE coefficients. To test its potential, the PCE method was applied to a 2D problem representative of the Molten Salt Fast Reactor physics. An in-house multi-physics tool constitutes the reference model. The studied responses are the maximum temperature and the effective multiplication factor. Results, validated by comparison with the reference model on 103 Monte-Carlo sampled points, prove the effectiveness of our PCE approach in assessing uncertainties of complex coupled models

Data for: Melting behavior of the Molten Salt Fast Reactor freeze-valve: a first parametric study

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Development of a high-fidelity multi-physics simulation tool for liquid-fuel fast nuclear reactors

The Molten Salt Reactor (MSR) is one of the six Generation-IV nuclear reactor designs. It presents very promising characteristics in terms of safety, sustainability, reliability, and proliferation resistance. Numerous research projects are currently carried out worldwide to bring this future reactor technology to a higher maturity, and in Europe efforts are focused on developing a fast-spectrum design: the Molten Salt Fast Reactor (MSFR). Numerical simulations are essential to develop MSR designs, given the scarce operational experience gained with this technology and the current unavailability of experimental reactors. However, modeling an MSR is a challenging task, due to the unique physics phenomena induced by the adoption of a liquid fuel that is also the coolant: transport of delayed neutron precursors, strong negative temperature feedback coefficient, distributed generation of heat directly in the coolant. Moreover, the geometry of the core cavity of fast-spectrum designs often induces complex three-dimensional flow effects. For these reasons, legacy codes traditionally used in the nuclear community often prove unsuitable to accurately model MSRs, in particular fast-spectrum designs, and must be replaced by dedicated tools.This thesis presents the development of one of these multi-physics codes, which aims at accurately modeling the three-dimensional neutron transport, fluid flow, and heat transfer physics phenomena characterizing a fast-spectrum liquid-fuel nuclear reactor. The coupling is realized between an incompressible Reynolds-Averaged Navier-Stokes model and a discrete ordinates neutron transport solver, both based on a discontinuous Galerkin Finite Element space discretization which guarantees high-quality of the solution.As the research was carried out in the context of the Euratom SAMOFAR project, the MSFR is taken as reference case study. We extensively analyze its behaviour at steady-state and during several transient scenarios, assessing the safety of the current design and thus deriving useful information on its further development.RST/Reactor Physics and Nuclear Material

Data for: Melting behavior of the Molten Salt Fast Reactor freeze-valve: a first parametric study

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A pressure-based solver for low-Mach number flow using a discontinuous Galerkin method

Over the past two decades, there has been much development in discontinuous Galerkin methods for incompressible flows and for compressible flows with a positive Mach number, but almost no attention has been paid to variable-density flows at low speeds. This paper presents a pressure-based discontinuous Galerkin method for flow in the low-Mach number limit. We use a variable-density pressure correction method, which is simplified by solving for the mass flux instead of the velocity. The fluid properties do not depend significantly on the pressure, but may vary strongly in space and time as a function of the temperature. We pay particular attention to the temporal discretization of the enthalpy equation, and show that the specific enthalpy needs to be ‘offset’ with a constant in order for the temporal finite difference method to be stable. We also show how one can solve for the specific enthalpy from the conservative enthalpy transport equation without needing a predictor step for the density. These findings do not depend on the spatial discretization. A series of manufactured solutions with variable fluid properties demonstrate full second-order temporal accuracy, without iterating the transport equations within a time step. We also simulate a Von Kármán vortex street in the wake of a heated circular cylinder, and show good agreement between our numerical results and experimental data.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.RST/Reactor Physics and Nuclear Material

A multi-physics solver for liquid-fueled fast systems based on the discontinuous Galerkin FEM discretization

Performing accurate numerical simulations of molten salt reactors is challenging, especially in case of fast-spectrum designs, due to the unique physics phenomena characterizing these systems. The limitations of codes traditionally used in the nuclear community often require the development of novel high-fidelity multi-physics tools to advance the design of these innovative reactors. In this work, we present the most recent code developed at Delft University of Technology for multi-physics simulations of liquid-fueled fast reactors. The coupling is realized between an incompressible RANS model and an SN neutron transport solver. The models are implemented in two in-house codes, based on the discontinuous Galerkin Finite Element discretization, which guarantees high-quality of the solution. We report and discuss the results of preliminary simulations of the Molten Salt Fast Reactor at steady-state and during a Total Loss of Power transient. Results prove our code has capabilities for steady-state and transient analysis of non-moderated liquid-fueled reactors.RST/Reactor Physics and Nuclear MaterialsRST/Radiation, Science and Technolog

A discontinuous Galerkin FEM multi-physics solver for the molten salt fast reactor

