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Solitary zonal structures in subcritical drift waves: a minimum model

Solitary zonal structures have recently been identified in gyrokinetic simulations of subcritical drift-wave (DW) turbulence with background shear flows. However, the nature of these structures has not been fully understood yet. Here, we show that similar structures can be obtained within a reduced model, which complements the modified Hasegawa–Mima equation with a generic primary instability and a background shear flow. We also find that these structures can be qualitatively reproduced in the modified Hasegawa–Wakatani equation, which subsumes the reduced model as a limit. In particular, we illustrate that in both cases, the solitary zonal structures approximately satisfy the same 'equation of state', which is a local relation connecting the DW envelope with the zonal-flow velocity. Due to this generality, our reduced model can be considered as a minimum model for solitary zonal structures in subcritical DWs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Experimental Investigation of Subcritical Neutron and Gamma Noise Methods at the Seven Percent Critical Experiment (7uPCX)

As part of a collaborative international effort organized by the Lawrence Livermore National Laboratory (LLNL), with key participants from the Institut de radioprotection et de sûreté nucléaire (IRSN), Los Alamos National Laboratory (LANL), and the Sandia National Laboratories (SNL), a series of high-multiplication subcritical neutron and gamma noise measurements was planned and executed. The primary aim of this article was to advance detector technology, assess the validity of gamma noise for subcriticality measurements, and nuclear criticality safety, focusing on collecting list-mode or time-series data from various reactor configurations with multiplication values ranging from 20 to 310. This comprehensive dataset enabled a detailed comparative analysis of multiple detector systems and the results of both neutron and gamma noise measurements. In this work, we focus on experimentally comparing the results from neutron and gamma noise measurements. We note good agreement between estimations of the prompt neutron decay constant and demonstrate the effects of changing reactor geometry on the efficiency of the differing methods. Our results agree well with independent experimental measurements and simulations performed by LLNL.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Subcritical Multiplication Ex-Core Calculations with Shift

This report details the development and testing of Virtual Environment for Reactor Applications (VERA) as applied to full core subcritical multiplication ex-core calculations with Shift. The limiting factor in being able to run these detector calculations with Monte Carlo is the amount of computational memory used by a fully-loaded full core problem. The main development features added to VERA in this effort were enabling source biasing and separable weight windows and integrating multithreading in Shift. With these capabilities, a subcritical multiplication detector response calculation on a full core Watts Bar Nuclear Plant Unit 1 (WBN1) ex-core model was successfully run on a moderately sized computing cluster.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Subcritical Californium Source Drive Noise Analysis Measurements With Unreflected Uranium (93.15) Hydride

On July 6, 1989, subcritical californium source-driven noise analysis (CSDNA) measurements were performed with bare uranium hydride cylindrical assemblies at the Los Alamos National Laboratory Critical Experiments Facility in KIVA 1. Three configurations of ~7.5 cm radius-enriched (93.15 wt. % 235 U) uranium hydride with a density of ~10 g/cm 3 cylinders were assembled with uranium hydride heights of ~11, ~14, and ~16 cm. The uranium hydride (~2 and ~3 cm high) was in thin-welded stainless steel cans. The neutron multiplication factors obtained on-line from the measured ratios of spectral densities were 0.942 ± 0.002, 0.917 ± 0.003, and 0.867 ± 0.004 for uranium hydride heights of ~16, ~14, and ~11 cm., respectively. Neutron multiplication factors for these three configurations calculated by Los Alamos National Laboratory Monte Carlo methods were 0.952 ± 0.005, 0.922 ± 0.005, and 0.860 ± 0.005, all of which are in good agreement with the measurements. The break frequency noise analysis data could be fitted to obtain the prompt neutron decay constant at all subcritical states. Some data presented in this report are from notes that are not in the logbooks. A discussion of the two different point kinetics theories of the measurements that illustrated the deficiencies of the rigorous theory at low neutron multiplication factors (k eff < 0.80) is given in an Appendix. These measurements may be the only configuration of unreflected, highly enriched uranium hydride configuration assembled. The presence of hydrogen diluted the uranium density, decreasing the reactivity, but this is offset by slowing down the neutron energy to the energy ranges of higher-fission cross sections. Extrapolations to delayed critical indicate that adding one more 3 cm can and one more 2 cm can would result in the unreflected cylindrical system being slightly above critical with a critical mass of ~37 kg, which is considerably less than the critical mass of an unreflected and unmoderated highly enriched uranium metal sphere. An unreflected, highly enriched uranium hydride sphere would have a critical mass less than 37 kg.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

