FINITE ELEMENT ANALYSIS OF AN EMPTY 37-ELEMENT CANDU® FUEL BUNDLE TO STUDY THE EFFECTS OF PRESSURE TUBE CREEP
Abstract
CANDU fuel bundles experience plastic deformations over time, and the horizontal configuration of the bundle in a crept pressure tube (PT) causes coolant to bypass the sagged lower half of the bundle. Bundle segments where the flow is limited may become more susceptible to dryout due to reactor aging. A finite element model of a 37-element fuel bundle was constructed using the commercial finite element software ANSYS to study the mechanical deformation behaviour of the bundle to maintain a coolable geometry. The main focus was on the contact between the fuel elements and between the fuel elements and PT. The complexity of the model due to all the contact pairs necessitated the use of high-powered computing hardware. Contact was demonstrated between the appendages, and sensitivity of the deformation to different boundary conditions (BC) was investigated. In particular, the radial position where the elements were welded to the endplate significantly impacted the magnitude of the element bowing. Expanding the PT up to 8% diametral creep demonstrated the proper functioning of the spacer pads (SP) and bearing pads in preventing sheath-to-sheath contact at the midplane and sheath-to-PT contact. However, the quarter plane was deemed to be the critical region due to the lack of SPs preventing excessive element bowing. This work has successfully illustrated the deformation of a CANDU fuel bundle, with contact, and its similarity with the bow profiles when compared with post-irradiation examination results and bundle heat-up tests.
Résumé
Les grappes de combustible des réacteurs CANDU subissent des déformations plastiques au fil du temps, et la configuration horizontale de la grappe dans un tube de force (TF) déformé amène le liquide de refroidissement à contourner la moitié inférieure affaissée de la grappe. Les segments de grappe où l’écoulement est limité peuvent devenir plus exposés que les autres à l’assèchement entraîné par le vieillissement du réacteur. Un modèle d’éléments finis d’une grappe de combustible à 37 éléments a été réalisé à l’aide du logiciel commercial d’éléments finis ANSYS pour étudier le comportement de déformation mécanique de la grappe afin de maintenir une géométrie qui peut être refroidie. L’accent a été mis sur le contact entre les éléments de combustible et entre les éléments de combustible et le TF. En raison de la complexité du modèle associée au grand nombre de paires de contacts, il a été nécessaire d’utiliser un matériel informatique de haute puissance. L’existence d’un contact a été démontrée entre les appendices et la sensibilité de la déformation aux conditions aux limites (CL) a été étudiée. En particulier, la position radiale dans laquelle les éléments ont été soudés à la plaque d’extrémité a influencé considérablement l’ampleur de la cambrure de l’élément. En présence d’une expansion du TF pouvant atteindre 8 % du fluage diamétral, il a été montré que les coussins d’espacement (CE) et les patins supports permettaient d’empêcher le contact entre les gaines au niveau du plan médian et le contact entre la gaine et le TF. Cependant, il a été déterminé que le quart de plan était la région critique en raison du manque de CE pour empêcher la flexion excessive des éléments. Ces travaux ont permis de montrer la déformation d’une grappe de combustible CANDU, avec contact, et sa similitude avec les profils de cambrure dans le cadre d’une comparaison avec les résultats de l’examen réalisé après l’irradiation et les essais d’échauffement des grappes.
1. Introduction
Over the lifetime of a CANDU reactor, the pressure tubes (PT) are affected by creep deformation and sag due to their horizontal configuration. Such creep deformation occurs over a long duration due to persistent loads, such as those caused by coolant pressure, temperature, and irradiation. The PT creep results in the increase of the diameter, length, and sag of the PT. In fact, the PT can creep up to 6% of its original diameter [1]. These combined effects increase coolant flow over the top of the fuel bundles as they sit horizontally inside the PT. Such flow bypass reduces the coolant flow through bundle sub-channels, resulting in reduced cooling of the fuel elements. The phenomena of bypass flow and components of a single bundle are labelled in Figure 1.
Figure 1.
The elements in the bundle itself can also sag due to the high temperatures, irradiation, and gravity-induced creep. This deformation further contributes to the potential lack of cooling and bypass flow because the coolant flow through the sub-channels is constricted. This leads to less heat transfer between the coolant and fuel elements and creates areas of high temperatures in the elements. With less and less coolant contacting the fuel elements, local hot spots could occur whereby the sheaths may rupture and release radioactive substances into the primary loop [2]. Thus, the effects of aging are of interest for CANDU power generation stations.
