Nuclear Science and Engineering ISSN: 0029-5639 (Print) 1943-748X (Online) Journal homepage: http://www.tandfonline.com/loi/unse20 Predicting Large Deflections of Multiplate Fuel Elements Using a Monolithic FSI Approach Franklin G. Curtis, James D. Freels & Kivanc Ekici To cite this article: Franklin G. Curtis, James D. Freels & Kivanc Ekici (2017): Predicting Large Deflections of Multiplate Fuel Elements Using a Monolithic FSI Approach, Nuclear Science and Engineering, DOI: 10.1080/00295639.2017.1379304 To link to this article: http://dx.doi.org/10.1080/00295639.2017.1379304 Published online: 26 Oct 2017. Submit your article to this journal View related articles View Crossmark data Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=unse20 Download by: [University of Missouri-Columbia] Date: 27 October 2017, At: 03:01 NUCLEAR SCIENCE AND ENGINEERING © American Nuclear Society DOI: https://doi.org/10.1080/00295639.2017.1379304 Predicting Large Deflections of Multiplate Fuel Elements Using a Monolithic FSI Approach Franklin G. Curtis, a,c * James D. Freels,b,c and Kivanc Ekici c a Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee Research Reactors Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee c University of Tennessee, Department of Mechanical, Aerospace and Biomedical Engineering, Knoxville, Tennessee Downloaded by [University of Missouri-Columbia] at 03:01 27 October 2017 b Received June 26, 2017 Accepted for Publication September 10, 2017 Abstract — As part of the Global Threat Reduction Initiative, the Oak Ridge National Laboratory is evaluating conversion of fuel for the High Flux Isotope Reactor (HFIR) from high-enriched uranium to lowenriched uranium. Currently, multiphysics simulations that model fluid-structure interaction phenomena are being performed to ensure the safety of the reactor with the new fuel type. A monolithic solver that fully couples fluid and structural dynamics is used to model deflections in the new design. A classical experiment is chosen to validate the capabilities of the current solver and the method. A single-plate simulation with various boundary conditions as well as a five-plate simulation are presented. Use of the monolithic solver provides stable solutions for the large deflections and the tight coupling of the fluid and structure and the maximum deflections are captured accurately. Keywords — Thermal hydraulics, fluid-structure interaction, high flux isotope reactor. Note — Some figures may be in color only in the electronic version. I. INTRODUCTION The High Flux Isotope Reactor (HFIR) at the Oak Ridge National Laboratory (ORNL) has the highest neutron flux in the Western world. The current design of the reactor utilizes highly enriched uranium (HEU) in a dispersion-type fuel.1 The U.S. Department of Energy’s (DOE’s) National Nuclear Security Administration is implementing the U.S. policy to minimize and eliminate the use of HEU in civilian applications by working to convert research and test reactors to the use of lowenriched uranium (LEU) through the Global Threat Reduction Initiative2 (GTRI). The goal of the GTRI is to convert the research reactor without major changes to the structure of the reactor while maintaining the current scientific mission and safety levels of the present design. *E-mail: email@example.com The design of the HEU core is based upon early research reactor experience, HFIR-specific experiments, and historical safety and design-basis calculations. Today, it is not economically feasible to perform extensive experiments to support the design of the fuel, and the use of computational models is becoming increasingly needed. Currently, the HFIR employs numerous safety calculations and codes, based upon empirical data as well as first-principles physics, to assess each cycle of the reactor. Each code and its implementation for the HFIR is described in detail in the Safety Analysis Report for the HFIR (Ref. 3). The two main codes used for the thermal-hydraulic analysis of the HFIR core and system are the Steady State Heat Transfer Code4 and a modified version of RELAP5 (Ref. 5), both of which model one-dimensional (1-D) flow physics. It is desired to utilize modern computational fluid dynamics techniques to better understand the thermal-hydraulic aspects of the core by using a commercial code, in particular 1 Downloaded by [University of Missouri-Columbia] at 03:01 27 October 2017 2 CURTIS et al. · LARGE DEFLECTIONS OF MULTIPLATE FUEL ELEMENTS COMSOL (Ref. 6). Previous analysis of the HFIR core using COMSOL has been limited to thermalhydraulics.7–16 The results of this analysis have also given rise to the simulation of the thermal-structure