Verification of multiphysics coupling techniques for modeling of molten salt reactors
Introduction
Molten salt reactors (MSRs) have recently gained renewed interest due to potential advantages compared to conventional reactors based on solid fuels; these include inherent safety features, low pressure operation, large negative feedback coefficients and the possibility for online fuel reprocessing. MSR designs, however, are typically characterized by a low technology readiness level and several challenges including the corrosion of the structure materials, developing a fuel cycle and protection against proliferation.
Among several conceptual MSR designs, the Molten Salt Fast Reactor (MSFR) has been selected as a Generation IV Reactor candidate (Boussier et al., 2012). The MSFR design concept is outlined in Fig. 1. The design has evolved over the years from having a cylindrical core to a segmented core geometry in the framework of the European SAMOFAR project (SAMOFAR, 2019). In the segmented design approach the core is toroidal, surrounded by a fertile salt blanket and has sixteen fuel inlets and outlets connected to sixteen heat exchangers. In case of an accident the fuel is supposed to drain into an emergency draining tank which is sealed with a freeze plug during normal operation. The molten fluoride salt enters the toroidal core at a nominal temperature of 650 °C, and the design temperature raise within the core is 100 °C at a nominal flow rate of 4.5 m3/s.
The liquid fuel in the core introduces several fundamental differences compared to a solid fueled reactor. In particular, the delayed neutron precursors (DNP) are no longer stationary, but move with the flow, resulting in a decreased effective delayed neutron fraction. Since the liquid fuel is also the primary coolant, turbulence effects have direct impact on the neutronics performance of the reactor. In addition to this and the application of gaseous fission product removal systems, the compressibility of the fuel contribute to the strong coupling between neutron kinetics and thermal hydraulics; thus requiring multiphysics modeling tools to study such reactors. Regulatory approved modelling tools have been developed specifically for solid fuel reactors and even though some of them can be extended or modified to address liquid fuels (Fletcher and Schultz, 1995, Zhang et al., 2018), no multiphysics analysis framework has been approved specifically for liquid fuel reactors. A short summary of some multiphysics tools developed and applied for the analysis of MSRs, in particular the MSFR, is presented in Table 1. A brief description of the codes and further references can be found in (Tiberga et al., 2020).
All codes in Table 1 are based on the solution of the neutron transport equation using either a diffusion or an SPX approximation (Cervi et al., 2019a, Fiorina et al., 2012, Fiorina et al., 2014). A new contribution to the original fast MSR benchmark developed by LPSC/CNRS-Grenoble (Aufiero, 2015; Laureau, 2015, Aufiero and Rubiolo, 2018) has recently been published (Tiberga et al., 2020). The original benchmark and the recent extension by Tiberga et al. can be used by multiphysics code developers to verify their modeling approaches. The structure of the benchmark, wherein coupling terms are introduced gradually, allows for easy debugging of the codes and identification of the sources for discrepancy. Unless otherwise stated the study here will refer only to the results from the recent publication by Tiberga et al.
For the present benchmark the CNRS code employs either a SP1 or a SP3 model for the neutronics combined with a thermal-hydraulics solver based on the finite volume C++ computational fluid dynamics (CFD) toolbox OpenFOAM (Weller et al., 1998). The PoliMi code uses a multi-group diffusion model for the neutronics and OpenFOAM on the thermal-hydraulics side. The PSI code implements a multi-group diffusion sub-solver in the OpenFOAM code. Finally the TUD code employs an multi-group model for the neutronics and a parallel solver for the incompressible Navier–Stokes equations.
In this paper, we present two multiphysics modeling approaches and verify them against the benchmark. The first approach (Nalbandyan et al., 2019) utilizes the Serpent2 (Leppänen et al., 2015) multiphysics interface (Valtavirta, 2016), allowing for high fidelity coupling of OpenFOAM and Serpent2. In this approach, Serpent2 serves as the main neutronics solver and is coupled to an OpenFOAM based thermal-hydraulics solver and a DNP transport solver implemented in OpenFOAM as well. The main advantage of this coupling approach is that it allows for using a high accuracy Monte-Carlo method to solve the neutron transport equations. In the following this approach will be referred to as the DTU approach. The second approach utilizes the SEALION framework. The SEALION framework, in its current iteration, employs a specialized thermal hydraulics solver based on OpenFOAM coupled with a custom-made modified point kinetics neutronics solver explicitly taking the altered neutron importance from DNP transport into account. The main advantage of this approach is that it allows for pre-determining the temperature feedback using Monte-Carlo codes such as Serpent2, leading to a significant reduction in computational requirements. In general point, kinetics solvers are expected to capture the physics of reactor systems, and provide a good approximation for a given reactor transient, as long as the transient is (mainly) driven by the fundamental form. It is therefore of interest to expand and demonstrate point kinetics methods for liquid fueled reactor systems such as MSRs. Despite their reduced order, point kinetics solvers are still being used extensively in nuclear reactor transient analysis codes such as RELAP5/7 (Fletcher and Schultz, 1995, Zhang et al., 2018).