The Canadian Nuclear Safety Commission provides trip guidelines to ensure the safety of operation for the public and the environment. These guidelines include fuel element cladding temperatures surpassing 600 °C and post-dry-out operations passing 60 seconds in duration [3]. Furthermore, each power plant has their own critical values of PT diametral creep ranging from 4% to 6% [4].
2. Past Efforts
Though deformation and fluid flow analysis have been performed with both physical experimentation and numerical modelling, little work has been done on investigating the combined effect that mechanical behaviour and PT creep has on bundle deformation and coolant flow. Fuel codes have been developed to study uniaxial and 2-dimensional (2-D) fuel element behaviour under different conditions; however, fuel codes were unable to capture the 3-D behaviour of a full bundle. Structural analysis of the partial and full CANDU and CANFLEX bundles have been explored [5], and the PT deflections due to creep have been studied by Atomic Energy of Canada Limited [6], but these models consist of limited contact. Table 1 summarizes different modelling efforts and approaches for the CANDU fuel for the deformations. Fuel elements that are represented as 3-D geometry do not consider the entire bundle, while full bundle models only consider the fuel elements as 1-D representations. Regarding fluid flow, both computational fluid dynamics and experimental work were performed on a nondeformed fuel bundle and on a crept and un-crept PT to study the effects of single and 2-phase flow [7]. However, little information is available for full bundle mechanical deformation modeling with contact and PT diametral creep, and analyses on mechanical and fluid coupling.
Table 1.
In addition to simulations, bundle heat up tests and post-irradiation examination (PIE) have been conducted to study new profiling techniques, observe bundle deformation, and measure bundle sag for different bundle test cases. The first studies were undertaken by Dennier et al. [8] on bundles from both out-reactor and in-reactor tests at Sheridan Park Engineering Laboratories (SPEL) and Whiteshell Laboratories. Out-reactor observations were performed using a Coordinate Measuring Machine on 16 bundles after a 40-day, zero power endurance test from Darlington unit 3. The first observation recorded from the tests were that the lower elements adjacent to the PT were found to display an “S” style deflection profile, and inward and outward bowing as seen in Figure 2. Elements in the bundle are labeled in the same manner as in Figure 3. Dennier et al. [8] also found agreement between out-reactor tested and irradiated samples.
Figure 2.
Figure 3.
PIE studies were also performed to determine how fuel performance is affected by CANLUB, which is a graphite layer on the internal sheath surface. Two CANDU-6 bundles were specially made and included select elements without the inner CANLUB coating. The bundles were then irradiated at Point Lepreau station in channels K08 and M15 achieving bundle-average burn ups of 199–202 MWh/kgU and linear powers of 47–48 kW/m for the outer elements [9]. The radial bowing of the outer elements was studied for both channels and is shown in Figure 4. The 2 outlines show both channel locations and the outer element profiles. The 2 bundles generally share the same deformation profile, as the lower and side outer elements bow outwards to fit the contours of the PT.
Figure 4.
3. Objectives
The objectives of the research were to develop a finite element model of a complete 37-element CANDU fuel bundle and to study the effects of PT diametral creep on the deformation response of the bundle. Because of the difficulty in mimicking exact reactor conditions, the intent was not to predict the exact deformed shape of the bundle due to in-reactor conditions. The goal was to represent the same overall deformed shape of the fuel elements based on limited PIE and bundle heat-up experiments. This research is a continued effort that builds upon Soni’s [10] work on validating a partial 37-element bundle model with an out-reactor experiment. Consequently, the current work uses the same material properties and the same assumption of empty elements (pellets are not included) as in Soni’s work.
The research was separated into 2 parts. The first step was to develop the full 37-element bundle model based on sensitivity studies of boundary conditions and loads on the entire bundle. This model was then used to simulate the interactions between a deformed bundle and a crept PT with increased PT diameters of 0%, 2%, 4%, 6%, and 8%. Only the diametral creep of the PT was considered rather than PT sag or axial elongation. The midplane and quarter planes of the bundle were studied to determine the effects of PT diametral creep on bundle deformation.