interaction in the HFIR performed by Jain et al.17 Chandler18 incorporated reactor kinetics into COMSOL to model the reactions of the LEU fuel for HFIR. Interest in the deflection of the fuel plates in research reactors has been a topic of research beginning with preliminary design experiments of the HFIR in 1948 by Stromquist and Sisman.19 Stromquist and Sisman were able to observe plate vibration for plates similar in thickness to the current HFIR design. Their experiments found that varying spacing between plates (one channel was 15.9 mm while the adjacent one was 3 mm) could produce buckling at the plate leading edges. Under nominal plate spacing, the maximum deflection of the plates was found to be approximately 2 mil (0.05 mm). Later, Miller developed a theoretical approach to determine the maximum velocity that a series of plates with fixed sides can sustain before collapse.20 Miller’s Critical Velocity Mc was based upon the assumption of incompressible, potential flow and it utilized an elastic wide-beam theory. Miller also assumed that the mass flow between all of the channels was identical. Miller’s approach determined the velocity in which the pressure difference between two adjacent channels is sufficient to maintain a deflection. The Miller Critical Velocity soon became the standard for safety analysis to determine the critical flow velocity of parallel reactor fuel plates. For a series of flat plates with fixed edges, the Miller Critical Velocity is defined as 1=2 15gEa3 h Mc ¼ ; ρb4 ð1 ν2 Þ ð1Þ where g = gravitational constant E = Young’s Modulus of the plate a = plate thickness h = flow channel thickness ρ = density of the coolant b = width or span of the plate ν = Poisson’s ratio of the plate. Experimental testing of the Miller Critical Velocity has been performed by many researchers.21–24 These investigators found that the Miller Critical Velocity was conservative, for flows tested up to 2 Mc produced no total plate collapse results. In fact, Groninger and Kane21 and Smissaert22 found that vibration occurs at approximately twice the Miller Critical Velocity. The only experiment in which total plate collapse occurred was performed by Ho et al.25 The collapse occurred at a velocity lower than Mc suggesting that this experiment may be an outlier. The shortcomings and inherent conservativism of the Miller Critical Velocity led many researchers to improve upon the theory. Johansson26 first expanded on the Miller Critical Velocity by including friction terms and the flow redistribution caused by the movement of plates. Kane27 explored how deviations from the design thickness can affect plate deflections. As expected, he found that large deviations can lead to larger deflections. Further, Scavuzzo28 included the entrance and exit effects at the leading and trailing edge of the plate. Wambsganss Jr.29 argued that the derivation first proposed by Miller can be improved upon by including second-order effects in the calculation of the critical velocity. Researchers began to reevaluate the assumptions Miller made in his derivation of the critical flow velocity. Other analysis techniques were developed, including a wave propagation/water-hammer approach,30 solving the series of plates as a system,31 and using Schlichting’s boundary layer (BL) theory.32 Cekirge and Ural33 used small deflection plate theory to update the critical flow velocity gaining only a 4% margin over the Miller Critical Velocity. To better capture the plate deflections, Pavone and Scarton34 employed a fourth-order structural model with laminar flow. Kerboua et al.35 used a potential flow analysis of one plate to analyze a multiplate channel and found that their method matched Miller’s Critical Velocity. All researchers up to this point had assumed 1-D steady-state flow. A Galerkin method was employed by Guo and Païdoussis36 to analyze a two-dimensional (2-D) plate with a three-dimensional (3-D) flow field. By combining turbulent effects with a frequency analysis of thin rectangular plates, Kim and Davis37 were able to obtain natural frequencies of a series of plates. They found that the natural frequency of the plates in a fluid was lower than the plates in vacuo; they also found that by decreasing the channel gap, the natural frequency of the plate would shift. On the other hand, Cui et al.38 used a whetting method to determine the natural frequency of the plates and found that the added fluid did not greatly affect the natural frequency of the plate. Using a stability criterion, Michelin and Llewellyn Smith39 analyzed an n-series of plates to determine the stability of the system as it relates to flutter. NUCLEAR