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Numerical simulation of involute-plate research reactor flow behavior using RANS, LES and DNS

This paper investigates the flow behavior of involute-plate research reactors by performing Reynolds-Averaged Navier Stokes simulation (RANS), Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) of the channel flow between fuel plates. By modeling turbulence with different numerical approaches, this study provides data with three levels of fidelity. For the RANS simulation, three widely used turbulence models, i.e., k-ε, k-ω, Reynolds Stress Turbulence model (RST) are applied by using the commercial CFD code STAR-CCM +. For LES and DNS, the open-source CFD code, Nek5000, is used given its outstanding scalability on High Performance Computer (HPC) and high-order technique. The results from RANS simulations are compared with that from LES and DNS for benchmarking. Both macroscale parameters and turbulence statistics, such as velocity magnitude, lateral velocity and turbulence kinetic energy, are presented and analyzed. The results from RANS simulation achieve good agreement with LES and DNS on velocity and turbulence kinetic energy prediction. The RST turbulence model predicts the most similar flow pattern of lateral velocity as compared to LES and DNS. The Lambda-2 (λ2) criterion with a reasonable threshold is used to demonstrate the instantaneous vortices distribution in the involute channel from both LES and DNS calculation. The DNS simulation captures more detailed turbulence especially near the corner, which explains the discrepancy between LES and DNS results near the corner. The normalized RMS error are defined and calculated to assess the performance of those turbulence models. The RST model captures the anisotropic feature of turbulence, which enable it to outperform other turbulence models for predicting the flow behavior in an involute channel. Although some discrepancies are found between LES and DNS results in the corner, the overall deviations between LES and DNS are found to be small. In conclusion, given that the computational cost of DNS calculation is an order of magnitude higher, using LES data for benchmarking RANS model is a cost-effective approach.

DNS↗

Involute Working Group – Validation of CFD Turbulence Models for Steady-State Safety Analysis

There are three research reactors in the world having fuel plates curved as circle-involute (a spiral generated around a circle): The Oak Ridge National Laboratory (ORNL) High Flux Isotope Reactor (HFIR) located in Tennessee, U.S.A. [ORNL, 2018]; The Laue-Langevin Institute (ILL) High Flux Reactor (RHF) located in Grenoble, France [ILL, 2018]; and, The Technical University of Munich (TUM) Research Neutron Source Heinz Maier-Leibnitz (FRM II) located in Garching, Germany [TUM, 2018]. All three reactors are currently using Highly Enriched Uranium (HEU, 235U/U ≥ 20 wt. %) as fuel and all three are actively engaged in activities to convert to Low Enriched Uranium (LEU, 235U/U < 20 wt. %) fuel. More information on these reactors can be found in Section two. For various reasons, these reactors have expressed interest in using Computational Fluid Dynamics (CFD) tools to perform their Steady-State Thermal-Hydraulic (SSTH) safety calculations. Using CFD tools for SSTH analysis represents generally a significant departure from traditional methods and requires thorough verification and validation (V&V) to be accepted by regulators. This is why Argonne National Laboratory (ANL) and the involute reactors formed an informal group to help each other in this endeavor. This so-called Involute Working Group (IWG) aims at supporting the qualification of CFD tools for SSTH safety calculations. Activities include benchmarking, code-to-code comparison, Verification and Validation (V&V) as well as technical support. More information on the IWG and the reasons why involute-plate reactors are interested in CFD can be found in Section three. The present study aims at testing three turbulence models commonly implemented in commercial software (namely K-Epsilon, K-Omega and Reynolds-Stress) and assessing their relevance for involute-plate reactor application. An experiment performed by Gambill and Bundy in 1961 was performed to measure heat transfer coefficients in conditions prototypic of the HFIR reactor [Gambill, 1961]. More details on this experiment are provided in Section four. Based on the information available, CFD models of this experiment have been created and the experimental results have been compared to the ones obtained with these CFD models. CFD models and the results of this comparison are provided in Section five.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Involute Working Group – Development and Validation of the Finite Element Models of the Cheverton-Kelley Experiments