Creating a model that could predict the deformation of a bundle would be extremely complex and would need to consider such aspects as thermal hydraulics, neutronics, and mechanical deformation. The purpose of the current model was to focus on the mechanical aspects of bundle deformation and to capture the mechanical interactions occurring between the surfaces of the fuel elements and the PT as well as the constraints provided by the connection between the fuel elements and the end plates. Since the focus was on mechanical interactions, force and temperature loading was assumed rather than being predicted using coupled simulations, and creep was not explicitly simulated, although its effects on deformation were included. Aforementioned PIE and bundle heat-up tests showed that fuel elements deformed into an “S” shape under normal operating conditions. Preliminary studies using a single fuel element showed that this “S” shape could be predicted for an empty fuel bundle with a constant temperature profile, and applied forces to qualitatively represent the effects of creep rather than applying thermal creep for the entire residence time [11]. PIE tests also show that the lower side elements sag outwards to fit the contours of the PT, whereas the upper half elements sag downwards. These are the qualitative benchmarks that the full bundle was compared with in the absence of a dedicated experimental test.
To further simplify the model, UO2 fuel pellets were omitted as well as heat generation from within the elements. The pellets were not required for obtaining the deformed shape of the fuel elements because this was achieved through careful consideration of the loading and boundary conditions within the model. Fuel parameters such as power ratings, burnups, or fission gas releases were not considered as well.
4. Model Development
The following sections detail the modelling approach, mesh, contact, material properties, and loads and boundary conditions for the full-bundle finite-element model. ANSYS was used for this study because of its multi-physics capabilities, compatibility with High Powered Computing (HPC) hardware and software, user-friendly graphic–user interface, and its robust contact definition package.
4.1. Modelling approach
The bundle design follows the Bruce Power and Darlington generating stations, whereas while the bundle geometry was the same as that used experimentally by CNL and Soni [10]. This design includes 3 planes of spacer pads (SP) and a staggered configuration of the bearing pads (BP) resulting in 5 planes of BP. The purpose of the model is to represent the deformed shape of a bundle including the interactions between the SPs and the BPs to the PT. This was achieved through the use of specific loading and boundary conditions as well as contact definitions. The orientation of the test geometry is such that the bundle sits on the PT with BPs of rods 9 and 10 at 260° and 280° when viewing the bundle axially.
To simplify the model, UO2 fuel pellets were omitted as well as heat generation from within the sheaths. Krasnaj [12] determined that a monolithic stack representation of the pellets resulted in stiffness only slightly higher than an empty sheath. Different pellet models result in a wide range of stiffness values, and lack of experimental studies on rigidity makes pinpointing the exact pellet representation difficult. The current research was only concerned with the qualitative radial deflections of the sheaths to match with experimental data. Irradiation creep and its effects on material properties were not considered and the temperature from the pellet heat generation was assumed as a sheath surface thermal load. Removing pellet-to-sheath and pellet-to-pellet contact definitions also allowed for a simplification of the sheath geometry and reduction in computing hardware. Other avenues of increasing the stiffness, such as increasing the Young’s modulus of the sheath or including the pellet as a single beam element were explored, but the deformed shape of the fuel elements was achieved through careful consideration of the loading and boundary conditions within the model rather than through explicit modelling of the pellets.
The elements, endplates, and PT were simplified to planar geometries as the thin walls relative to the length and diameter of the sheath and PT allowed for 3-D shell elements to be assigned rather than 3-D solids. All other components, including the appendages, endcaps, and endplates, were maintained as solid bodies. The PT was assumed to be a rigid surface, and the diameter was expanded to 2%, 4%, 6%, and 8% of its nominal diameter to represent PT diametral creep. The SPs are not in-line, but instead, the SP pairs are configured in an “X” formation to mitigate sheath-to-sheath contact. Because of this “X” configuration and endplate design, symmetry along any geometric plane was not possible.
The analysis was assumed to be static and steady state as the loading was not time dependent, and no inertial effects or creep were included. The high degree of nonlinearity due to the multiple contact definitions and the large number of nodes necessitated HPC hardware and software that were acquired from CMC Microsystems. The models were run on a CentOS 7 Linux operating system with an Intel Xenon CPU with 16 cores running at 2.60 GHz and 125 GB of memory.
4.2. Mesh
A total of 126 contact pairs assigned between the SPs, and between the BPs and the PT, necessitated a careful mesh selection to decrease the node count and to ensure solution convergence. The planar geometry of the elements, PT, and endplates were meshed with 4-sided linear elements. The solid endcaps were meshed with tetrahedral elements and the solid spacers and BPs were meshed with hexahedral elements. Smaller elements were used in contact regions, such as for the SPs and the BPs, to aid in solution convergence. Larger elements were used for the bulk of elements and the PT to reduce the node count and the computational demands.