(U) SENSMG: First-Order Sensitivities of Neutron Reaction Rates, Reaction-Rate Ratios, Leakage, k eff , α , and Subcritical Multiplication Using PARTISN

SENSMG is a tool for computing first-order sensitivities of neutron reaction rates, reaction-rate ratios, leakage, k eff , α, and subcritical multiplication using the PARTISN multigroup discrete-ordinates code. SENSMG computes sensitivities to all of the transport cross sections and data (total, fission, a nu, chi, and all scattering moments), two edit cross sections (absorption and capture), and the density for every nuclide and energy group. It also computes sensitivities to the mass density for every material and derivatives with respect to all interface locations and outer boundaries. It computes sensitivities to user specified reactions whose cross sections are available in a user-supplied NJOY output file. The tool can be used for one-dimensional spherical and slab (r) and two-dimensional cylindrical (r-z) geometries. The tool can be used for fixed-source and eigenvalue problems. For most responses, the tool implements Generalized Perturbation Theory (GPT) as discussed by Williams and Stacey. The tool is thus limited to computing sensitivities only for GPT-allowable responses. For subcritical multiplication, the tool implements sensitivities derived by O’Brien and Clark. SENSMG has a similar role as the old SWANLAKE (Ref. 8), FORSS (Ref. 9), and SENSIT (Ref. 10) codes. It has capabilities similar to those of SUSD3D (Refs. 11 and 12), which also uses PARTISN. Section II of this report describes the theory behind adjoint-based sensitivities, gives the equations that SENSMG solves, and defines the sensitivities that are output. Section III describes the user interface, including the input file and command line options. Section IV describes the output. Section V gives some notes about the coding that may be of interest. Section VI presents some sample problems and discusses verification, which is ongoing. Section VII lists needs and ideas for future work. Appendix A lists most of the input files whose results are presented in Sec. VI. Appendix B provides some useful details on one of the cross-section libraries that SENSMG supports.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Subcriticality Measurements for a Changing Concentration Uranyl Nitrate Solution Tank by Californium Source-Driven Noise Analysis

Subcritical californium source-driven noise analysis (CSDNA) measurements were performed at the Oak Ridge Critical Experiments Facility in 1983 using a stainless-steel tank with an inside diameter of 76.2 cm and a height of 91.4 cm but only filled with a uranyl (93.16 wt.% 235 U) nitrate solution to a height of 76.2 cm for all measurements. The free acid content of the uranyl nitrate solution was less than 0.01 N to minimize hazards in handling. The total available highly enriched uranium for these measurements was 5,296 g. The concentration of the solution was varied from the highest density of 14.71 grams of uranium per liter (g U/L) initially in 16 steps, lowering the concentration to 0.3492 g U/L, and finally using a tank filled with only water. The tank had a Plexiglas lid to minimize evaporation. The Cf source was contained in a re-entrant Lexan tube which could be in the solution parallel to the axis of the cylindrical tank. The detectors were 3 He proportional counters in the solution in shrink-fit tubing to isolate the counters from the fissile solution and adjacent to the outside of the tank. In some cases, the detectors were scintillators adjacent to the outside of the tank. In other cases, the source was external to the tank. Some data presented in this report are from notes and are not in the logbook. The prompt neutron decay constant was obtained from fitting the date from the CSDNA measurements. The purpose of this report is to document the experimental information for the measurements performed so that later, researchers could perform the required uncertainty and calculational analyses and documentation to use these data for an International Nuclear Criticality Safety Benchmark Program (ICSBEP) or a Nuclear Energy Agency benchmark. The prompt neutron decay measurements could be the basis of as International Reactor Physic Benchmark Program. The data from these measurements are available from the Records Management Services Department of Oak Ridge National Laboratory, and the logbook is also available from the ICSBEP at Idaho National Laboratory. Preparation of the present report is part of a larger cooperative effort between Idaho National Laboratory (INL) and Oak Ridge National Laboratory (ORNL) to document more than 15 undocumented critical and subcritical experiments enumerated in ORNL/TM-2019/18 and performed by ORNL at ORCEF and other USDOE critical experiments facilities using more than 500 operational days of critical facility time.

