Measurement of effective delayed neutron fraction for NASA Zero Power Reactor I
Measurement of effective delayed neutron fraction for Zero Power Reactor I
NEUTRON↗
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Data Assimilation using Non-invasive Monte Carlo Sensitivity Analysis of Reactor Kinetics Parameters [Slides]
Sensitivity coefficients of prompt neutron decay constant (α) and effective delayed neutron fraction (β eff ) to Pu-239 nuclear data were calculated using a newly available tool (ACEtk). Uncertainty calculations showed the following trends: (1) The prompt neutron decay constant can be used to reduce nuclear data-induced uncertainty in Pu-239(n,f) and (2) the effective delayed neutron fraction can be used to effectively reduce nuclear data-induced uncertainty in Pu-239 total fission $\tilde{v}$. Sensitivity/uncertainty analysis can be used to determine optimal experiment/detector setup to identify compensating errors in nuclear data. Upcoming work includes investigating other nuclide-reaction pairs and response sensitivities, such as Δ$\rho$, neutron leakage spectra, and reaction rate measurements to constrain nuclear data of interest.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
A simple json format for storing and exchanging code calculation and experimental results
Calculation codes and code systems give their results in a plethora of different formats and/or files. For instance, MCNP gives a user the MCNP specific output file, the mctal file, the ptrac file, etc. while PARTISN has a PARTISN specific output file and a number of binary files with various kinds of information about the calculation. However, the results we are interested in are always the same. These can be single values such as the effective multiplication factor k eff or the effective delayed neutron fraction β eff . It can be histogram data (such as particle spectra, reaction rates, sensitivity profiles, etc.) or even pointwise data (for example the nuclide composition as a function of time, etc.). It is also worthwhile to note that this would also apply to experimental data that we may wish to compare with as well. Calculation and experimental results can basically be split into two components: attributes (or metadata) and the actual result itself. Attributes represent information about the result that are not necessarily required for its’ interpretation but that are still good to have. Often, these attributes are what we will want to filter results on. This means that these attributes are often the answer to specific questions we may have about the result. The following is a non exhaustive list of such basic questions: what type of result is it: e.g. the effective multiplication factor k eff , the effective delayed neutron fraction β eff , etc.; which case does it relate to: e.g. a specific ICSBEP case such as PU-MET-FAST-001-001; which code and version produced this result: e.g. MCNP 6.2, etc.; which nuclear data library was used to obtain the result: e.g. ENDF/B-VIII.0 or JEFF 3.3; which nuclide and reaction does it apply to (for reaction rates and sensitivity profiles); which volume in the geometry was it calculated in? The second component of the calculation or experimental result is the actual numerical data of the result. It is this data that we want to compare, exchange, plot, interpret, etc. It consists of values with optional uncertainties and units. It also includes the underlying structure (if any structure is required to interpret the result). Depending on the type of result, it may be a single value (e.g. the effective multiplication factor), an array of values (e.g. a reaction rate or particle spectrum) or even a multidimensional array. In order to exchange results between different organisations, for instance for benchmarking, people often resort to spreadsheets or custom text files that need to be filled out. While this approach works well if little information is to be exchanged, it can become cumbersome when dealing with large amounts of data (like for instance particle spectra for thousands of cases). In addition, such an approach does not always capture the metadata we may be interested in to allow for automated processing of these files. The purpose of this report is to propose a standardised json structure to store any type of result and present an associated python interface to interact with these results directly. For such a structure to be useful, it must fulfill a specific set of functional requirements that we try to meet with this proposal. The format must allow for the calculation result to stand by itself. This means that we should not have to look in multiple places to be able to understand it. For example, if the result relates to a particle spectrum, the group structure in which the result is given should be stored with it. The format should be code agnostic. This means that we do not need to know where it came from to understand it. The format should be result type agnostic. This means that the format must be generic enough so that we can even use it for results we have not thought of yet. The format should be relatively easy to interact with through different scripting or programming languages (i.e. the machine interface) while still providing a clean structure that can be used directly by any human.
