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

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

A high-order discontinuous Galerkin solver for the incompressible RANS equations coupled to the k−ϵ turbulence model

Accurate methods to solve the Reynolds-Averaged Navier-Stokes (RANS) equations coupled to turbulence models are still of great interest, as this is often the only computationally feasible approach to simulate complex turbulent flows in large engineering applications. In this work, we present a novel discontinuous Galerkin (DG) solver for the RANS equations coupled to the k−ϵ model (in logarithmic form, to ensure positivity of the turbulence quantities). We investigate the possibility of modeling walls with a wall function approach in combination with DG. The solver features an algebraic pressure correction scheme to solve the coupled RANS system, implicit backward differentiation formulae for time discretization, and adopts the Symmetric Interior Penalty method and the Lax-Friedrichs flux to discretize diffusive and convective terms respectively. We pay special attention to the choice of polynomial order for any transported scalar quantity and show it has to be the same as the pressure order to avoid numerical instability. A manufactured solution is used to verify that the solution converges with the expected order of accuracy in space and time. We then simulate a stationary flow over a backward-facing step and a Von Kármán vortex street in the wake of a square cylinder to validate our approach.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.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 MaterialsRST/Radiation, Science and Technolog

Preliminary investigation on the melting behavior of a freeze-valve for 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 Gen. 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. Melting and draining must be passive, relying on decay heat and gravity, and must occur before the reactor incurs structural damage. In this work, we preliminarily investigate the freeze-plug melting behavior, assessing the influence of various design configurations and parameters (e.g., sub-cooling, recess depth). We used COMSOL Multiphysics® to simulate melting, adopting an apparent heat capacity method. Results show that single-plug designs generally outperform multi-plug ones, where melting is inhibited by the formation of a frozen layer on top of the metal grate hosting the plugs. The layer thickness strongly depends on sub-cooling and recess depth. For multi-plug designs, the P/D ratio has a negligible influence on melting and can therefore be chosen to optimize the draining time. The absence of significant mixing in the pipe region above the plug leads to acceptable melting times (i.e., <1000 s) only for distances from the core up to 0.1 m, considered insufficient 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. Consequently, we conclude that the current freeze-plug design based only on decay heat to melt is likely to be unfeasible. A design improvement, preserving passivity and studied within the SAMOFAR project (http://samofar.eu/), consists in accelerating melting via heat stored in steel masses adjacent to the draining pipe.RST/Reactor Physics and Nuclear MaterialsRST/Radiation, Science and Technolog

Analysis of the Molten Salt Fast Reactor using reduced-order models

In this paper, we present a reduced-order modeling approach to study the Molten Salt Fast Reactor (MSFR). Our approach is nonintrusive and based on the proper orthogonal decomposition method. We include adaptivity in selecting the sampling points both in time and parameter space. Steady-state and transient analysis were both performed using the developed models. In the steady-state analysis, we capture the effect of 30 model parameters on the spatial distributions of fission power and temperature, and on the multiplication factor. The dimensionality of the fission power was reduced from the 104288 nominal dimensions in the physical space to 10 dimensions in the reduced space, whereas the temperature was reduced from 220972 dimensions to 3. The reduced model was then used for uncertainty and sensitivity study of the maximum temperature in the reactor and the multiplication factor. In the transient analysis, the reduced model captured the effect of perturbations in the flow rate of salt in the intermediate circuit on the fission power density and temperature. The reduced models were successfully tested on a set of points that were not part of the snapshots used during the construction stage.RST/Reactor Physics and Nuclear MaterialsRST/Radiation, Science and Technolog

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 non-intrusive 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.RST/Reactor Physics and Nuclear Material

A nonintrusive adaptive reduced order modeling approach for a molten salt reactor system

We use a novel nonintrusive adaptive Reduced Order Modeling method to build a reduced model for a molten salt reactor system. Our approach is based on Proper Orthogonal Decomposition combined with locally adaptive sparse grids. Our reduced model captures the effect of 27 model parameters on keff of the system and the spatial distribution of the neutron flux and salt temperature. The reduced model was tested on 1000 random points. The maximum error in multiplication factor was found to be less than 50 pcm and the maximum L2 error in the flux and temperature were less than 1%. Using 472 snapshots, the reduced model was able to simulate any point within the defined range faster than the high-fidelity model by a factor of 5×106. We then employ the reduced model for uncertainty and sensitivity analysis of the selected parameters on keff and the maximum temperature of the system.RST/Reactor Physics and Nuclear MaterialsRST/Radiation, Science and Technolog