Elsevier

Annals of Nuclear Energy

Volume 130, August 2019, Pages 184-191
Annals of Nuclear Energy

Deflection predictions of involute-shaped fuel plates using a fully-coupled numerical approach

https://doi.org/10.1016/j.anucene.2019.02.001Get rights and content

Abstract

This paper describes the modeling and simulation of fluid structure interactions (FSI) of involute-shaped fuel plates used in nuclear research reactors. We believe this to be the first time that this type of application is described in the literature using a fully-coupled, and monolithic, finite element approach. The simulations are validated against plate deflection data for the conceptual design of the Advanced Neutron Source Reactor (ANSR), which was envisioned to be the world’s most powerful nuclear research reactor for neutron scattering and other applications, but was ultimately never completed. The high performance of the ANSR creates a bounding envelope for involute-shaped research reactors such as that used in the High Flux Isotope Reactor (HFIR) at the Oak Ridge National Laboratory (ORNL) which is undergoing research for the conversion from highly-enriched uranium (HEU) to low-enriched uranium (LEU) fuel. As such, the findings from the present FSI analyses carried out herein for the ANSR plates provide good guidelines and inform designers what should be expected for the next generation of plates in the HFIR. It is shown herein that the current approach can accurately capture the leading-edge deflections of the involute-shaped plates and simulations can predict the ‘S-shaped’ deflection of the first mode instilling confidence in the methodology.

Introduction

The High Flux Isotope Reactor (HFIR), located at the Oak Ridge National Laboratory (ORNL), has been providing the highest neutron flux in the United States since 1965. Conceptual designs of the reactor began in 1958 utilizing highly-enriched uranium (HEU) to run at 100 MWtherm. The reactor ran at this power until 1986 when embrittlement of the reactor vessel became a concern and the power was reduced to 85 MWtherm where it continues to run today (HFIR Website, 2014).

A call has been issued by the U.S. Department of Energy’s (DOE) National Nuclear Security Administration (NNSA) that states that all research reactors in the United States should convert their HEU fuel to low-enriched uranium (LEU) fuel as part of the Global Threat Reduction Initiative (GTRI) (GTRI Website, 2014). As part of the call, the research reactors are to be converted to use the LEU fuel without significant changes to the design of the reactors while ensuring a high level of safety without compromising the scientific capabilities of the reactors.

HFIR is one of the remaining five high performance research reactors to be converted in the United States. Because the internal fuel meat of the fuel plate is being redesigned for the LEU fuel, the safety basis for the operating reactor must be updated, and extensive thermal-hydraulics analyses must be performed with the redesigned fuel. For each cycle of the reactor, the current safety assessment is performed using various calculations and codes. The two main codes used for the thermal hydraulic calculations of the HFIR are the Steady State Heat Transfer Code (SSHTC) (McLain and Fuel, 1967) and a modified version of RELAP5 (Morris and Wendel, 1993), both of which are based on one-dimensional flow physics. For detailed information about the implementations of these codes, the readers are referred to the Safety Analysis Report (SAR) (Ornl, 2013). To improve our understanding of the multiphysical phenomena in the reactor, state-of-the-art high-fidelity codes must be utilized. For this purpose, COMSOL Multiphysics (COMSOL, 2016) code is chosen. In particular, COMSOL has been used for investigating the thermal-hydraulics (Tschaepe et al., 2008, Freels et al., 2010, Renfro et al., 2011, Bodey et al., 2011, Freels and Jain, 2011, Khane et al., 2012, Khane et al., 2012, Travis et al., 2013, Wang et al., 2013, Travis, 2014), thermal-structure interaction (Jain et al., 2012) and reactor kinetics (Chandler, 2011) of the HFIR core.

The current design of the HFIR core consists of 540 involute shaped fuel plates placed in two concentric elements with 171 plates in the inner element and 369 plates in the element. The plates are 50mils thick and they are separated by a spacing of the same distance as depicted in Fig. 1. The primary goal of this work is to determine the deflection of the aluminum plates due to cooling water flow in order to predict changes in the flow channel geometry between the plates.

Plate deflection has been an area of interest beginning with preliminary investigations of high-flux plate reactors at ORNL in 1948 (Stromquist and Sisman, 1948). During their experiments, Stromquist and Sisman observed vibrations for plates with thicknesses similar to the current HFIR design. Miller later developed an estimate of the maximum flow speed that a series of parallel plates could sustain before collapse, aptly named the Miller Critical Velocity, Mc (Miller, 1960). For a flat plate with fixed edges, the Miller Critical Velocity is defined asMc=15Ea3hρb41-ν21/2where E is the Young’s Modulus of the plate, a is the plate thickness, h is the flow channel thickness, ρ is the density of the coolant fluid, b is the width or span of the plate, and ν is the Poisson’s ratio of the plate. Equation 1 is based on the assumption of incompressible, potential flow and an elastic wide-beam theory. Miller also assumed identical mass flow rates between all channels. The resulting equation roughly predicts the velocity for which the pressure difference between the plates is sufficient to result in a finite level of deflection. Because of its simplicity, the Miller Critical Velocity has become a standard for plate deflection analyses.

The Miller Critical Velocity has been (and continues to be) the topic of many experiments to understand the applicability of the theory. Most researchers (Groninger and Kane, 1963, Smissaert, 1968, Swinson et al., 1993, Kennedy et al., 2012) found that the Mc was based on conservative assumptions. Groninger and Kane (1963) and Smissaert (1968) found that the plates began to vibrate around twice the value of Mc. An exception to this finding was reported by Ho et al. (2004) for which plate buckling was observed at a speed below Mc suggesting the Ho study to be outside the norm.