The sheath mesh size was determined from a mesh convergence study performed on a single element without any appendages, end components, or PT. A temperature load of 320 °C and the pellet weight as a vertical load were applied, and the element ends were axially constrained. The sheath mesh size was varied from 1 mm to 7 mm, and the displacements of the element are plotted against the node count as shown in Figure 5. Displacements were determined to be insensitive to the mesh size when a mesh size smaller than 2 mm, or at least 4880 nodes was used for the single element. This mesh was applied to the full bundle model resulting in a final node count of 958 501.
Figure 5.
4.3. Contact
A total of 82 frictional contact pairs were defined resulting in 78 pairs between the pairs of SPs and 4 pairs between the lowest 4 outer BPs and the PT. There are 18 SP pairs in the outer ring, 24 SP pairs between the outer and middle ring, 12 SP pairs within the middle ring, 12 SP pairs between the middle and inner ring, and 6 pairs between the inner ring and centre element. A coefficient of friction of 0.1 was used which is the same used by Atomic Energy of Canada Limited for their modeling of the CANFLEX bundle with BPs made from Zircaloy-4 material [13]. Forty-two frictionless contact pairs were assigned for the remainder of the BP to PT contact.
An additional 360 bonded contact pairs were defined between: the sheath and the endcap, the endcap and the endplate, the lowest 2 centre BPs to PT, SPs to sheaths, and BPs to sheaths. Two of the middle BPs at the bottom of the bundle were bonded to the PT because of the assumption that the bundle sits on the PT throughout the analysis. The outer BPs on the lowest 2 elements were defined as frictional contact. Only bonding the centre BPs while assigning the outer BPs as frictional still allowed the bundle to lengthen. Contact was not expected to occur between the 4 BPs at the top of the bundle and the PT; therefore, contact was not prescribed in this region to simplify the model and reduce the runtime.
4.4. Material properties
A value of 91.3 GPa for Young’s modulus, Poisson’s ratio of 0.2, and a coefficient of thermal expansion of 0.000006721 °C−1 were used [14]. These values from MATPRO [14] for the Zircaloy-4 (Zr-4), were the same as those used in Soni’s validated bundle model [10].
Several assumptions were made for the material properties to simplify the analysis. First, the Zircaloy-4 properties were assumed to be isotropic. Next, despite the PT’s material being a Zirconium alloy with 2.5% Niobium, the PT was also assigned as Zircaloy-4 because it only acted as a structural support. Finally, the temperature used for this model is lower than the alpha-beta transition that occurs at around 800 °C; therefore, only the alpha grain structure was considered in the model.
4.5. Loads and boundary conditions
A sensitivity analysis was conducted for the loads and boundary conditions based on the experimental data seen in Figures 2 and 4. The aim of the studies was to determine the most appropriate endplate constraint and load combination required to obtain the inward and outward deflection shape seen in Figure 2 and the element sag shown in Figure 4.
For all models, the PT was modelled as a rigid surface with fixed boundary conditions. Rigid body motion of the bundle was prevented, as the center BPs of the lowest 2 elements were bonded to the PT. Gravity was applied to all components of the bundle. A constant temperature of 320 °C was applied to the sheaths, which is slightly above normal operating conditions and below the accidental conditions and the Zr-4 grain boundary transition. A pellet weight of 6.1 N was applied to each rod. The weight was calculated from the pellet stack volume and the density of ceramic uranium dioxide without consideration for buoyant forces from the coolant.
4.5.1. Boundary conditions
In the reactor, the bundles are placed end to end and when irradiated, they can sag, axially elongate, and contact adjacent bundles. In addition, dishing and rotation of the end plates and bundle “parallelogramming” can occur due to the PT sag, deformation, and hydraulic load from the coolant. In the simulation, axially fixing each endplate face to represent contact with the adjacent bundles was too restrictive and resulted in unrealistic deformations. To relieve some of the thermal stress buildup while still preserving the same overall constraints, different radial webs on the endplates were fixed axially as seen in Table 2. This allowed the elements’ endcaps to deform locally. The boundary conditions were only applied to webs with no connected endcaps, as this allowed for minimal interference with how the elements would deform. These 6 test cases were considered to simulate the endplates’ tilting to determine the effect of web constraint and to provide a balance between axial constraint and the ability of the bundle to elongate.
Table 2.
