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PHYSOR 2018: Reactor Physics paving the way towards more efficient systems Cancun, Mexico, April 22-26, 2018

Proceedings of the PHYSOR 2018, Cancun, Mexico

NEUTRONICS MODELING AND SIMULATION OF TEMPERATURE-DEPENDENT EXPERIMENTS PERFORMED AT THE WALTHOUSEN

REACTOR CRITICAL FACILITY (RCF) USING PROTEUS-SN

Matthew D. Eklund1*, Mathieu Dupont1, Peter F. Caracappa1, Wei Ji1, and Vijay Mahadevan2

1Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute, 110 8th St, Troy NY 12180 (*[email protected])

2Argonne National Laboratory, 9700 Cass Ave, Lemont IL 60439

ABSTRACT

The Walthousen Reactor Critical Facility (RCF), owned and operated by Rensselaer Polytechnic Institute (RPI), is a low-power nuclear reactor for performing reactor physics critical experiments. Its open-pool capabilities allow for novel and unique experiments that would not be possible in other high-powered research reactors. As part of the effort to develop critical experiments to validate multiphysics coupling models in the SHARP toolkit, critical experiments need to be modeled and simulated by Proteus-SN, a finite element neutronics solver in SHARP based on discrete ordinates (SN) method. Proteus-SN requires unstructured mesh geometry to model nuclear reactors. In previous work, the RCF reactor has been modeled and simulated in MCNP6 and Serpent 2 based on constructive solid geometry. In current work, RCF pin cell and full-core models in 2D and 3D are constructed based on unstructured mesh geometry. Eigenvalue problems based on these models are simulated in Proteus-SN, using the cross-section data prepared by Serpent 2. Several critical experiments, including reactivity measurements at atmospheric pressure and at varying temperatures, are simulated by MCNP6, Serpent 2 and Proteus-SN. Results are compared with each other to verify Proteus-SN for the modeling and analysis of RCF. In addition, reactivity values predicted by Proteus-SN are compared against the RCF experimental values for model validation.

KEYWORDS: Proteus, RCF, Neutronics, Reactor Physics, Reactor Experiment Validation

1. INTRODUCTION 1.1. Research Background and Motivation The design and monitoring of in situ nuclear reactor experiments are undeniably valuable for the nuclear engineering community. The measured and carefully-processed data from these experiments have formed the basis for developing and designing more advanced nuclear power systems since the beginning of the atomic age. As nuclear reactor designs have become more complicated and advanced, particularly with the Generation IV reactor developments, there is a co-requisite for developing higher fidelity modeling and simulations toolkits. In particular, developing the computational capacity to accurately capture the interaction of the multiple physics within a nuclear reactor is vital for predicting reactors’ behaviors in

Eklund et al., Neutronics Modeling and Simulation of Temperature-Dependent Experiments Performed at the Walthousen Reactor Critical Facility (RCF) Using Proteus-SN


any situation. The available benchmark datasets for these types of multiphysics experiments is lacking, however, in the current literature, signifying the immediate need of more multiphysics experiments. This work is part of a Department of Energy project with the goal of designing and performing critical reactor experiments to validate computational modeling and simulation toolkits utilizing the Walthousen Reactor Critical Facility (RCF), a low-power research reactor [1] that is further detailed in the following subsection. The RCF has been operated and monitored using critical core pin configurations and at varying temperatures [2,3]. This work describes the computational modeling and simulation of the RCF critical experiments using the NEAMS SHARP toolkit [4] which includes the Proteus-SN neutronics code [5]. Previous simulation results based on other codes have been published in previous work [6,7]. In this paper, the Proteus-SN results are compared against other neutronics codes, including MCNP6 [8] and Serpent 2 [9], as well as the experimental data. 1.2. Walthousen Reactor Critical Facility The RCF is an open pool, low-power research nuclear reactor facility owned and operated by Rensselaer Polytechnic Institute (RPI). A photograph of the RCF core is included in Fig. 1. The reactor is currently fueled with excess fuel from the SPERT (Special Power Excursion Reactor Test) experiments [10]. The RCF currently operates with this fuel at a license limit of less than 100 watts. This low operating power is incredibly advantageous for performing a wide range of experimental procedures that would not be possible with a higher-powered reactor due to their increased licensing requirements and safety limitations. The low-powered nature of the reactor allows for many experimental procedures, such as determining the water criticality height (as the reactor is sub-critical when the water is drained from the pool). The low neutron flux in the core does not permit for certain experiments such as neutron activation analysis (NAA) of samples that will produce radioisotopes of long half-lives, but this is advantageous because samples inserted into the core for reactivity experiments do not require a substantial length of time to decay to be safely handled.