98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗

Delayed Critical and Subcritical Experiments with Polyethylene Moderated Unreflected Thin 15 in. Diameter HEU Metal Plates

The thin ~15 in. diameter highly enriched uranium (HEU) metal plates were assembled to delayed criticality at the Oak Ridge Critical Experiments Facility (ORCEF) in 1969 with various thicknesses of polyethylene (varying from 1/16 to 2$\frac{3}{8}$ inches) between uranium metal plates. The average 235 U enrichment was 93.27 wt. %. These unreflected critical configurations contained 4$\frac{2}{3}$ to 20$\frac{5}{6}$ thin 15 in. diameter HEU metal plates (on loan from Los Alamos National Laboratory [LANL] and shipped to Oak Ridge National Laboratory [ORNL] on June 3, 1969). Depending on the thickness of polyethylene, the enriched uranium masses varying from 28,053 to 135,148 grams. Fractional plate sections consisted of the appropriate number of 60° pie sections. In addition to the measurement at delayed criticality, subcritical measurements were also performed by the inverse kinetic rod drop method. Prompt neutron decay constant measurements were also performed by the Rossi alpha and randomly pulsed neutron method using a time-tagged spontaneous fission californium neutron source; these are briefly reported here. At the time of these measurements in 1969, the thin HEU metal plates were in near-pristine condition with extremely little oxidation, allowing better descriptions of the uranium plates than the use of these plates in a heavily oxidized and deteriorated condition in recent reflected benchmark experiments at the LANL facility at the Nevada Test Site with these same thin highly enriched uranium metal plates. This report documents the experimental information for the measurements performed so that later researchers can perform the required uncertainty and calculational analyses and documentation to use these data for an International Nuclear Criticality Safety Benchmark Evaluation Program (ICSBEP) or a Nuclear Energy Agency (NEA) benchmark. Data from the experiments described should be acceptable for use as criticality safety benchmark experiments for the ICSBEP and the NEA nuclear criticality safety benchmark program once the uncertainty analysis on the measured neutron multiplication factors is completed. Additional data—such as the dimensional inspection reports, uranium isotopic information, and other relevant particulars—should be retrieved from the Y-12 Plant or LANL and incorporated in the final ICSBEP benchmark. Based on previous ICSBEP benchmarks with this enriched uranium metal at ORCEF, the uncertainties in $k_{eff}$ could be as low as ± 0.0002 for some configurations. Other experiments with smaller-diameter than 15 in. diameter HEU metal plates have been benchmarked in HEU-METFAST-001. The prompt neutron time decay measurements could be the basis for an International Reactor Physics Benchmark Program. Preparation of the present report is part of an effort at ORNL to document more than 15 undocumented critical and subcritical experiments enumerated in ORNL/TM-2019/18 and performed by ORNL at ORCEF and other US Department of Energy critical experiments facilities using more than 500 operational days of critical facility time. This work for this report publication was supported by the Nuclear Criticality, Radiation Transport and Safety NCSP Program at ORNL.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Validation of New MCNP6.3 Features for Critical and Subcritical Benchmark Simulations [Slides]

A separate MCNP6.3 V&V document reports on all the default calculations for all test suites was introduced. Here, we look at new optional features of the MCNP6.3 code. Then, Fission-matrix-based options with Convergence and population testing and Automated acceleration of the fission source and Doppler Broadening Resonance Correction and HDF5 Particle Track Output (PTRAC) and Validation benchmarks: criticality, Rossi-α, and subcritical multiplication. All the new MCNP6.3 options give statistically equivalent results and should be considered for default usage in criticality and subcritical multiplication calculation work. Discussed are two separate papers at the upcoming 2023 International Conference on Nuclear Criticality Safety (ICNC 2023) that give more details on the results presented here.