SCIENCE AND ENGINEERING · VOLUME 00 · XXXX 2017 Downloaded by [University of Missouri-Columbia] at 03:01 27 October 2017 LARGE DEFLECTIONS OF MULTIPLATE FUEL ELEMENTS · CURTIS et al. Until recently, the use of high-fidelity computational models to simulate fluid-structure interactions (FSIs) between fuel plates and coolant flow has been too computationally expensive. Roth40 simulated the fluid flow between the fuel plates but was not able to model plate deflections. Kennedy24 used two separate codes, one for solving the fluid domain and the other one for solving the structural domain. Their approach utilizes a time-dependent solver for each code to complete the runs. The loose coupling of the physics resulted in an unstable solution process. In the present work, a fully coupled (monolithic) approach that eliminates the stability issues inherent in loosely coupled models is used.41 To the best of our knowledge, this is the first study reported in the literature that models FSI phenomenon in high aspect ratio channels (such as those seen in HFIR) using a high-fidelity monolithic approach. Furthermore, this work provides the first known high-fidelity numerical results of monolithic FSI simulations including more than two plates of Smissaert’s five-plate experiment. Multiplate simulations provide information of the interaction between adjacent plates that single-plate simulations would not provide. In his experimental description, Smissaert describes the nominal plate thickness to be 0.0625 in. while he presents a table in the same work which lists the thickness as 0.058 in. 0.002. The bounds for the plate thickness suggest that this is the as-built thickness and 0.058 is used in the simulations presented in this work. The material properties of the plates are presented in Table I. III. COMPUTATIONAL MODEL The computational domain consists of the five PVC plates, spaced evenly apart at 0.250 in. and held fixed along their length. The FSI computations were performed using the commercial code COMSOL (Ref. 6). This code uses the finite element method to discretize the governing equations. The working fluid is water modeled by the incompressible Reynolds-Averaged Navier-Stokes equations: Ñ uf ¼ 0 II. SMISSAERT’S EXPERIMENTAL SETUP Duf ¼ ρf g Ñp þ μÑ2 uf ; Dt ð3Þ where uf = velocity of the fluid ρf = density of the fluid g = gravity p = pressure in the fluid μ = viscosity of the fluid. Consistent with Smissaert’s experiment, the inlet velocity is set to 3.087 m/s which gives a Reynolds number of 37 141 where the length scale is the hydraulic diameter of the channel between plates. Therefore, the flow is treated as turbulent and a modified k-ε turbulence TABLE I Properties of the PVC Plate Used by Smissaert in His Experiment Property English Values Metric Values Width Thickness Length Modulus of elasticity Poisson’s ratio Density 4.500 in. 0.058 ± 0.002 in. 45.000 in. 4.8 × 105 lbf/in.2 0.25 90.4 lbm/ft3 0.1143 m 1.473 ± 0.051 mm 1.143 m 3.310 × 109 Pa 0.25 1448.1 kg/m3 NUCLEAR SCIENCE AND ENGINEERING · VOLUME 00 · XXXX 2017 ð2Þ and ρf In order to validate the COMSOL code for use in the analysis of the LEU fuel conversion for the HFIR, a classical experiment designed by Smissaert22 was modeled. Smissaert performed a sequence of experiments utilizing a series of flat plates constructed from polyvinyl chloride (PVC) plastic in configurations of five, seven, and nine plates. Smissaert’s plates were 0.0625 in. thick, 4.5 in. wide, and 45 in. long. The plates were spaced evenly with channel thicknesses of 0.250 in. and the channels above and below the last plates were the same thickness. For the following simulations, the five-plate configuration was chosen. It must be noted that there is a discrepancy for the plate thickness used by Smissaert. 3 4 CURTIS et al. · LARGE DEFLECTIONS OF MULTIPLATE FUEL ELEMENTS model with wall functions is used.42 Table II provides the constants used for the turbulence model. The structural dynamics of the PVC plates is modeled using the following linear elastic model: ρs @ 2 us ¼ Ñ σ þ Fs @t2 ð4Þ where ρs = density of the plate Downloaded by [University of Missouri-Columbia] at 03:01 27 October 2017 us = displacement of the plate σ = strain Fs = external body forces on the plate. The boundary condition at the fluid-structure interface couples the work done on the structure by the fluid viscous and pressure terms and the work done on the fluid by the structure by feeding the wall velocity back into the fluid. The fluid solution and structural mechanics are coupled using a monolithic or fully coupled approach. This approach incorporates both fluid and structural domains in the same