Figure 1. Photograph of the RCF reactor.

Reactor Physics paving the way towards more efficient systems


The open-pool design dictates that the reactor operates at atmospheric pressure and can be accessed manually when the reactor is shutdown. Several reactor configurations are well known and analyzed with the capacity to have non-standard reactor configurations for future experimental setups. Standard reactor configurations include varying fuel loading, with the standard reactor setup ranging anywhere from 329 to 333 pin setups. For cases where larger experiments are inserted into the reactor, higher pin numbers may be used to over 400 pins in total.

2. COMPUTATIONAL MODELING AND SIMULATION OF RCF For the computational simulation and analysis of the RCF reactor, computational modeling and simulation of the reactor is important for several purposes. The first is to model and simulate existing experiments so the computer models used in the simulation tools can be validated by the experimental measurements. This is important for ensuring the computer model accurately depicts the reactor design and criticality. The eigenvalue solution and neutron flux characterization across the core are particularly useful for this purpose. This can be useful for also characterizing and comparing uncertainties in simulation codes, as is the purpose for this project. The second purpose is for the prediction of reactor behavior for future experimental designs and for ensuring the reactor safety for untested reactor configurations. The third purpose is to train students and reactor operators and to teach them how the reactor should operate under any expected condition. As the RCF is an open-pool design, it does not require forced convection for cooling. For this reason, the most important physics that must be modeled and simulated in the reactor is the neutronics behavior. The primary software used for modeling and simulating the behavior of the RCF during its operation in the past has been MCNP6. The reactor has been modeled for various reactor pin and experimental configurations and used for safety analysis reports as well as student and reactor operator training courses. The MCNP6 model has facilitated the experiential learning process for students and researchers to gain knowledge by simulation techniques of how the reactor is to operate. Recently, the RCF reactor has been modeled using other neutronics codes, including Serpent 2 and Proteus. Serpent 2, a 3D Monte Carlo-based neutronics code similar in function to MCNP6, is specifically made for nuclear reactor core simulation of neutronics behavior. It is particularly useful for comparing against other Monte Carlo neutronics codes, such as MCNP6. Serpent 2 allows for customization in geometry for creating collapsed multigroup cross sections for use in other deterministic neutronics codes. The macroscopic cross section generation feature is used as the basis for all the cross sections used with Proteus-SN in this work. Images of the RCF geometry as output by Serpent 2 for a standard 333 pin configuration are included in Fig. 2.



Figure 2. Computer-generated images of RCF reactor from Serpent 2. Left: side view. Right: top-

down view. The main thrust of this research project is to validate Proteus-SN, a deterministic neutronics code with several solver types with 2D and 3D capabilities, against the RCF experiments. Unlike MCNP and Serpent 2 which both model reactor geometry using constructed solid geometries (CSG), Proteus-SN requires a 2D or 3D mesh for the neutron transport solvers. These conformal meshes must be provided from an outside software package, such as Cubit [11] or its academic and industrial version, Trelis [12]. This means that the mesh must be carefully tuned to be fine where neutron transport is at a peak. Proteus-SN can use first-order, second-order, or higher-order elements for its solution discretization, although it is typically more suited for first-order elements with a smaller mesh size (particularly where reactor geometry is highly heterogeneous). The 3D solid geometry of the RCF reactor (with the surrounding water removed for visibility) as created using Cubit 15.0 is displayed in Fig. 3. In addition to this 3D solid geometry, other models of portions of the RCF reactor were created and meshed in Cubit, including a 2D pin and a full core model in 2D, both using one-fourth symmetry to reduce the total number of nodes in the problem. These figures are introduced and discussed in the following subsections. 2.1. 2D RCF pin simulation As part of the neutronics modeling and simulation of the RCF reactor, the simplest problem is a two-dimensional pin section. This was simulated in Serpent 2 as a two-dimensional geometry for comparison of eigenvalues, along with a representative pin in MCNP6 with all reflective boundary conditions. MCNP6 and Serpent 2 used over 100,000 particles per generation and at least 5,000 active cycles. Proteus-SN used a 2D mesh with 4813 vertices, 11 energy groups, and 40 angular moments (7 polar angles, 9 azimuthal angles) with the Legendre-Tchebychev cubature scheme. The mesh and resulting thermal and fast neutron flux profiles for this 2D RCF pin simulation in Proteus-SN are displayed in Fig. 4. The comparative eigenvalues are listed in Table I.