As it became clear that the Miller Critical Velocity was conservative, many researchers began to search for improvements to the model. As such, investigators started accounting for more advanced physical models. For example, Johansson (1959) incorporated viscous and flow redistribution effects. Kane (1962) developed a model that incorporated manufacturing deviations to the flow channels and found that large channel deviations resulted in greater plate deflections. Scavuzzo (1965) modeled entrance and exit effects and Wambsganss (1967) pointed out the need for the inclusion of second-order effects to the original version of Miller’s equation.

Researchers then began to include other analytical techniques in order to provide a better estimate of the plate deflections of parallel fuel plates. Wick (1969a) explored a wave propagation technique, and also investigated an eigenfrequency approach with end plate effects (Wick, 1969b). Kim and Scarton (1977) used Schlichting’s boundary layer theory while Kerboua et al. (2008) incorporated potential flow theory around a single plate to analyze a series of plates. Cekirge and Ural (1978) and Pavone and Scarton (1983) both focused on improving the plate theory to enhance the model.

It became evident that one-dimensional flow simplification used in previous studies was insufficient and researchers began to use two- and three-dimensional models for the fluid flow. Guo and Païdoussis (2000) utilized a Galerkin method to model a two-dimensional plate with a three-dimensional flow field. Several researchers sought to determine the natural frequencies of the plates including Kim and Scarton (1977), who combined turbulent effects with a frequency analysis of thin plates. In a different study, Cui et al. (2008) used a whetting method to determine the frequencies, and Michelin and Llewellyn Smith (2009) analyzed flutter by examining n-series of plates.

Although these techniques provided good insight into the deflection of parallel plates, there is still much to be studied about fluid-structure interactions in such systems. As high performance computing (HPC) resources become more available, the use of computational models to simulate fluid-structure interaction (FSI) between the plates and the coolant flow is becoming more feasible. Recently, Roth (2012) was able to use computational fluid dynamics (CFD) to simulate the flow between fuel plates but was unable to observe plate deflections. Kennedy (2015) used two segregated codes, one for modeling the fluid flow and another for modeling the structural response. This approach resulted in a loosely-coupled approach, which proved to have significant stability problems. To address the potential numerical stability issues, the work presented herein utilizes a fully-coupled (monolithic) approach which incorporates the flow physics and structural mechanics in a unified solver (Curtis et al., 2013). In previous work (Curtis et al., 2017), this approach has been shown to produce reasonably accurate computations and results have been validated against the experimental data of Smissaert (1969).

This work builds upon the previous reported analyses and is particularly focused on accurate modeling of involute plate configurations that are representative of the HFIR. In the late 1980s and early 1990s, a new reactor, called the Advanced Neutron Source Reactor (ANSR), was proposed at the ORNL to provide another high-flux source of neutrons. During the development of this reactor design, numerous experiments were performed, including deflection experiments of the involute-shaped fuel plates. These experiments provide the only available plate deflection data to date for involute-curved plates. As such, the ANSR experiments were chosen to validate the adopted monolithic methodology for accurate prediction of deflections for a proposed updated design of the HFIR LEU-fueled plates.

Section snippets

ANSR experiment

As discussed earlier, the Advanced Neutron Source Reactor was proposed as an alternative high-performance, heavy-water research reactor at ORNL. The reactor design incorporated involute fuel plates – similar to those used in the HFIR – with cooling flow rates at approximately 25m/s. The design met or exceeded the neutron flux characteristics of the HFIR yielding what would have been the highest neutron flux reactor in the world. Due to the challenges associated with extremely high flow rates,

Computational model

As mentioned earlier, the ANSR experiment utilized PVC plates with Eq. (2), (3) used to predict the coolant speeds for the equivalent aluminum plate deflections. For the computational model, the properties of the aluminum plate and PVC plate were used to compare to the deflections from the experiments. The FSI computations were performed using the commercial software COMSOL (COMSOL, 2016), which uses a finite element method (FEM) for the discretization of the governing equations that model

Validation study for the ANSR experiment

Previous analyses of the ANSR and HFIR by Luttrell (1995) predicted an “S-shaped” deflection at the leading edge as shown in Fig. 3. This prediction is used in the HFIR SAR where an eigenfrequency analysis of the 1st mode of the plates confirms this “S-shape” assumption. The simulation of the plates, using the present FSI formulations, also results in a similar type of deflection at the leading edge as presented in Fig. 4.

Deflection calculations were performed for a single plate to compare the

HFIR fuel plate deflection predictions

The ANSR designers also measured deflections of a single HFIR IFE plate in their test rig. Because the main purpose of the experiment was to determine the deflections of the ANSR fuel plates, the HFIR plate experiment only measured the leading edge deflections of a single HFIR plate. Again, the plate was made using PVC and lower velocities were used to predict a prototype aluminum deflection. In this work, several simulations are performed to help guide the HFIR safety analyses for best

Conclusion

The transition from the simulation of flat fuel plates to involute-curved fuel plates is essentially straightforward. The techniques developed for the simulations of the previously-analyzed Smissaert (Curtis et al., 2017) flat plate experiment worked well for the more complex geometry of the curved plates. As with the Smissaert experiments, the leading edge deflection is accurately predicted in the ANSR experiments and the trailing edge deflections are slightly less accurate.

Predicting the

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  • Cited by (3)

    This manuscript has been authored by UT-Battelle, LLC under Contract No. DE-AC05-00OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy.gov/downloads/doe-public-access-plan).

    1

    Computational Sciences and Engineering Division.

    2

    Department of Mechanical, Aerospace and Biomedical Engineering.

    3

    Retired from Research Reactors Division.

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