matrix, including all appropriate boundary conditions. In order to avoid inverted meshes from the large deflections, Winslow mesh smoothing43 is TABLE II Constants Used for the k-ε Turbulence Model for This Study Constant Value Cμ Cε1 Cε2 σk σε 0.09 1.44 1.92 1.0 1.3 employed. Initially, a steady-state solution technique was used but proved to be unstable for the large deflections of the plates. A transient flow solver was used to obtain a steady-state solution which is a very common solution technique for very stiff problems. The use of a monolithic approach has proven to be very stable compared to other segregated approaches.44 The computational analysis of this experiment went through several iterations in order to determine the most appropriate approach to capture the physics of the setup. Initially, a one-plate simulation was proposed and explored various fluid boundary conditions above and below a single plate in order to replicate the five-plate experiment (Fig. 1); the boundary conditions at the half- and full-domain boundaries included periodic, symmetric, and no-slip wall conditions. IV. ONE-PLATE MODEL The one-plate model was intended to reduce the computational complexity and cost of the simulations. Because only one plate was being simulated, the boundary conditions for the fluid domain played an important role in the deflection of the plate. The periodic nature of the plates prompted the use of periodic boundary conditions above and below the plate. The 3-D domain consisted of the single plate with half a channel 0.125 in. above and below the plate. Smissaert did not provide the entrance and exit lengths of his experimental setup and an initial 2-D simulation was performed to determine suitable lengths. The inlet and outlet length was determined by comparing the pressure drop of a 2-D simulation without moving plates. It was found that 10 in. upstream and downstream of the plates provided good agreement with the experiment as shown in Fig. 2. This simulation was also used to determine the appropriate mesh needed Fig. 1. Domain for the simulation of a single plate with various fluid boundary conditions. NUCLEAR SCIENCE AND ENGINEERING · VOLUME 00 · XXXX 2017 Downloaded by [University of Missouri-Columbia] at 03:01 27 October 2017 LARGE DEFLECTIONS OF MULTIPLATE FUEL ELEMENTS · CURTIS et al. 5 Fig. 2. Pressure drop for 2-D simulation to determine the appropriate inlet and outlet lengths. around the plates in order to properly capture the fluid solution and to satisfy the wall offset requirements for the k-ε turbulence model. The meshes in Fig. 2 contained the following number of elements: 1. Mesh 1: 30 000 elements Fig. 3 for increasing mesh densities with the final mesh consisting of 300 388 mesh elements. Three meshes were utilized to obtain the results: 1. Mesh 1: 103 136 elements (free mesh with BL elements used to obtain initial conditions) 2. Mesh 2: 31 648 elements (BL elements around plate) 2. Mesh 2: 150 144 elements (mapped mesh) 3. Mesh 3: 55 476 elements (BL elements around plate and along walls) The simulations utilized the PARDISO direct solver and a monolithic or fully coupled approach. This highly stable method allowed the solver to capture the large deflections at the leading edge of the plates. Other methods including segregated solvers (solving for the fluid domain separately from the structural domain) and iterative methods were explored but no converged results were obtained. Another approach employed wall boundary conditions along the top and bottom boundaries of the domain. This approach also required plate offset to induce deflections. For this case, both the full channel and a half channel were used above and below the plate in order to determine which approach was appropriate. The halfchannel simulation was created by reducing the channel thickness from the nominal 250 to 125 mil. The meshes used for the symmetry boundary conditions were utilized again for these cases. As can be seen in Fig. 4, the fullchannel simulations resulted in deflections much smaller than those predicted by Smissaert and the half-channel simulations provided leading-edge deflections much closer to those predicted in the experiments. 