97 MATHEMATICS AND COMPUTING↗

Oxidation of Alloy X in Subcritical, Transition, and Supercritical Water

This work investigates the oxidation of a nickel-based superalloy, namely Alloy X, in water at elevated temperatures: subcritical water at 261°C and 27 MPa, the transition between subcritical and supercritical water at 374°C and 27 MPa, and supercritical water at 380°C and 27 MPa for 100 h. The morphology of the sample surfaces were studied using scanning electron microscopy coupled with focused ion beam milling, and the surface chemistry was investigated using x-ray diffraction, Raman spectroscopy, energy dispersive x-ray spectroscopy, and x-ray photoelectron spectroscopy before and after exposure studies. Surfaces of all samples were identified to comprise of a ferrite spinel containing aluminum.

Materials Science↗

Feasibility Study for a Proposed Subcritical Assembly at Oak Ridge National Laboratory

Nuclear Criticality Safety (NCS) staff use the guidelines in the ANSI/ANS-8.26 standard to establish and maintain their training and qualifications. Section 7.4 of the standard requires NCS staff to participate in hands-on experiments meant to “…demonstrate how varying the properties of a fissionable material system can affect neutron multiplication.” This training is performed to ensure NCS and operations staff are aware of the risks involved with conducting operations with fissionable materials outside reactors. A new, inherently safe, subcritical assembly, to be housed at Oak Ridge National Laboratory (ORNL) is being considered to augment the current training capabilities of the US Department of Energy/National Nuclear Security Administration (DOE/NNSA) Nuclear Criticality Safety Program (NCSP), which conducts hands-on subcritical and critical experiments to support the training and qualifications of NCS staff. This paper reports the results of a feasibility study performed by ORNL.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

MCNP Neutronic Design Optimization of an Accelerator-Driven Subcritical Assembly for Mo-99 Production

Molybdenum-99 (99Mo) has been in short supply in the recent decades. The most common productionmechanism, irradiation in a reactor fueled by highly enriched uranium (HEU), raisesproliferation concerns. Novel efforts are being pursued to meet the demand for 99Mo withoutHEU irradiation, relying on the processing of low-enriched uranium or natural uranium. Onesuch concept is to use an electron linear accelerator to generate bremsstrahlung that, through aphotonuclear reaction, can help multiply neutrons in a subcritical assembly. The goal of this workwas to neutronically optimize the subcritical assembly for keff and 99Mo production. This optimizationis unique for The design was optimized in terms of reflector type, pitch, and LEU andNU mass. Results of the paper show the effects of fuel mass, pitch, and reflector material on keffand the NU fission fraction. keff was found to be mostly driven by LEU mass, and the NU fissionfraction was dependent on several parameters, primarily pitch and mass.

Conant, Andrew↗

Leak detection in a subcritical boiler

Thermal power plants experience cycling duty leading to the fatigue of the boiler and heat exchanger tubes. As a result, tube failures occur frequently in coal fired fleets leading to forced outages. Furthermore, because the tube leaks have been the major source of unwanted shutdowns and the number of outages is increasing, present work focuses on the detection and isolation of the leak in a subcritical boiler based upon the process data from a commercial coalfired power plant. The mass balance equation around the steam drum was analyzed using timeseries data collected from a 300 MW power plant. The ratio of the feed water mass flow rate to the steam mass flow rate was defined as a key parameter for detecting leaks. The difference in slope between the feedwater and steam mass flow rate during the normal and faulty operations was established as the upper control limit for real time monitoring. To reduce false alarm rates that arise when raw signal is directly compared against the threshold due to common process fluctuations, an optimal filter was derived for smoothing. It was found that the optimal filter reacted much more quickly to process changes than an exponential moving average filter, around 8 h earlier on average. Occurrence of relatively high false alarm rates even in the filtered responses was related to the cycling of the boiler from the base load condition. Variable threshold was established to keep false alarm rates to the minimum while maintaining the leak detection rate. Finally, the leak was located at the economizer and this could readily be isolated by investigating the magnitude of the mass flow rates ratio and the temperature at the economizer outlet.