Figure 3. Image of three-dimensional RCF reactor geometry as constructed in Cubit 15.0.

Figure 4. Computer-generated imagery of one-fourth symmetry RCF reactor pin. Left: geometry and mesh as produced by Cubit 15.0. Middle: thermal neutron flux from Proteus-SN. Right: fast

neutron flux from Proteus-SN. Table I. Table of simulation eigenvalues of RCF Pin: Eigenvalue calculations in simulations performed by MCNP6, Serpent 2, and Proteus-SN for the two-dimensional RCF pin using one-fourth symmetry and

reflective boundary conditions.

MCNP 6.1 Serpent 2 Proteus-SN Eigenvalue ( ) 1.41739(7) 1.41745(2) 1.41579

The results of this simulation show excellent agreement between MCNP6 and Serpent 2, within 6 pcm difference of one another, and a difference within 160 pcm of Proteus-SN. The possibility of the difference in eigenvalue solutions may be due to the difference in method of solution or the need to further refine the energy and spatial discretization of the solution in Proteus-SN.



2.2. 2D RCF full core simulation The 2D full core simulations of the RCF have been performed for a two-dimensional plane with the control rods inserted. This has also been simulated in MCNP6 and Serpent 2 for comparison. There are two meshes that were used in Proteus-SN; one is a coarser mesh with a total of approximately 39 thousand vertices, and a finer mesh with approximately 59 thousand vertices. MCNP6 and Serpent 2 used over 100,000 particles per generation and at least 5000 active cycles. The Proteus-SN simulations used two 2D meshes of differing refinement with 39,142 vertices for the coarser mesh and 59,348 vertices for the finer mesh, 11 energy groups, and 48 angular moments (5 polar angles, 7 azimuthal angles) with the Legendre-Tchebychev cubature scheme. The outer boundary conditions on the four outer edges were set to reflective. This 2D simulation implies an axially infinite reactor core configuration, essentially eliminating neutron leakage. For this reason, the 2D results are for comparing between the neutronics codes and not directly against experimental values. The Proteus-SN mesh and thermal and fast neutron flux profiles are included in Figure 5. The eigenvalue results are included in Table II.

Figure 5. Computer-generated imagery of one-fourth symmetry 2D RCF reactor with 333 pins and

control rods. Left: geometry and mesh as produced by Cubit 15.0. Middle: thermal neutron flux from Proteus-SN. Right: fast neutron flux from Proteus-SN.

Table II. Table of simulation eigenvalues for RCF 2D full-core: Eigenvalue calculations in simulations

performed by MCNP, Serpent, and Proteus-SN for the two-dimensional RCF full core using one-fourth symmetry.

MCNP 6.1 Serpent 2 Proteus-SN

(Coarser Mesh) Proteus-SN

(Finer Mesh) Eigenvalue ( ) 1.02174(6) 1.02102(7) 1.02485 1.02365

As with the 2D pin example, the 2D full core example shows excellent agreement between both Monte Carlo codes (MCNP and Serpent 2) with a larger difference in Proteus-SN for the coarse and finer meshes. The difference being less than 300 pcm for the finer mesh and less than 400 for the coarser mesh suggest that the Proteus-SN solution may not yet be fully resolved and an even finer mesh may give more accurate results.



2.3. RCF 3D full core Along with two-dimensional simulations of the RCF core, three-dimensional unstructured meshes were created and simulated in Proteus-SN. MCNP6 and Serpent 2 used over 100,000 particles per generation and at least 5000 active cycles. Proteus-SN used 3D meshes of 147,778 vertices and 377,363 vertices for the coarser and finer meshes, respectively, 11 energy groups, and 120 angular moments (9 polar angles, 11 azimuthal angles) using the Legendre-Tchebychev cubature scheme. Once again, the eigenvalue results were compared against Serpent 2. The eigenvalue results are included in Table III, and the 3D flux plots from Proteus-SN are included in Fig. 6 and Fig. 7.

Table III. Table of eigenvalues comparing full-core 3D Proteus-SN: Eigenvalue calculations in simulations performed by MCNP, Serpent, and Proteus-SN for the three-dimensional 333-pin RCF core

using one-fourth symmetry.

MCNP 6.1 Serpent 2 Proteus-SN

(Coarser Mesh)Proteus-SN

(Finer Mesh) Eigenvalue

( ) 0.99922(3) 0.99982(3) 1.03594 1.03483

Figure 6. Three-dimensional computer-generated imagery of one-fourth symmetry RCF reactor with 333 pins from Proteus-SN. Left: thermal neutron flux. Right: fast neutron flux.



