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Sensitivity Studies, Gap Analysis, and Benchmark Experiment Optimization for Reactor Physics and Criticality Safety Applications

Many new reactor designs, such as advanced reactors and micro reactors, have materials that lack nuclear data validation. This is also true for many other applications in criticality safety and global security. Both differential and integral experiments are needed to validate cross-section data. Without this, a user cannot have confidence in the predicted results of a radiation-transport code. This work describes an approach called ARCHIMEDES (Application Relevant Critical/Subcritical HEU/Pu-based Integral Measurements for Enhancing Data and Evaluating Sensitivities) to design new criticality experiments that have similar k eff cross-section sensitivities to an application of interest. This process involves simulations to generate cross-section sensitivities to a parameter of interest (such as k eff ), a gap analysis to determine which existing benchmarks are most similar to the application, and an experiment optimization. Recently, there has been a great deal of interest in the reactor physics community on advanced reactors, micro reactors, and accelerator driven systems (ADS). This work will apply the described method to specific examples in this area. The focus of this work will be on the sensitivity study and gap analysis, while future work will include experiment design.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Formulation of the density eigenvalue problem in neutron transport for relevant engineering applications

A new formulation of the density eigenvalue problem for the neutron transport equation is presented. This new eigenvalue, named ζ eigenvalue can be introduced freely in the transport model, acting on a selected portion of the phase space. Despite its broader applications and its connection with the nature of the transport operator, the ζ eigenvalue has been presented here mainly as a design-oriented technique for the efficient evaluation of the critical concentration for a specific nuclide (or mixture of nuclides). This new eigenvalue is particularly adequate to study the definition of the material composition in the criticality design process of a multiplying system. The method is then applied for the study of classical problems such as the critical moderation ratio and the poison concentration to control the reactor. Some results are presented in one dimensional configuration using the multi- group spherical harmonics approach. This eigenvalue formulation proves to be a convenient and useful way to attain criticality, also for complex, realistic systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Approach and Model Used to Represent a Timeline Analysis for Security Design Enhancements

Next-generation reactors will be able to use risk to inform and performance base the licensing of many aspects of the reactor, facility, and site design, including attributes of physical security. There are several factors related to security, including site topography, reactor design, and physical protection system components, to consider when designing the physical protection system into the overall facility design and plan of operation. With the versatility of advanced reactors, especially micro reactors, methods are needed to simplify and quickly evaluate potential timelines for designing a site configuration. This report describes an approach to generate qualitative and quantitative insights using a risk-informed simulation. The modeling process is described in detail, focusing on three aspects: (1) the facility mission time (the time required to control the plant until safe), (2) the attacker timeline (the time to potential sabotage), and (3) the response timeline (the time to counter the facility attack). The modeling capabilities also are extended to include facility physical phenomena such as thermal-hydraulics and heat transfer to capture realistic representation of dynamic changes to a facility. While the plant models and examples are hypothetical and do not represent a real facility, these modeling approaches could be used for future security-by-design engineering in advanced reactors. The outputs and insights from the modeling approach may be used to modify and optimize the security posture of a facility by efficiently making modifications to the model and seeing the overall impact from the modification. Lastly, use of the approach described in this report can also provide the technical basis for a physical protection program, describing how the facility and security strategy will cope with off-normal events.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Nuclear Criticality Safety [Book Chapter]

Nuclear Criticality Safety is a field of nuclear engineering that involves worker and public safety during the handling, processing, transportation, and storage activities of fissile isotopes ( 233 U, 235 U, and 239 Pu) outside of nuclear reactors. Criticality accidents release energy as a result of accidentally producing a self-sustaining fission chain reaction. If these occur during hands-on operations the results can be lethal to worker within about 4.6 m (15 ft.) of the accident. There have been 22 process criticality accidents in the world between 1953 and 1999 resulting in physical injury, on and off-site dose, or death. Nuclear Criticality Safety involves work by qualified persons to preclude criticality accidents and their consequences by ensuring activities with fissionable materials remain subcritical, i.e., safe, during all normal and credible abnormal conditions. This article presents information about those nuclear fuel cycle steps presenting Nuclear Criticality Safety concerns that must be considered to ensure worker and public safety is assured.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Modeling and simulation of multiphase flows