42 ENGINEERING↗

Osmotic control of the spacing of parallel shear cracks in shale growing subcritically in geologic past

The geological genesis of natural cracks in sedimentary rocks such as shale is a problem that needs to be understood to improve the technology of hydraulic fracturing as well as deep sequestration of harmful fluids. Why are the vertical natural cracks roughly parallel and equidistant, and why is the spacing roughly 10 cm rather than 1 cm or 100 cm? Fracture mechanics of critical cracks cannot answer this question. Neither can the material heterogeneity. The growth of critical parallel cracks is impossible because the relative crack face displacements would immediately localize into one crack, leading to an earthquake. The cracks must have formed, on the tectonic time scale, by a slow growth of subcritical shear cracks governed by the Charles-Evans law. The idea advanced here is that what controls the crack spacing is the balance between the reduction, due to shear dilatancy, of the concentration of ions such as Na + and Cl - in each fracture process zone (PFZ), which decelerates the cracks, and the restoration of ion concentration by diffusion of ions from the space between the cracks into the FPZ. This diffusion of water is driven mainly by the osmotic pressure gradient, which offsets the deceleration and depends strongly on the crack spacing. A simple analytical solution of the steady state is rendered possible by approximating the ion concentration profiles between adjacent cracks by parabolic arcs. Applying this theory to Woodford shale yields the approximate crack spacing of 10 cm, which is realistic. Furthermore, the stability of unlimited parallel mode II frictional crack growth is proven by examining the second variation of the free energy. Water concentration drop in the FPZ due to shear dilatancy and its restoration by water diffusion from the inter-crack space have similar effect, although probably much weaker.

42 ENGINEERING↗

Verification of Subcritical Limits in ANSI/ANS-8.1-2014

The first edition of the current American National Standards Institute (ANSI)/American Nuclear Society (ANS) standard ANSI/ANS-8.1-2014, “Nuclear Criticality Safety in Operations with Fissionable Materials Outside Reactors,” was published in 1964 as ASA N6.1-1964, “Safety Standard for Operations with Fissionable Materials Outside Reactors.” In 1969, that standard was revised as ANSI N16.1-1969, “Nuclear Criticality Safety in Operations with Fissionable Materials Outside Reactors.” ANSI N16.1-1969 includes a variety of subcritical limits (SCLs) for uniform aqueous solutions and metals containing fissile nuclides of 233 U, 235 U, and 239 Pu. Furthermore, SCLs are also included for uranium-water lattices. In the 1983 version of ANSI/ANS-8.1 (a revision of ANSI N16.1-1975), the suite of SCLs in the standard was expanded to include 235 U enrichment limits for homogeneous uranium-water mixtures and dry/damp oxides, uniform aqueous solutions of low-enriched uranium, and uniform aqueous mixtures of Pu(NO 3 ) 4 containing 240Pu in addition to the SCLs included in ANSI N16.1-1969. The SCLs have changed little in subsequent revisions (ANSI/ANS-8.1-1998 and ANSI/ANS-8.1-2014). The ANSI/ANS-8.1-2014 standard is currently being revised to include new SCLs (uranium metal and compounds with enrichments up to 20 wt% 235 U) and possible updates to the current SCLs already in the standard, although these new/updated SCLs will not be available to the nuclear criticality safety (NCS) community for a number of years. The original bases for these SCLs were documented in papers in journals such as Nuclear Science and Engineering and in ANS meeting transactions; however, these bases are ambiguous enough that sites and regulators in the United States have not widely endorsed them for safety purposes. Overall, the purpose of this paper is to present the results of a comparison study for the SCLs in the ANSI/ANS-8.1-2014 standard using modern codes (SCALE and MCNP) and cross sections (ENDF/B-VIII.0) to provide some assurance about their quality (bias and bias uncertainty) for use in NCS applications and for consideration by the ANS-8.1 Working Group as a reference for future revisions.