Figure 7. Three-dimensional computer-generated imagery of one-fourth symmetry RCF reactor with 333 pins from Proteus-SN. Left: absorption rates. Right: nu-fission rates.

The full-core 3D results from Proteus-SN show similar neutron flux shapes in Fig. 6 as compared to the 2D flux shapes in Fig. 5. The eigenvalue differences between the full 3D core in Proteus-SN and Serpent 2 and MCNP6 are approximately 3500 pcm, a significant amount. As with the 2D full core example, the higher scale models require a significant number of elements to provide an accurate solution. Due to the computational resource limitations at the time, a model numbering in the millions of elements that would be required to reach a satisfactory solution was not possible. The full 3D case as described in Table III was run on 300 CPUs and required 9 hours of computation time for the coarse mesh and 240 CPUs and over 15 hours for the finer mesh case. Increasing the mesh size to tenfold more vertices or higher would not be possible for this particular computer cluster due to memory and other constraints. With access to computational clusters at Argonne National Laboratory and significantly more memory and computational power in the future, this should allow for future simulations to be performed with higher fidelity. 2.3. RCF 3D full core at various temperatures With the RCF core modeled in three-dimensions, this leads to the modeling and simulation of the full 3D core as compared against the RCF experiments. This is desirous to both validate the Proteus-SN simulations against experiment and to predict the behavior of the RCF reactor for future experiment design. As was shown in the results in the previous subsection, the eigenvalues were not exactly in accord between the Proteus-SN and Serpent 2 simulations. The difference in eigenvalues will be more valuable in determining the change in eigenvalues to see if a similar trend exists between the two codes and with the experimental measurements. Both Serpent 2 and Proteus-SN have been simulated at 11 different temperatures elevated above room temperature (293 K) which correspond to the same 11 temperatures at which the RCF reactor operated with the rods fully extended and the power period measured. This provides the calculation of the reactivity of the RCF reactor for each of these measurements, which are then be compared against the simulation results. Proteus-SN was run using the coarser 148k vertices mesh from Table III, 11 energy groups and 48 angular moments (5 polar angles, 7 azimuthal angles) using the Legendre-Tchebychev cubature scheme. The simulation eigenvalues in Serpent 2 for each temperature and the change in eigenvalue divided by the change in temperature between each data point are displayed in Table IV. The



Proteus-SN simulation values are included in Table V in a similar arrangement. In Tables IV and V, the differences from the simulated eigenvalue between each temperature are included in the third column in pcm (= 1E-5). The fourth column includes the eigenvalue change per degree change in Kelvin from the previous data point. Table IV. Eigenvalues from Serpent 2 simulations: Serpent 2 eigenvalues of the RCF core with a 333

pin configuration and at various core temperatures. The numbers in parentheses in column 2 are the standard deviations.

Temperature (K)

Serpent 2 Eigenvalue Difference in Serpent 2 Eigenvalue at Previous

Temperature (pcm)

Eigenvalue Change per Degree Change, Δ Δ

(pcm/K) 302.9 0.99854(3) - - 304.2 0.99835(3) -19 -14.9 305.5 0.99813(3) -22 -16.5 306.9 0.99795(3) -18 -12.5 308.8 0.99769(3) -26 -13.8 310.9 0.99745(3) -24 -11.7 313.2 0.99696(3) -49 -21.5 314.9 0.99664(3) -32 -18.0 316.3 0.99639(3) -25 -18.7 317.6 0.99620(3) -19 -14.3 318.7 0.99600(3) -20 -18.9

Table V. Adjusted eigenvalues from Proteus-SN simulations: Proteus-SN eigenvalues of the RCF core

with a 333 pin configuration and at various core temperatures.

Temperature (K)

Proteus-SN Eigenvalue

Difference in Proteus-SN Eigenvalue at

Previous Temperature (pcm)

Eigenvalue Change per Degree Change, Δ Δ

(pcm/K)

302.9 1.03481 - - 304.2 1.03454 -27 -21.1 305.5 1.03445 -9 -6.75 306.9 1.03416 -29 -20.1 308.8 1.03392 -24 -12.7 310.9 1.03366 -26 -12.6 313.2 1.03325 -41 -18.0 314.9 1.03290 -35 -19.7 316.3 1.03262 -28 -21.0 317.6 1.03231 -31 -23.3 318.7 1.03223 -8 -7.58