4. Mesh 4: 125 012 elements (refinement of mesh 3) 5. Mesh 5: 220 194 elements (refinement of mesh 4). Using the half-channel domain presented in Fig. 1, periodic boundary conditions were used for the fluid domain. These simulations were unsuccessful and resulted in unstable solutions with no observed deflections of the plates. The next logical step was to impose symmetric boundary conditions on the fluid domain above and below the plate. The symmetric boundary conditions again resulted in an unstable solution. In order to produce deflections, the entire plate was off set by a small amount (1 to 5 mil) creating different sized channels on the bottom and top of the plate (this approach was also attempted with the periodic boundary, again with no success). The offset was inspired by Kane27 who describes how inlet deviations affect the deflections of flat plates. A small displacement of 2.5 mil provided enough perturbation to allow deflections to occur. The deflection along the centerline of the plate is provided in NUCLEAR SCIENCE AND ENGINEERING · VOLUME 00 · XXXX 2017 3. Mesh 3: 300 388 elements (refinement of mesh 2). Downloaded by [University of Missouri-Columbia] at 03:01 27 October 2017 6 CURTIS et al. · LARGE DEFLECTIONS OF MULTIPLATE FUEL ELEMENTS Fig. 3. Deflection for a one-plate calculation with an offset of 2.5 mil and symmetry boundary conditions. Fig. 4. Deflection for a one-plate calculation with an offset of 2.5 mil and wall boundary conditions. Although the single-plate approach shows reasonable agreement with the leading-edge deflections of the experiment, it is desired to understand the effect of modeling multiple plates. Therefore, a full five-plate simulation was performed next. V. FIVE-PLATE MODEL The five-plate simulation was constructed to model the Smissaert experiment as described in the paper. All five plates were included utilizing the linear structural model with fixed edges along both sides of each plate. The side walls and top and bottom walls were modeled as fixed wall boundaries with entrance and exit lengths of 10 in. The simulation was performed using a series of increasing mesh sizes to ensure grid convergence and the final mesh consisted of 815 680 mesh elements. The final mesh around the leading edge of one of the plates is provided in Fig. 5. The final mesh was also checked to satisfy the wall distance requirements for the k-ε turbulence model. The initial condition for the course mesh transient solution was NUCLEAR SCIENCE AND ENGINEERING · VOLUME 00 · XXXX 2017 Downloaded by [University of Missouri-Columbia] at 03:01 27 October 2017 LARGE DEFLECTIONS OF MULTIPLATE FUEL ELEMENTS · CURTIS et al. 7 Fig. 5. The mesh around the leading edge of one of the plates used for the final mesh simulation with 815 680 total mesh elements. taken from a steady-state solution of the flow variables. The simulations were performed on an eight node cluster with 12 cores per node and Table III provides the run times for each mesh. As with the single-plate simulations, a monolithic approach with a direct solver was utilized. For the five-plate simulations, the use of initial plate deviations was not needed and all of the flow channels were taken as 0.250 in. thick. The plate deflections were induced by the nonmoving walls at the top and the bottom of the computational domain. The total deflections for each plate are provided in Fig. 6. According to Groninger and Kane,21 adjacent plates always deflect in opposite directions and the three middle plates, plates 2, 3, and 4, follow this trend. The top and bottom plate, plates 1 and 5 respectively, do not seem to follow this trend because of their interactions with the nonmoving top and bottom walls. Comparison of the deflections of the plates with the experiment is provided in Fig. 7 and shows good agreement with the leading-edge deflections. Plate 3, the middle plate, matches well with the large leading-edge deflection provided by Smissaert. In his paper, Smissaert also provided three deflection points for a plate adjacent to the middle plate, either plate 2 or 4, and this is also provided in Fig. 7. The leading-edge deflection of plate 2 of the simulation again matches quite well with the reported deflection of one of the plates adjacent to the middle plate. Smissaert embedded strain gauges in the plastic plates in order to determine the deflections along the plates. It is unclear how the gauges and subsequent wiring affects the flow field in the experiments as well as the structural integrity of the plates. This may account for the less accurate capturing of the plate deflections downstream from the leading edges. Figure 8 provides visualization of the flow redistribution around the leading edge of the deflected plates. The flow and pressure fields of Figs. 8 and 9 demonstrate there is a significant difference in flow speed and pressure between adjacent plates. The results presented in this work show that the TABLE III Run Times for Each Subsequent Mesh Performed on Mintaka at ORNL for the Simulation of the Smissaert Experiment* Number of Elements 89 89 115 815 Degrees of Freedom 080 080 640 680 