Multiphase flow can be found in a wide range of natural and industrial systems, such as sediment flow in rivers and coasts to pipeline transport, and reactors of all types. Computational fluid dynamics (CFD) modeling provides a rigorous physics-based method to visualize and quantify these flows and to assess their influence on their surroundings. This presentation will highlight computational research on two varied technologies in the energy sector: carbon capture and wellbore acoustics.

acoustic analysis↗

SAM: A Modern System Code for Advanced Non-LWR Safety Analysis

The System Analysis Module (SAM), developed at Argonne National Laboratory and by collaborators at other organizations, is for advanced non–light water reactor safety analysis. SAM aims to provide fast-running, modest-fidelity, whole-plant transient analysis capabilities that are essential for fast-turnaround design scoping and engineering analyses of advanced reactor concepts. To facilitate code development, SAM utilizes the MOOSE object-oriented application framework, its underlying finite element library, and linear and nonlinear solvers to leverage modern advanced software environments and numerical methods. SAM aims to solve tightly coupled physical phenomena, including fission reaction, heat transfer, fluid dynamics, and thermal-mechanical responses in advanced reactor structures, systems, and components with high accuracy and efficiency. Finally, this paper gives an overview of the SAM code development, including goals and functional requirements, physical models, current capabilities, verification and validation, software quality assurance, and examples of simulations for advanced nuclear reactor applications.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

IN-PILE MEASUREMENTS OF FUEL ROD DIMENSIONAL CHANGES UTILIZING THE TEST REACTOR LOOP PRESSURE FOR MOTION

Different types of materials are being considered for fuel, cladding, and structures in existing and advanced nuclear reactors. These materials can undergo significant dimensional and physical changes during irradiation. Currently in the US, such changes are measured with the ‘cook and look’ method (i.e. repeatedly irradiating a specimen for a specified period of time and then removing it from the reactor for evaluation). The time and labor to remove, examine, and return irradiated samples for each measurement makes this approach expensive. In addition, such techniques provide limited data, and handling may disturb the phenomena of interest. Therefore, in-pile detection of changes in geometry is sorely needed to understand real-time behavior during irradiation testing of fuels and materials in high flux US Material and Test Reactors (MTRs). This paper presents development results of an advanced Linear Variable Differential Transformer (LVDT)-based test rig capable of detecting real-time changes in diameter or length of fuel rods or other material samples during irradiation in US MTRs. This test rig is being developed at the Idaho National Laboratory (INL), and will provide experimenters with a unique capability to measure dimensional changes associated with fuel and clad swelling, pellet-clad interaction, and crud buildup. This novel LVDT design uses the MTR’s loop pressure to drive the test specimen at a constant rate. This leads to a simplified construction, that is, the use of fewer components than other diameter gauge test rigs. This simplified design only requires three pressure boundary penetrations. Further, a key component of this test rig is a leak tight hydraulic ram capable of actuating under low differential pressure, and is able to survive the high irradiation tests at Pressurized Water Reactor (PWR) conditions. The sensor has been proven on a benchtop scale, and shows repeatability and reliability. Measurement accuracies of ±3 µm for diameter and ±90 µm for length have been achieved.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Architecture Improvements and Retesting of the Microscopic Depletion Implementation in the MAMMOTH Reactor Physics Application

Nuclear fuel experiments conducted at the Transient Reactor Test Facility (TREAT) will be analyzed with the MAMMOTH reactor physics application, currently under development at Idaho National Laboratory. MAMMOTH natively couples with the BISON, RELAP-7, and Rattlesnake applications within the MOOSE framework. The implemented methods allow for simulating the irradiation of fuel in a nuclear reactor from the beginning of life in a nuclear reactor until it is placed in TREAT for fuel testing using the same finite element mesh throughout the analysis retaining a very high level of resolution and fidelity. The calculation of the isotopic distribution in fuel requires the solution to the decay and transmutation equations coupled to the neutron transport equation. This report focuses on three significant improvements to the MAMMOTH micro-depletion capability. First, the depletion architecture within MAMMOTH is modified to improve the flexibility and speed of burnup calculations. The results of various benchmark tests demonstrate that the refactoring of the previously implemented capability does not introduce any regression. The second improvement involves the expansion of the data functionality. MAMMOTH can now read the decay data files used by the Oak Ridge Isotope Generation (ORIGEN) code, thus enabling access to data of more than 1,600 isotopes. The third improvement is the capability to perform depletion at a constant power level which was verified via a comparison to ORIGEN.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Cryogenic Hydrogen Fuel for Controlled Inertial Confinement Fusion (Cryogenic Target Factory Concept Based on FST-Layering Method)