Upon first viewing the results in Tables IV and V, the Proteus-SN code shows a shift in eigenvalue from the Serpent 2 results by about 3000 pcm. This is a strong indication that the mesh and/or angular resolution has not been completely resolved for this model. Thus, the difference in eigenvalues between



temperatures may provide more useful information. The changes in simulation eigenvalues between temperatures (in column 3 of these tables) between Serpent 2 and Proteus-SN show a difference ranging from 2 to 13 pcm at each point. The change in eigenvalue between each measurement per degree Kelvin change (column 4 in each table) range between 0.8 and 11.4 pcm/K at each data point. A larger dataset spanning a larger temperature change may be able to provide more insight as to why these data seem to vary more than would be expected. The systematic shift in eigenvalues for the Proteus-SN simulations from Serpent 2 is noteworthy and will be considered in future simulations. The reactivities as provided from the RCF experiments using power measurements over time are used to calculate eigenvalue using Eq. (1), and the resulting eigenvalues are summarized in Table VI.

1 1⁄ , (1)

Table VI. RCF reactor experiment eigenvalues: Eigenvalue results from RCF using power period measurements with a 333 pin configuration and at various core temperatures.

Temperature (K)

RCF Experiment Eigenvalue

Difference in Proteus-SN Eigenvalue at

Previous Temperature (pcm)

Eigenvalue Change per Degree Change, Δ Δ (pcm/K)

302.9 1.00137 - - 304.2 1.00126 -11 -9.20 305.5 1.00123 -2 -1.79 306.9 1.00118 -6 -4.01 308.8 1.00102 -15 -8.01 310.9 1.00088 -14 -7.02 313.2 1.00074 -14 -6.28 314.9 1.00055 -19 -10.6 316.3 1.00048 -7 -5.47 317.6 1.00034 -13 -9.96 318.7 1.00025 -9 -9.14

Table VI, as compared with Tables IV and V, show that the eigenvalues are higher than those simulated in Serpent, but approximately 3000 pcm below those calculated in Proteus-SN. Again, the shifted baseline indicates a non-resolved mesh and/or angular resolution for the Proteus-SN model. A much higher resolution mesh with greater angles (particularly in the azimuthal direction) would provide higher accuracy. Figure 8 includes the eigenvalues at each temperature, and Figure 9 includes the graph for the Δk/ΔT values from Tables IV, V and VI for Serpent 2, Proteus-SN, and RCF experiment values, respectively.



Figure 8. Eigenvalues for RCF critical experiments for a 333 pin core configuration and simulations from Serpent 2 and Proteus-SN.

Figure 9. Change in eigenvalues over change in temperature ( ⁄ ) for RCF critical experiments

for a 333 pin core configuration and simulations from Serpent 2 and Proteus-SN. In each of these three-dimensional simulations and comparisons, a significant difference in the eigenvalue has been seen between Proteus-SN and Serpent 2 and the experimental results. This is most likely due to the fact that the unstructured mesh used in the three-dimensional simulations requires significant refinement in order for the model to be resolved. This added refinement makes the problem much more taxing on computational resources. The mesh will continue to be refined in order to hopefully achieve a more accurate solution as compared to MCNP6, Serpent 2, and experimental measurements.



3. CONCLUSIONS The RCF reactor is a unique experimental facility that allows for significant modification and usability. It has the capacity for many unique and valuable multiphysics experiments for validation purposes. It has been modeled and simulated in MCNP6, Serpent 2, and now Proteus-SN. The Proteus-SN solver has also been used to simulate the reactor operation at several temperatures at which the reactor has been operated and the positive power period measured. The Proteus-SN model will continue to be refined, particularly in terms of its spatial discretization by refining its unstructured mesh to achieve more accurate simulation results. It is also intended to continue from this work to use the Proteus-SN deterministic code in conjunction with Nek5000 in the SHARP package for fully-coupled neutronics-thermal hydraulics modeling of the RCF code.

ACKNOWLEDGMENTS Appreciation and thanks go to Emily Shemon and Changho Lee at Argonne National Laboratory for their assistance in the setup and use of Proteus-SN. Thanks are also given to Rajeev Jain and Iulian Grindeanu for their aid in the production of the unstructured meshes used for this article. Grateful acknowledgement must go to the computing resources provided on Blues and Bebop, high-performance computing clusters operated by the Laboratory Computing Resource Center at Argonne National Laboratory. This material is based upon work supported by the Department of Energy Office of Nuclear Energy under Award Number DE-NE0008439.

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8. T. Goorley, et al., "Initial MCNP6 Release Overview," Nuclear Technology, 180, pp. 298-315 (2012). 9. J. Leppanen, et al., “The Serpent Monte Carlo code: Status, development and applications in

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