42 ENGINEERING↗

Numerical investigation of inertial sphere impaction on a cylinder in subcritical flow

We investigated the accuracy of a Lagrangian scheme for simulating both the motion and wall impaction of neutrally buoyant inertial spheres (8.85 ≤ St ≤ 18.04) moving in the subcritical regime (Re = 10,972 and 22,366) of flows past a circular cylinder. The accuracy of the eddy-resolving simulations of the flow field was verified based on available data at nearly comparable flow conditions. The accuracy of the eddy-resolving simulations of the flow field was verified based on available data at nearly comparable flow conditions. The accuracy of the particle tracking scheme was verified with respect to corresponding experimental data in a laboratory flume. Particle dispersion en route to the circular cylinder is mostly driven by the flow disturbance from the particle injector tube. The trends in collision rates are largely explained by the rate of particle entertainment into the boundary layer around the cylinder and the inertial condition of the spheres in this proximity region—both of which can be better assessed by post-processing of the numerical outcomes. Here, the primary incentive to undertake this work was the need for validating a particle-based method for quantifying the hydraulic stressors leading to bodily damage of fish passing flows influenced by hydraulic infrastructure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Investigation of methods for targeted search of dominant higher modes in subcritical systems

The reactor physics modeling of subcritical systems requires a substantially different approach from that of a critical reactor due to the presence of the so-called higher modes. Earlier investigations showed that the dominant higher modes lie in the inner part of the eigenvalue spectrum, making the conventional eigenvalue searches unfeasible and calling for a targeted search. This paper investigates the possibility of targeted and multitudinous eigenvalue calculation by testing the Krylov-Schur and the Dynamic Modes Decomposition (DMD) method for simple, analytically tractable problems. While the DMD method clearly showed its efficiency in a one-group homogeneous problem, modal analysis of a three-dimensional reflected reactor in two-groups approximation demonstrated that the increasing complexity poses challenges for both methods. (authors)

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Predictive modeling of a subcritical pulverized-coal power plant for optimization: Parameter estimation, validation, and application

As renewable power generation deployment increases, fossil fuel plants are increasingly required to operate more flexibly. Many coal-fired power plants were originally designed to operate at base load and do not operate optimally at partial load. Predictive first-principles plant-wide models can be employed to identify opportunities for flexibility improvements and diagnose low-load operating issues. This paper describes the application of the Institute for the Design of Advanced Energy Systems Integrated Platform (IDAES) to model and optimize flexible power plant operations. The key benefits of using IDAES are that it provides an open-source, fully equation-oriented modeling framework for efficient modular model construction, reuse, and customization, together with a mathematical optimization framework leveraging powerful, state-of-the-art solvers. The process systems engineering workflow from predictive process simulation to parameter estimation, model validation, and plant optimization is applicable to a variety of existing and next-generation energy systems as well as other chemical and environmental processes. Here, to demonstrate this capability, a physics-based, steady-state model was developed to improve full- and part-load performance of the Escalante Generating Station, a 245 MWe (net) subcritical pulverized coal-fired power plant owned and operated by Tri-State Generation and Transmission Association. Specifically, sixty-nine model parameters were simultaneously estimated from several months of operating data enabling prediction of flow rates, temperatures, pressures, and steam quality throughout the plant. The validated model was leveraged by Escalante to reduce the minimum operating load from 90 MW to 50 MW by diagnosing a low-load water-hammer issue, enabling coal usage and emissions reductions during periods of low power demand. Additionally, opportunities for heat rate reduction (i.e., efficiency improvement) through a steeper sliding-pressure approach to load-following and optimization of other boiler operating variables were also identified and quantified. For example, a potential efficiency improvement of 0.7 percentage points was observed at half-load operation.

01 COAL, LIGNITE, AND PEAT↗