A central element of a power plant based on inertial confinement fusion (ICF) is a target with cryogenic hydrogen fuel that should be delivered to the center of a reactor chamber with a high accuracy and repetition rate. Therefore, a cryogenic target factory (CTF) is an integral part of any ICF reactor. A promising way to solve this problem consists in the FST layering method developed at the Lebedev Physical Institute (LPI). This method (rapid fuel layering inside moving free-standing targets) is unique, having no analogs in the world. The further development of FST-layering technologies is implemented in the scope of the LPI program for the creation of a modular CTF and commercialization of the obtained results. In this report, we discuss our concept of CTF (CTF-LPI) that exhibits the following distinctive features: using a FST-layering technology for the elaboration of an in-line production of cryogenic targets, using an effect of quantum levitation of high-temperature superconductors (HTSCs) in magnetic field for noncontacting manipulation, transport, and positioning of the free-standing cryogenic targets, as well as in using a Fourier holography technique for an on-line characterization and tracking of the targets flying into the reactor chamber. The results of original experimental and theoretical investigations performed at LPI indicate that the existing and developing target fabrication capabilities and technologies can be applied to ICF target production. The unique scientific, engineering, and technological base developed in Russia at LPI allows one to make a CTFLPI prototype for mass production of targets and delivery thereof at the required velocity into the ICF reactor chamber.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

The 2019 Edition of the IRPhEP Handbook

The International Reactor Physics Experiment Evaluation Project (IRPhEP) [1] was established to preserve and evaluate integral reactor physics experiment data, including separate or special effects measurements for nuclear energy and technology applications. Numerous international experiments have been performed over the past several decades to support reactor operations, safety, measurements, and design. Those experiments represent a significant investment of infrastructure, cost, and expertise that, in many instances, cannot be as easily reproduced. They represent valuable resources of data for present and future research, and provide the basis for recording, development, and validation of methods [2]. The primary focus of the IRPhEP is to provide an extensively peer-reviewed set of reactor physics integral data suitable for reactor designers and safety analysts to not just validate the analytical tools necessary to design next-generation nuclear reactors, but to establish the safety basis for their operation. Contributors worldwide collaborate to evaluate and review selected benchmark experiments for inclusion in the International Handbook of Evaluated Reactor Physics Benchmark Experiments (IRPhEP Handbook) [3]. More detailed discussion of the IRPhEP, including highlighted reactor physics benchmark evaluations, can be found in the November and December 2014 editions of Nuclear Science and Engineering [1]. Several new evaluations, and revisions to existing benchmarks have been prepared for inclusion in the 2019 edition of the IRPhEP Handbook (see Table I).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Time Scale Effects on the Temperature Coefficient of Reactivity

For a nuclear reactor, the temperature coefficient of reactivity (TCR) is of significance for both power control and safety analysis, but it is not always a constant. For example, the TCR may be dependent upon temperature due to Doppler broadening, and may be also dependent upon time scale due to heat transfer and thermal expansion. A fast burst reactor is a favorable nuclear facility to simulate the time scale effects on the TCR. Fast burst reactors are generally unmoderated research reactors of enriched uranium metal or uranium alloys. The neutrons are fast and the Doppler broadening effects can be neglected, and the TCR is mainly contributed by fuel thermal expansion. Fast burst reactors can operate on both steady state power mode and burst power mode. In steady state power mode, the systems are assumed to be in thermal equilibrium. In burst mode, the full width at half maximum (FWHM) of the power is from tens of microseconds to a few milliseconds, and the heat transfer is generally neglected. If FWHM is short enough, thermal expansion will have a time delay due to inertial effect. This paper is aimed to study the exact time scale effects on the TCR due to thermal expansion. The TCR contributed by the Doppler broadening effects was neglected, because it is relatively small (The k{sub eff} as a function of temperature was also calculated using the Monte Carlo particle transport code JMCT by our group, and no definite difference due to the temperature change was obtained near room temperature), and there is no method to evaluate the time scale dependence of the Doppler broadening effects yet. In the time scale from 1 x 10{sup -6} s to 1 x 10{sup 5} s, the TCR of a Godiva-like spherical fast burst reactor was calculated with perturbation theory. A Godiva-like spherical fast burst reactor was studied, the calculation of the time scale effects on TCR involved thermal conduction, thermoelasticity and reactivity variation analysis. Both the thermal and the thermoelastic problems were solved using ANSYS software. ANSYS is software implementation of finite element simulations, which is widely used in engineering field. The reactivity variation due to thermal expansion was calculated with perturbation theory.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