Numerical simulations of fast MSRs constitute a challenging task. In fact, classical codes employed in reactor physics cannot be used, and new dedicated multi-physics tools must be developed, to capture the unique features of these systems: the strong coupling between neutronics and thermal-hydraulics due to the use of a liquid fuel, the effects on reactor kinetics induced by the precursors drift, the internal heat generation, and the shape of the core having no fuel pins as a repeated structure. In this work, we present a novel multi-physics tool being developed at TU Delft. The coupling is realized between an SN radiation transport code (PHANTOM-SN) and a RANS solver (DGFlows). Both in-house tools are based on a Discontinuous Galerkin Finite Element space discretization, characterized by local conservation, high-order accuracy, and allowing for high geometric flexibility. Implicit discretization in time is performed adopting Backward Differentiation Formulae. Cross sections are computed on an element base, starting from the local average temperature and a set of libraries generated at reference temperatures with Monte Carlo or deterministic codes. Comparison of the results obtained performing a suitable numerical benchmark created at LPSC/CNRS/Grenoble with those available in literature shows that the multi-physics tool is able to capture the unique phenomena characterizing fast liquid-fueled systems.RST/Reactor Physics and Nuclear MaterialsRST/Radiation, Science and Technolog

Preliminary assessment of the freeze-plug melting behavior in the Molten Salt Fast Reactor

This paper focuses on the freeze-plug, a key safety component of the Molten Salt Fast Reactor, one of the six Generation IV nuclear reactors that must excel in safety, reliability, and sustainability. The freeze-plug is a valve made of frozen fuel salt, designed to melt when an event requiring the core drainage occurs. It must melt passively, relying on the decay heat, and before the reactor incurs structural damages. This work aims at preliminarily investigating the freeze-plug melting behavior, assessing the influence of various design parameters (e.g., sub-cooling temperature, number of plugs, height of cavity above the plug). An apparent heat capacity method available within COMSOL Multiphysics (R) was adopted for the simulations. Results showed that the single-plug designs generally outperform the multi-plug ones, where melting is inhibited by the formation of a frozen layer, whose thickness is strongly dependent on the sub-cooling temperature and the cavity height, on top of the metal grate. The P/D ratio negligibly influences melting and, therefore, should be chosen to minimize the draining time. Due to the absence of significant mixing in the draining cavity, acceptable melting times (i.e., below 1000 s) were observed only for cavity heights up to 0.1 m. Such distance from the core is considered not sufficient to host all the cooling equipment on the outside of the draining pipe and to protect the plug from possible large temperature oscillations in the core. Hence, it is concluded that a freeze-plug design based only on decay heat to melt is likely unfeasible. A suggested design improvement, preserving passivity, consists in enhancing melting via heat stored in metal structures adjacent to the draining pipe

Results from a multi-physics numerical benchmark for codes dedicated to molten salt fast reactors

Verification and validation of multi-physics codes dedicated to fast-spectrum molten salt reactors (MSR) is a very challenging task. Existing benchmarks are meant for single-physics codes, while experimental data for validation are absent. This is concerning, given the importance numerical simulations have in the development of fast MSR designs. Here, we propose the use of a coupled numerical benchmark specifically designed to assess the physics-coupling capabilities of the aforementioned codes. The benchmark focuses on the specific characteristics of fast MSRs and features a step-by-step approach, where physical phenomena are gradually coupled to easily identify sources of error. We collect and compare the results obtained during the benchmarking campaign of four multi-physics tools developed within the SAMOFAR project. Results show excellent agreement for all the steps of the benchmark. The benchmark generality and the broad spectrum of results provided constitute a useful tool for the testing and development of similar multi-physics codes

A fully adaptive nonintrusive reduced-order modelling approach for parametrized time-dependent problems

We present an approach to build a reduced-order model for nonlinear, time-dependent, parametrized partial differential equations in a nonintrusive manner. The approach is based on combining proper orthogonal decomposition (POD) with a Smolyak hierarchical interpolation model for the POD coefficients. The sampling of the high-fidelity model to generate the snapshots is based on a locally adaptive sparse grid method. The novelty of the work is in the adaptive sampling of time, which is treated as an additional parameter. The goal is to have a robust and efficient sampling strategy that minimizes the risk of overlooking important dynamics of the system while disregarding snapshots at times when the dynamics are not contributing to the construction of the reduced model. The developed algorithm was tested on three numerical tests. The first was an advection problem parametrized with a five-dimensional space. The second was a lid-driven cavity test, and the last was a neutron diffusion problem in a subcritical nuclear reactor with 11 parameters. In all tests, the algorithm was able to detect and include more snapshots in important transient windows, which produced accurate and efficient representations of the high-fidelity models.</p