Both modelling approaches are explained in greater details in Section 4.
In Section 2, a detailed description of the benchmark is provided. Section 3 describes the various phases and steps that constitutes the benchmark. The assumptions for every step of the benchmark as well as the output observables are described in this section. The two code packages used in paper will be presented in Section 4. The results obtained from applying these codes to the benchmark are presented and analyzed in Sections 5 Benchmark results, 6 Phase 2: Time dependent coupling.
Section snippets
Description of the benchmark
One of the traditional benchmark cases used to verify thermal-hydraulics solvers for incompressible flow is the lid driven cavity model (Aufiero, 2015, Laureau, 2015). The geometry is fairly simple, it captures the main characteristics of the flow and provides a clear identification of relevant parameters for the simulation. The benchmark geometry has been adapted in (Tiberga et al., 2020) as well as this work for verification of the neutronics-thermal hydraulics coupling techniques for MSRs;
Phases and steps of the benchmark
The multiphysics benchmark is performed in three main stages: first the individual solvers for the neutronics and the thermal-hydraulics are tested, then a fully coupled steady state analysis of the model is carried out, and finally the coupling is tested for a forced convection transient scenario.
Hence, the benchmark stages are structured as follows:
- •
Single physics testing: Phase 0
- •
Steady-state simulation: Phase 1
- •
Time dependent simulation: Phase 2
Serpent2 to OpenFOAM coupling technique
The coupling scheme is represented in Fig. 3. Two distinct software and three distinct solvers are involved: Serpent2 software is used for neutronics part, whereas the DNP transport and the thermal-hydraulics are calculated by the OpenFOAM software. The procedure is as follows (here explained for steady-state mode):
- •
Serpent2 Criticality Source Simulation (Serpent CSS) is run on the same mesh as used for thermal-hydraulics, using the Serpent2 multiphysics interface capabilities. The heat source
Benchmark results
In this section the main results are presented and compared to the benchmark analysis (Tiberga et al., 2020). For the sake of transparency the step numbers in the figures and tables refer to the step numbering used in the benchmark analysis.
Phase 2: Time dependent coupling
The left panel in Fig. 12 shows the power gain as a function of frequency. The right panel in Fig. 12 compares the results for the power phase shift compared to the wave. A discrepancy for the SEALION code of is observed for the gain diagrams. These numbers are to be compared to a code-wise and average relative discrepancy for benchmark participants of less than 1%. For the phase diagrams the agreement is better yielding a code-wise discrepancy for the SEALION code of
Conclusion
This paper presents the results of a code-to-code verification of two multiphysics coupling techniques for molten salt reactor modeling. The coupled Serpent2-OpenFOAM method and an in–house developed SEALION software are compared for several multiphysics software features in a benchmark defined for a generic fast MSR (Tiberga et al., 2020).
The standalone physics modules yield almost identical results with the benchmark participants. Gradual introduction of coupling terms shows that both
CRediT authorship contribution statement
J. Groth-Jensen: Software, Validation, Formal analysis, Investigation, Data curation, Visualization. A. Nalbandyan: Methodology, Software, Validation, Formal analysis, Investigation, Data curation, Writing - original draft. E.B. Klinkby: Supervision, Writing - review & editing, Validation. B. Lauritzen: Supervision, Writing - review & editing, Project administration. P. Sabbagh: Conceptualization, Methodology, Software. A.V. Pedersen: Conceptualization, Methodology, Software.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors would like to express their appreciation to the authors of (Tiberga et al., 2020, Aufiero, 2015, Aufiero and Rubiolo, 2018) for their highly useful and inspirational work. The authors would also like to acknowledge the reviewers, who gave useful suggestions for improving the manuscript. The three-year SEALION project is partially funded by the Eurostars programme - Eurostars E!11837 SEALION. As European joint programme, co-funded by the Eureka countries and the European Union
References (41)
- et al.
Benchmark spectral results on the lid-driven cavity flow
Computers & Fluids
(1998) - et al.
Development of a multiphysics model for the study of fuel compressibility effects in the molten salt fast reactor
Chemical Engineering Science
(2019) - et al.
Development of an neutron transport solver for the analysis of the molten salt fast reactor
Nuclear Engineering and Design
(2019) - et al.
Neutron point kinetics model with precursors’ shape function update for molten salt reactor
Nuclear Engineering and Design
(2020) - et al.
A family of embedded runge-kutta formulae
Journal of Computational and Applied Mathematics
(1980) - et al.
Neutron kinetics of fluid-fuel systems by the quasi-static method
Progress in Nuclear Energy
(2004) - et al.
Modelling and analysis of the msfr transient behaviour
Annals of Nuclear Energy
(2014) - et al.
Gen-foam: a novel openfoam based multi-physics solver for 2d/3d transient analysis of nuclear reactors
Nuclear Engineering and Design
(2015) - et al.
High-re solutions for incompressible flow using the navier-stokes equations and a multigrid method
Journal of Computational Physics
(1982) - et al.
Dyn1d-msr dynamics code for molten salt reactors
Annals of Nuclear Energy
(2005)