The 2018 Edition of the IRPhEP Handbook

The International Reactor Physics Experiment Evaluation Project (IRPhEP) was established to preserve and evaluate integral reactor physics experiment data, including separate or special effects measurements for nuclear energy and technology applications. Numerous international experiments have been performed over the past several decades to support reactor operations, safety, measurements, and design. Those experiments represent a significant investment of infrastructure, cost, and expertise that, in many instances, cannot be as easily reproduced. They represent valuable resources of data for present and future research, and provide the basis for recording, development, and validation of methods. Contributors worldwide collaborate to evaluate and review selected benchmark experiments for inclusion in the International Handbook of Evaluated Reactor Physics Benchmark Experiments (IRPhEP Handbook). Several new evaluations, and revisions to existing benchmarks have been prepared for inclusion in the 2018 edition of the IRPhEP Handbook. Additionally, an IRPhEP Uncertainty Guide was discussed to provide further guidance regarding the evaluation of reactor physics measurements besides criticality. Recent changes to the IRPhEP Handbook include five minor revisions, the revision of a previous benchmark evaluation to include new data, publication of a new draft benchmark evaluation, final approval for the formal publication of two formerly draft benchmark evaluations, and the inclusion of ten new benchmark evaluations. The IRPhEP Handbook now contains a total of 159 experimental measurement series from 54 unique reactor facilities. International participants are actively engaged in ongoing evaluation activities to prepare content for future editions of the IRPhEP Handbook. There are numerous experiment and reactor facilities worldwide from which benchmark data can be evaluated. Those interested in serving as evaluators and/or reviewers for the IRPhEP are encouraged to participate.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

System of Standard Neutron Sources on Neutronic Setups for Monitoring, Certification, and Calibration of Apparatus and Equipment

A methodological provision system for neutron measurements performed using neutronic setups is described. The metrological characteristics of standard sources of neutrons of five different groups, created based on nuclear reactors and 14 MeV neutron generators, are presented. The neutron spectra are calculated by a standard method and presented in a unified analytical form as a superposition of physically validated spectra.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Generalization of NESTLE into a Multi-Energy N-Group Formulation

The NESTLE code is a few-group, diffusion-based core simulation code that employs the Nodal Expansion Method (NEM). NESTLE has the capability to solve both steady-state and transient problems, using either Cartesian or hexagonal geometry, and to apply thermal-hydraulic feedback including single and two-phase flow. A modern version of the NESTLE nodal-diffusion simulator is currently maintained and developed at the University of Tennessee. The original version of the code was limited to only two or four neutron energy groups, therefore, this article describes recent work carried out to expand NESTLE into a general multi-group solver. Generalization of a fixed group finite-difference diffusion theory into arbitrary N groups is a well-known problem [3], however, this paper describes the intricacies associated with the generalization of the Nodal Expansion Method, and the methodical and computational challenges encountered and managed along the way.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

On/Off State Classification of a Reactor Facility Using Gas Effluence Measurements

Inferring on/off operational state of a reactor facility using measurements from an independent monitoring system is critical to the assessment of its compliance to agreements. In this paper, we consider the problem of inferring on/off state of a reactor facility using measurements of Ar-41, Cs-138, and Xe-138 gas effluence types collected at the facility’s off-gas stack. We present classifiers based on thresholding measurements of individual effluence types, and then present fusers that combine their outputs or measurements. We present five fusers based on simple majority rule, Chow’s pattern recognition function, Fisher’s combined p-value statistic, physics-based Poisson radiation counts model, and correlation coefficient method. In addition, we also test five machine learning methods based on non-linear classifiers, which are available as R packages. Finally, our results show that: (i) these gas effluence measurements are effective in inferring on/off state of a reactor facility; for example, best fusers achieve ~97% detection at ~1% false alarm rate, and (ii) fusers that combine all effluence types based on physics-based models, correlation coefficient and Fisher’s method outperform simple majority rule, Chow’s fusers and machine learning methods, as well as when they are applied to individual and pairs of effluence types.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