4.5.2. Loading conditions
Determining the appropriate vertical load such that the side elements bow outwards to fit the PT contours was the goal of the load sensitivity analysis. Given the complexity of the bundle operating environment, irradiation effects, pellet heat generation, and fission gas release considerations were neglected. Rather, gravitational loading and an applied temperature were included. Creep is the main driver for the downward sag of the bundle but running the model for a bundle lifetime was unrealistic due to computational constraints. This could be achieved simply by applying a distributed force on the elements rather than simulating creep. Vertical downward forces of the pellet weight, 60 N, 120 N, and 240 N were distributed over the elements. Increasing the thermal load was not considered because the goal was a downward sag rather than a uniform radial expansion. The effects of the applied vertical loads can be estimated to be greater than the pellet weight because of the sag due to creep.
5. Results
The interaction and deformed shape of the elements were examined for the boundary conditions (BC) and load sensitivity analyses. The BC and loading that produced the most realistic bundle deformation were then used to study the effects of diametral creep on bundle deformation.
Overall, as the bundle was loaded, the elements displaced downwards, and the SPs came into contact causing the elements to stack on top of each other. Thermal expansion caused the elements to elongate and expand radially. Due to the axial constraint, thermal compressive stresses were relieved radially and caused bowing of the elements.
5.1. Boundary condition: sensitivity analysis on endplate radial web constraint
The different BC test cases from Table 2 were explored with the goal of matching the experimental results in terms of the overall sag, especially for the upper half and outer side elements, and the inward/outward bowing profile of the lowest elements. Table 3 presents axial and side views of the vertical deflections for the 6 different web constraint configurations.
Table 3.
The location, shape, and magnitude of the element bowing is highly dependent on the amount of constraint, the location of the constraints, and how close the elements are to the constrained web. Boundary conditions that are more constraining resulted in more bowing, such as case 1 and 2 where the outer elements bow outwards more than the other test cases, specifically elements 16, 17, 18, and 29.
Elements closest to the stiffer web intersections experience more bowing than elements connected to the middle of the webs. This observation is consistent with out-reactor tests done at SPEL and analysis by Whiteshell Laboratories [8]. Consequently, the radial location on the endplate where the elements are connected becomes a significant factor in element bowing. When both endplates had either the outer or inner webs fixed, the outer elements bowed inwards, as opposed to outwards like Figure 4. In all cases, the top elements deformed more than the bottom elements as the bottom elements were in contact with the PT.
When the end plates are allowed to tilt by constraining the bottom and leaving the top free (Case 6) or by constraining the middle and leaving the top and bottom free (Case 4), the top element sags downwards and behaves more realistically. The sensitivity analysis indicated that fixing one end plate while only constraining the lower part of the webs on the other end plate (Case 6) produced a deflected shape that was the similar to the PIE and bundle heat-up tests—the lower elements produced the “S” shape and the upper elements sagged downwards to contact the elements below them. In Figure 6a, the deformation was magnified 13× and is similar to the PIE radial view. Figure 6b showed the downward sag of all the elements and even the endplates as it droops down. The remnant of an “S” shape remained in the 2 lowest elements as indicated in Figure 6c. The vertical deflections of element 10 is illustrated in Figure 6d. The endcaps also are drooping due to the endplates, but still displays the inward/outward bowing. Fixing the lower 4 webs provided the most realistic deformation and was selected to study the effects of loads and crept PTs.
Figure 6.
5.2. Load conditions: sensitivity analysis on exaggerated vertical load
Figures 7 and 8 show the vertical deflection of the bundle under vertical downward forces of the pellet weight and 60 N, respectively, and with PT having a nominal diameter and an 8% diametral creep. Exaggerated vertical loads of 120 and 240 N were also considered. Having just the pellet weight was insufficient to cause the side elements to contact the PT as shown in Figure 7. As the forces were increased, the BPs on the lower half of the elements started to come in contact with the PT. The elements stack on top of each other and the downwards force causes the lower elements to displace outwards towards the PT. However, with more PT diametral creep, fewer lower and side elements come into contact with the PT.
Figure 7.
Figure 8.
The greater force of 240 N and larger diameter of 8% creep caused more endplate drooping to the point of having endcap to PT contact, which is not realistic. Sheath-to-sheath contact occurred on the quarter plane with vertical loads of 120 N and 240 N. As a result, 60 N was chosen to obtain the realistic shape of a deformed bundle during normal operating conditions, as seen in Figure 8. The vertical deflection of a bundle with a 60 N force was compared to an undeformed bundle, as indicated in Figure 9. The lower side elements bow outwards and the upper half elements sag downwards similar to the PIE shown in Figure 4.
Figure 9.