573 573 1 060 8 712 048 048 635 387 Physical Time (s) Wall-Clock Time (s) Time Steps Steady state 5.0 0.01 0.168 1 096 53 831 38 945 2 246 400 (26 days) Steady state 140 108 220 *8 nodes, 12 cores per node. NUCLEAR SCIENCE AND ENGINEERING · VOLUME 00 · XXXX 2017 Downloaded by [University of Missouri-Columbia] at 03:01 27 October 2017 8 CURTIS et al. · LARGE DEFLECTIONS OF MULTIPLATE FUEL ELEMENTS Fig. 6. Deflection of each plate in units of mil. For visualization, the distance between each plate has been increased from 250 to 400 mil and the deflection is exaggerated by 25 times. Fig. 7. Deflection along the centerline of the plates compared to the experimental deflections. deflections at the leading edge of the plates play a role in the pressure drop and redistribution of flow between the plates. The area reduction can be calculated from these simulations and is presented in Table IV. The changes in area for the Smissaert cases are quite large; however, for HFIR this should not be the case because the HIFR plates are stiffer because they are curved and made of aluminum. An accurate prediction of flow reduction can be used to better predict the performance of the thermal hydraulics of the reactor during its operation. Ultimately, our goal is to couple this solution with a thermal-hydraulic solution (fluid-structure-thermal interaction) for the HFIR core. VI. CONCLUSION Simulations of FSI problems with large deflections require special computational considerations in order to NUCLEAR SCIENCE AND ENGINEERING · VOLUME 00 · XXXX 2017 Downloaded by [University of Missouri-Columbia] at 03:01 27 October 2017 LARGE DEFLECTIONS OF MULTIPLATE FUEL ELEMENTS · CURTIS et al. 9 Fig. 8. 2-D cut plane of the velocity (m/s) along the midplane of the plates at the leading edge of the plates. The inlet is 10 in. from the leading edge of the plate. Fig. 9. 2-D cut plane of the pressure (Pa) along the midplane of the plates at the leading edge of the plates. The inlet is 10 in. from the leading edge of the plate. obtain accurate solutions. For small deflections, the fluid and structure are usually loosely coupled but as the deflections grow due to higher flow rates, the interaction between the fluid and structure becomes more important. Because of this, a monolithic approach is required that solves the fluid and structural mechanics in a fully coupled fashion.44 Although this is computationally expensive, the benefits NUCLEAR SCIENCE AND ENGINEERING · VOLUME 00 · XXXX 2017 of capturing the flow field and plate deflections justifies this cost. As clusters and larger workstations become more available, this issue becomes less of a hindrance. This validation case gives confidence that this approach will provide reasonable results for future analysis of the HFIR core and by coupling the solution with the heat transfer, a better idea of the core physics can be achieved. 10 CURTIS et al. · LARGE DEFLECTIONS OF MULTIPLATE FUEL ELEMENTS Changes in Flow Area for Each Channel of the Five-Plate Simulation* 6. COMSOL, COMSOL Multiphysics® Version 5.2, COMSOL AB, Stockholm, Sweden (2016); www.comsol. com (current as of June 26, 2017). 7. L. TSCHAEPE et al., “Evaluation of HFIR LEU Fuel Using the COMSOL Multiphysics Platform,” ORNL/TM2008/188, Oak Ridge National Laboratory (2008). TABLE IV Channel New Area (in.2 ) Percent Change in Area 1 2 3 4 5 6 1.0400 1.1775 1.2878 0.8536 1.3936 0.9974 −7.5600 4.6682 14.4736 −24.1211 23.8795 −11.3402 Downloaded by [University of Missouri-Columbia] at 03:01 27 October 2017 *Channel 1 is below plate 1. Acknowledgments This manuscript has been authored by UT-Battelle, LLC under contract DE-AC05-00OR22725 with the U.S. DOE. The U.S. Government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for U.S. Government purposes. The DOE 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). ORCID Franklin G. Curtis http://orcid.org/0000-0002-51381259 Kivanc Ekici http://orcid.org/0000-0001-8839-5374 References 1. HFIR website, “The High Flux Isotope Reactor at Oak Ridge National Laboratory,” Neutron Sciences; http://neutrons.ornl. gov/facilities/HFIR/history/ (current as of June 26, 2017). 2. GTRI website, “Global Threat Reduction Initiative,” National Nuclear Security Administration; http://nnsa.energy.gov/abou tus/ourprograms/dnn/gtri (current as of June 26, 2017). 3. ORNL TEAM, “High Flux Isotope Reactor Safety Analysis Report,” ORNL/HFIR/SAR/2344, Oak Ridge National Laboratory (2013). 4. H. A. McLAIN, “HFIR Fuel Element Steady State Heat Transfer Analysis: Revised Version,” ORNL/TM/1904, Oak Ridge National Laboratory (1967). 5. D. G. MORRIS and M. W. 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