The MP{sub N} method: a new angular discretization method based on piecewise polynomial interfaces fluxes

In transport calculations, it is well known how S{sub N} method is extremely inefficient in problems where the particle physics is dominated by streaming. The ray-effect eventually produced by the insufficient angular discretization, appears to be extremely persistent with respect to the refinement of the angular quadrature. The MP{sub N} method, that relies on continuous angular representation, offers a robust remedy to such an issue. MP{sub N} is based on the decomposition of the unit sphere into solid angles and on a piecewise continuous definition of interface fluxes, which are expanded in polynomials in each solid angle. This allows propagating more than one angular degree of freedom simultaneously while maintaining unaltered the block-diagonal pattern of the displacement plus removal operator. The method is therefore well suited for the flux resolution by means of a conventional sweep algorithm. Furthermore, unlike the S{sub N} method, MP{sub N} does not rely on discrete directions and, thus, on an angular quadrature formula, but rather constructs a set of linear equations solving for the angular moments of the flux for all discrete solid angles within the sweep. MP{sub N} shows an error convergence rate higher than S{sub N} at the expense of an increased size of the coefficient matrices, so of the computational cost. Although MP{sub N} is not free from ray-effect, the latter is effectively mitigated and less persistent with respect to the increase of the angular refinement order. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Implementation of Depletion Architecture in the MAMMOTH Reactor Physics Application

Nuclear fuel experiments conducted at the Transient Reactor Test Facility (TREAT) will be analyzed with the MAMMOTH reactor physics application, currently under development at Idaho National Laboratory. MAMMOTH natively couples with the BISON, RELAP-7, and Rattlesnake applications within the MOOSE framework. The methods currently implemented allow for simulating the irradiation of fuel from the beginning of life in a nuclear reactor until it is placed in TREAT for fuel testing using the same finite element mesh throughout the analysis thereby retaining a very high level of resolution and fidelity. The calculation of the isotopic distribution in fuel requires the solution to the decay and transmutation equations coupled to the neutron transport equation. This work focuses on two significant improvements to the MAMMOTH micro-depletion capability. First, the depletion architecture within MAMMOTH is modified to improve the flexibility and speed of burnup calculations. The results of various benchmark tests demonstrate the accuracy of the modified implementation. The second improvement involves the expansion of the data functionality. MAMMOTH can now read the decay data files used by the Oak Ridge Isotope Generation (ORIGEN) code, thus enabling access to data of more than 1,600 isotopes. Comparison of ORIGEN and MAMMOTH for a selected benchmark problem was performed. Both codes yield very similar results, with differences of 0.03% that can be attributed to differences in precision between the two codes. Future work will focus on comparisons between MAMMOTH and ORIGEN for more complex problems.

07 ISOTOPE AND RADIATION SOURCES↗

Application of linear prolongation to coarse mesh finite difference acceleration in CASMO5

The Coarse-Mesh Finite Difference (CMFD) method has been used for over a decade to accelerate the convergence of the Method of Characteristics (MOC) solution to the two- dimensional particle transport equation in CASMO5. Numerical testing, along with widespread use in production-level calculations, have shown that the current CMFD implementation provides stability and robustness for a wide range of realistic reactor physics problems. However, the recent development of linear prolongation has attracted attention from the community as a way to further improve the performance and stability of CMFD. Two interpolation methods for linear prolongation are presented in this work and implemented into a test version of CASMO5. The performance of the proposed interpolations, referred to as the bilinear and linear directional schemes, is evaluated in terms of runtime relative to the default constant or uniform scaling update. Numerical results indicate that the use of linear prolongation can reduce the transport solver runtime on average by approximately 10% when tested with two hundred randomly selected cases. The new directional linear interpolation, combined with default constant boundary updates, is found to provide the highest reduction in runtime for the cases analyzed. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