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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.
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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: curtisfg@ornl.gov
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
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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.
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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
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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.
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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).
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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
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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.
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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
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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
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*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. WENDEL, “High Flux Isotope
Reactor System RELAP5 Input Model,” ORNL/TM-11647,
Oak Ridge National Laboratory (1993).
8. J. D. FREELS et al., “Two- Dimensional Thermal
Hydraulic Analysis and Benchmark in Support of HFIR
LEU Conversion Using COMSOL,” ORNL/TM- 2010/
018, Oak Ridge National Laboratory (2010).
9. D. G. RENFRO et al., “Low-Enriched Uranium Fuel
Conversion Activities for the High Flux Isotope Reactor,
Annual Report for FY 2011,” ORNL/TM-2011/507, Oak
Ridge National Laboratory (2011).
10. I. T. BODEY, R. V. ARIMILLI, and J. D. FREELS,
“Complex Geometry Creation and Turbulent Conjugate
Heat Transfer Modeling,” 2011 COMSOL Conf., Boston,
Massachusetts, October 13–15, 2011.
11. J. D. FREELS and P. K. JAIN, “Multiphysics Simulations
of the Complex 3D Geometry of the High Flux Isotope
Reactor Fuel Elements Using COMSOL,” 2011 COMSOL
Conf., Boston, Massachusetts, October 13–15, 2011.
12. V. B. KHANE, P. K. JAIN, and J. D. FREELS, “COMSOL
Simulations for Steady State Thermal Hydraulics Analyses
of ORNL’s High Flux Isotope Reactor,” 2012 COMSOL
Conf., Boston, Massachusetts, 2012.
13. V. B. KHANE, P. K. JAIN, and J. D. FREELS,
“Development of CFD Models to Support LEU
Conversion of ORNL’s High Flux Isotope Reactor,” ANS
Winter Mtg., San Diego, California, November 11–15,
2012.
14. A. R. TRAVIS, K. EKICI, and J. D. FREELS, “Simulating
HFIR Core Thermal Hydraulics Using 3D-2D Model
Coupling,” 2013 COMSOL Conf., Boston, Massachusetts,
October 9–11, 2013.
15. D. WANG, P. K. JAIN, and J. D. FREELS, “Application of
COMSOL Pipe Flow Module to Develop a High Flux
Isotope Reactor System Loop Model,” 2013 COMSOL
Conf., Boston, Massachusetts, October 9–11, 2013.
16. A. R. TRAVIS, “Simulating High Flux Isotope Reactor
Core Thermal- Hydraulics Via Interdimensional
Model Coupling,” MS Thesis, University of Tennessee
(2014).
17. P. K. JAIN, J. D. FREELS, and D. H. COOK, “3D
COMSOL Simulations for Thermal Deflection of HFIR
Fuel Plate in the Cheverton-Kelley Experiments,”
ORNL/TM-2012/138, Oak Ridge National Laboratory
(2012).
18. D. CHANDLER, “Spatially-Dependent Reactor Kinetics
and Supporting Physics Validation Studies at the High
Flux Isotope Reactor,” PhD Thesis, University of
Tennessee-Knoxville (2011).
NUCLEAR SCIENCE AND ENGINEERING · VOLUME 00 · XXXX 2017
LARGE DEFLECTIONS OF MULTIPLATE FUEL ELEMENTS · CURTIS et al.
19. W. K. STROMQUIST and O. SISMAN, “High Flux
Reactor Fuel Assemblies Vibration and Water Flow,”
ORNL-50, Oak Ridge National Laboratory (1948).
20. D. R. MILLER, “Critical Flow Velocities for Collapse of
Reactor Parallel-Plate Fuel Assemblies,” KAPL-1954,
Knolls Atomic Power Lab (1960).
21. R. D. GRONINGER and J. J. KANE, “Flow Induced
Deflections of Parallel at Plates,” Nucl. Sci. Eng., 16, 218
(1963); https://doi.org/10.13182/NSE63-A26503.
Downloaded by [University of Missouri-Columbia] at 03:01 27 October 2017
22. G. S. SMISSAERT, “Static and Dynamic Hydroelastic
Instabilities in MTR-Type Fuel Elements Part 1.
Introduction and Experimental Investigation,” Nucl. Eng.
Des., 7, 535 (1968).
23. W. F. SWINSON et al., “Fuel Plate Stability Experiments
and Analysis for the Advanced Neutron Source,” ORNL/
TM-12353, Oak Ridge National Laboratory (1993).
24. J. C. KENNEDY, “Development and Experimental
Benchmarking of Numeric Fluid Structure Interaction
Models for Research Reactor Fuel Analysis,” PhD Thesis,
University of Missouri (2015).