In an involute-plate reactor, the fuel plates and side-plates are subjected to a non-uniform distribution of loads. Temperature variation derives from a variation in power distribution throughout the core. Due to small imperfections in the channel thickness, the coolant flowing in between the plates produces pressure differentials with a non-uniform distribution on the plate surface. The main goal of the analysis presented in this technical report is to investigate the ability of the commercial software STAR-CCM+ to model deformation of involute plates subjected to mechanical and thermal loads, representative of involute reactor operation conditions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Involute Working Group – FSI Analysis of Fuel Plates Using Finite Volume and Finite Element Methods

The three involute plate research reactors RHF, HFIR, and FRM II have expressed an interest in using computational software to carry their steady-state safety analysis. Since these tools represent a significant departure from the methods used currently (one-dimensional), the acceptability of the new approach by regulators requires thorough verification and validation of these tools. Therefore, Argonne National Laboratory and the three involute-plate reactors formed an informal group called the Involute Working Group aiming at qualifying computational tools to perform steady-state safety analysis. The present report focuses on a comparison of finite volume and finite element methods to model solids in fluid-structure interaction problems with the goal to estimate the coolant flow-induced fuel plate deflections obtained with the two methods. The finite volume method will be obsoleted in STARCCM+ by the end of 2021, nevertheless, this evaluation is important because the method was used by ANL researchers to model the response of the fuel plates, despite its drawbacks, which are discussed in the report. It was essential to check how those estimates compare to the results obtained with the finite element method that is considered superior for structural analysis. Various geometries, i.e., flat, cylindrical and circle-involute fuel plates, as well as coolant flow speed, were considered. The comparison shows that, independently of the plate geometry, the finite volume method significantly underestimates the deflection as compared to finite element method for coarser meshes. When the discretization is developed as a result of a mesh sensitivity study using finite element method, the result obtained using finite volume method can be a few times smaller than the corresponding finite element method solution. A code-to-code comparison , between STAR-CCM+ and LS-DYNA was included in the analysis. Within the LS-DYNA models, two types of finite element formulations were used: solid and shell finite elements. Mesh sensitivity study showed that both approaches converge to a similar value that was obtained with STAR-CCM+ finite element solver. The evaluation of the computational solvers was extended by adding two benchmark cases from the STAR-CCM+ Verification Suite and presented in the Appendix A. The selected cases are: (1) bending of a cantilever beam under external load, and (2) cylindrical shell deformation analysis, known in the literature as ‘Scordelis-Lo roof’. The problems were solved with finite volume, and finite element methods, and the results confirmed the previously discussed findings. The analysis shows that the finite element solver is superior to the finite volume solver in terms of representation of model geometry and estimating the structural behavior of fuel plates. Depending on the ratio of the load to the flexibility of the plate, the finite volume solver can greatly under- or overestimate the structural response if a very carefully selected mesh is not used.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Monte Carlo Analyses of the FOEHN Experiment

The FOEHN critical experiment, which has been carried out at Cadarache (France) in the reactor EOLE in the early 70s, was designed to verify RHF design analyses. This study focuses on the impact of the FOEHN experiment uncertainties on the calculation of the energy deposition. The latter has been obtained by the Monte Carlo codes Serpent and MCNP. In the calculation of the energy deposition, the first code relies on KERMA factors whereas the latter code relies on Q-values. The two Monte Carlo codes share the same geometry and material specifications. In addition to the design and experiment parameters uncertainties, nuclear data also impacts the calculation of the energy deposition. In this study, the MCNP simulations use three different nuclear data library sets: ENDF/B versions VII.0, VII.1, and VIII.0. Finally, the ksens card of MCNP, using perturbation theory, has been used to identify the cross sections and isotopes with largest impact on the effective multiplication factor. By showing that the use of different software and computational methodologies and design parameters uncertainties do not significantly impact the core power distribution, this work demonstrate the appropriateness of the tools and methods employed for the conversion of involute-plate reactors.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