5.3. Crept PT bundle deformation comparisons
The 60 N vertical load and the boundary conditions that produced a realistic deformed bundle were implemented for a PT with 0%, 2%, 4%, 6%, and 8% diametral creep for comparison. The axial views of the vertical deflection results of the entire bundle, midplane, and quarter planes at true scale are indicated in Figures 10a–10c for the nominal diameter, 4% and 8% diametral creep.
Figure 10.
As expected, an increase in bypass flow area was observed with increasing PT creep. There were fewer BPs contacting the PT on the sides as the diameter expanded. When observing the midplane, the sub-channels maintained their areas because of the SPs preventing further sag and highlighted the robust design of the SPs.
However, the quarter plane was deemed to be the critical region due to the lack of SPs. In particular, the gap between elements 9 and 24, as indicated in red in Figures 10a–10c were measured and compiled in Figure 11. There is an overall decreasing quadratic trend between increasing the PT diameter and a reduction in the sheath to sheath clearance.
Figure 11.
6. Limitations
A finite element model of a 37-element CANDU fuel bundle was established, along with a better understanding of endplate boundary conditions and PT diametral creep, but this model has limitations:
•
The elements were empty and did not account for the increased stiffness or heat generation from the pellets within the fuel sheath.
•
The current model does not account for other factors as observed in PIE, such as endplate dishing and doming due to ring-to-ring power difference, and bundle parallelogramming.
•
Material considerations with irradiation effects were not included.
•
PT sagging and axial elongation were also not accounted for.
•
Non-uniform fission heating and differing local powers were not included.
However, the model was based on a partial 12-element model developed by Soni [10] with experiments from CNL. Even with the limitations, the paper is the first to illustrate a full 37-element CANDU fuel bundle deformation model including contact and is supported by detailed sensitivity analyses that agree with PIE and bundle heat-up tests. Possible future works include:
- Coupled heat transfer and fluid analysis
- Simulation of full residence time
- Incorporate effects of pellets
7. Conclusion
A finite element model of a 37-element CANDU fuel bundle was constructed to study the effects of PT diametral creep on the bundle deformation. It was shown that a simplified model that excluded fuel performance considerations such as the UO2 fuel pellets, heat generation, fission gas release, PT sag, PT elongation, creep, and anisotropic material properties could be used to mimic experimental profilometry results from PIE and bundle heat-up tests as long as appropriate boundary conditions and loading were used. It was also necessary to include contact between the SPs and between the BPs and the PT for the fuel elements to interact with each other.
A sensitivity analysis on the boundary conditions showed that the radial location of the connection between the fuel element and the endplate played a significant factor in how the elements would bow within a bundle. Constraining only the lowest 4 webs provided the most suitable deformations similar to experimental tests with the outward bow for the lower and side elements and the downward sag for the upper elements.
An increase in vertical force resulted in a more pronounced element deformation and caused sheath-to-sheath contact at the quarter plane. These same trends are expected as creep increases over time. However, for the current load study, a vertical force was necessary to balance between bundle sagging effects while preventing sheath-to-sheath and endcap-to-PT contact.
When the PT diameter was increased, an increase in bypass flow was expected. However, the sub-channel areas in the midplane remained constant with changing diameters due to the SPs limiting the amount of sag that could occur. The quarter plane was determined to be critical in terms of the risk of reaching dryout with increasing diametral creep, due to the lack of SPs that would prevent sheath to sheath contact.
Acknowledgements
The authors would like to thank the technical support teams from CMC Microsystems and SimuTech, especially Chris Donnelly, Alex Pickard, and Peter Budgell, without whom the research would have been much more difficult. The authors would also like to extend their appreciation towards Defence Research and Development Canada (DRDC), CANDU Owners Group (COG), and Natural Science and Engineering Research Council of Canada (NSERC) for their financial aid in allowing A/S Lt. Lee to pursue his graduate studies.
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CNL Nuclear Review
Volume 10 • Number 1 • January 2021
Pages: 39 - 51
Editor: Frederick Powell Adams
History
Received: 13 May 2020
Accepted: 28 September 2020
Version of record online: 7 May 2021
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KyuhwanLee, DianeWowk, and PaulChan. 2021. FINITE ELEMENT ANALYSIS OF AN EMPTY 37-ELEMENT CANDU® FUEL BUNDLE TO STUDY THE EFFECTS OF PRESSURE TUBE CREEP. CNL Nuclear Review.
10(1): 39-51. https://doi.org/10.12943/CNR.2020.00003
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