25. M. HO, G. HONG, and A. N. F. MACK, “Experimental
Investigation of Flow-Induced Vibration in a Parallel Plate
Reactor Fuel Assembly,” 15th Australasian Fluid
Mechanics Conf., Sydney, New South Wales, Australia,
December 13–17, 2004, p. 13.
26. E. B. JOHANSSON, “Hydraulic Instability of Reactor
Parallel-Plate Fuel Assemblies,” KAPL-M-EJ-9, General
Electric Company (1959).
27. J. J. KANE, “The Effect of Inlet Spacing Deviations on the
Flow-Induced Deflections of Flat Plates,” Nucl. Sci. Eng.,
15, 305 (1962); https://doi.org/10.13182/NSE63-A26441.
28. R. J. SCAVUZZO, “Hydraulic Instability of Flat ParallelPlate Assemblies,” Nucl. Sci. Eng., 21, 463 (1965); https://
doi.org/10.13182/NSE65-A18790.
29. M. W. WAMBSGANSS, JR., “Second Order Effects as
Related to Critical Coolant Flow Velocities and Reactor
Parallel Plate Fuel Assemblies,” Nucl. Eng. Des., 5, 268 (1967).
30. R. S. WICK, “Hydro-Elastic Behavior of Multiple-Plate
Fuel-Assemblies—I: Pressure Wave Propagation,” J. Nucl.
Energy, 23, 387 (1969).
31. R. S. WICK, “Hydro-Elastic Behavior of Multiple-Plate
Fuel-Assemblies—II: Hydro-Static Divergence,” J. Nucl.
Energy, 23, 7, 407 (1969).
NUCLEAR SCIENCE AND ENGINEERING · VOLUME 00 · XXXX 2017
11
32. Y. T. KIM and H. A. SCARTON, “Flow Induced Bending
of Rectangular Plates,” J. Appl. Mechanics, 44, 207 (1977).
33. H. M. CEKIRGE and E. URAL, “Critical Coolant Flow
Velocities in Reactors Having Parallel Fuel Plates,” Comp.
Math. With Appls., 4, 153 (1978).
34. S. J. PAVONE and H. A. SCARTON, “Laminar Flow
Induced Deflections of Stacked Plates,” Nucl. Eng. Des.,
74, 1, 79 (1983).
35. Y. KERBOUA et al., “Modelling of Plates Subjected to
Flowing Fluid Under Various Boundary Conditions,” Eng.
Appl. Comp. Fluid Mech., 2, 525 (2008).
36. C. GUO and M. PAÏDOUSSIS, “Analysis of Hydroelastic
Instabilities of Rectangular Parallel-Plate Assemblies,”
J. Press. Vessel Technol., 122, 4, 502 (2000).
37. G. KIM and D. DAVIS, “Hydrodynamic Instabilities in
Flat-Plate-Type Fuel Assemblies,” Nucl. Eng. Des., 158,
1, 1 (1995).
38. Z.-D. CUI et al., “Flow- Induced Vibration and Stability of
an Element Model for Parallel-Plate Fuel Assemblies,”
Nucl. Eng. Des., 238, 1629 (2008).
39. S. MICHELIN and S. G. LLEWELLYN SMITH,
“Linear Stability Analysis of Coupled Parallel Flexible
Plates in an Axial Flow,” J. Fluids Struct., 25, 1136
(2009).
40. G. D. ROTH, “CFD Analysis of Pressure Differentials in a
Plate-Type Fuel Assembly,” MS Thesis, Oregon State
University (2012).
41. F. G. CURTIS, K. EKICI, and J. D. FREELS, “FluidStructure Interaction Modeling of High-Aspect Ratio
Nuclear Fuel Plates Using COMSOL,” 2013 COMSOL
Conf., Boston, Massachusetts, October 9–11, 2013.
42. D. KUZMIN, O. MIERKA, and S. TUREK, “On the
Implementation of the k-ε Turbulence Model in
Incompressible Flow Solvers Based on a Finite Element
Discretisation,” Int. J. Comput. Sci. Math., 1, 2, 193
(2007).
43. A. M. WINSLOW, “Numerical Solution of the Quasilinear
Poisson Equation in a Nonuniform Triangle Mesh,”
J. Comput. Phys., 1, 2, 149 (1966).
44. M. HEIL, A. L. HAZEL, and J. BOYLE, “Solvers for
Large-Displacement Fluid-Structure Interaction Problems:
Segregated Versus Monolithic Approaches,” Comp. Mech.,
43, 1, 91 (2008).
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