97 MATHEMATICS AND COMPUTING↗
Preservation of kinetics parameters generated by Monte Carlo calculations in two-step deterministic calculations
The generation of accurate kinetic parameters such as mean generation time Λ and effective delayed neutron fraction β eff via Monte Carlo codes is established. Employing these in downstream deterministic codes warrants another step to ensure no additional error is introduced by the low-order transport operator when computing forward and adjoint fluxes for bilinear weighting of these parameters. Another complexity stems from applying superhomogenization (SPH) equivalence in non-fundamental mode approximations, where reference and low-order calculations rely on a 3D full core model. In these cases, SPH factors can optionally be computed for only part of the geometry while preserving reaction rates and K-effective, but the impact of such approximations on kinetics parameters has not been thoroughly studied. This paper aims at studying the preservation of bilinearly-weighted quantities in the Serpent–Griffin calculation procedure. Diffusion and transport evaluations of IPEN/MB-01, Godiva, and Flattop were carried out with the Griffin reactor physics code, testing available modeling options using Serpent-generated multigroup cross sections and equivalence data. Verifying Griffin against Serpent indicates sensitivities to multigroup energy grid selection and regional application of SPH equivalence, introducing significant errors; these were demonstrated to be reduced through the use of a transport method together with a finer energy grid.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Estimating β eff from static, late-time Feynman neutron noise measurements
The effective delayed neutron fraction, β eff , is a kinematic parameter describing the contribution of delayed neutrons to the effective multiplication factor, $\kappa$ eff , and is of great interest to the nuclear criticality safety community and beyond. In fact, $\kappa$ eff presently must be inferred (as opposed to directly measured) since variables like β eff must be obtained from simulation, reference tables, or a dynamic or pulsed measurement where the assembly of fissile material is perturbed and not in steady state. Several recent works have proposed neutron noise techniques to estimate β eff from static measurements (such as benchmark experiments). This work experimentally investigates an approach based on looking at late-time (up to thousands of seconds) correlated neutrons in Feynman histograms. This work utilizes measurements of weapons grade plutonium and highly enriched uranium to construct late-time Feynman histograms and investigate a proposed methodology of estimating β eff from a fit of the distribution. Data is shown from both He-3 detectors and an organic scintillator array. This work is preliminary in nature, demonstrating some experimental feasibility and proposing improvements for future investigations.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Data Assimilation using Non-invasive Monte Carlo Sensitivity Analysis of Reactor Kinetics Parameters
Accurately predicting the criticality of an experiment before interacting with the experimental components is very important for criticality safety. Radiation transport software can be utilized to calculate the effective neutron multiplication factor of a nuclear system. Because of the integral nature of the effective neutron multiplication factor, the value calculated contains various sources of nuclear-data induced uncertainty. The sensitivity analysis and data assimilation technique presented in this paper exhibit one possible method of identifying and reducing the effective neutron multiplication factor nuclear-data induced uncertainty. The results presented in this work show that it is possible to use relative sensitivity coefficients of the prompt neutron decay constant and the effective delayed neutron fraction to 239 Pu nuclear data to reduce nuclear-data induced uncertainties in the effective neutron multiplication factor. This work has been utilized by members of the Los Alamos National Laboratory project EUCLID (Experiments Underpinned by Computational Learning for Improvements in Nuclear Data) for optimally designing a new experiment, which will be used to reduce compensating errors in 239 Pu nuclear data.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Alternative analysis of the MINERVE ZPR oscillation experiments
Delayed neutrons are of fundamental importance in the field of nuclear reactor dynamics and control. However, the precursor yield fraction for a given nuclear reactor are dependent on the properties of the reactor. Thus, in-pile experiments, such as oscillation experiments are conducted in order to measure those values. In this work, an alternative analysis of the piston oscillation experiments that have been conducted in the MINERVE reactor in 2013 is performed. A new method which evolves effective terms that cancel out undesired drifts of the flux during the experiments is presented. The evaluation of the uncertainty on the values of the response function is also presented. Moreover, the effective delayed neutron fraction β{sub eff} is evaluated and is compared to results in previous works. As the analysis has led to an estimation of β{sub eff} with a large uncertainty, it has been deduced that the oscillation experiments that have been conducted in MINERVE are not a reliable method of experimentation to determine the value of β{sub eff} in the reactor and that the noise experiments are better suited for that purpose.
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
Implementation of Perturbation Theory and Sensitivity Capabilities in Griffin
Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor Multiphysics analysis application, jointly developed by Argonne and Idaho National Laboratories under the DOE-NE NEAMS program. This fiscal year, capabilities for reactivity and sensitivity evaluation using perturbation methods were implemented and verified. The First Order Perturbation Method (FOPT) was employed to compute reactivity worth resulting from small perturbations in input parameters, while the Generalized Perturbation Theory (GPT) was used to evaluate sensitivities of a range of response types, including reaction rate ratio, k-eigenvalue, neutron generation time, and effective delayed neutron fraction. These perturbation methods enable users to quantify how response quantities change due to a perturbation in a input parameter without explicitly performing an additional transport simulation for each perturbed state. In particular, the GPT formulation accounts for indirect effects arising from flux changes by solving generalized inhomogeneous equations, for which a Neumann series-based iterative solution method was developed and implemented in Griffin. The implemented reactivity and sensitivity evaluation capabilities were verified using two test problems: an infinite homogeneous system and a two-dimensional hexagonal core. The results showed excellent agreement with reference solutions obtained by a direct method based on finite difference approximation as well as GPT-based results from the PERSENT code, confirming the accuracy of both reactivity and sensitivity evaluations. Additionally, preliminary uncertainty quantification (UQ) results were obtained by combining the sensitivity values computed using GPT and external covariance data, demonstrating that the implemented sensitivity results can be reliably used for uncertainty calculations. To further demonstrate the generality and practical strength of the implementation, the sensitivity evaluation capability was successfully applied to the Empire microreactor with a geometrically complex design that poses significant modeling challenges. The results confirm that Griffin enables sensitivity evaluations even for irregular and highly heterogeneous reactor configurations, thereby establishing a foundation for UQ applications in advanced reactor designs and analyses.
22 GENERAL STUDIES OF NUCLEAR REACTORS↗
Uncertainty quantification and sensitivity analysis of a nuclear thermal propulsion reactor startup sequence
The research presented in this article describes progress in applying stochastic methods, uncertainty quantification, parametric studies, and variance-based sensitivity analysis (also known as Sobol sensitivity analysis) to a full-core model of a nuclear thermal propulsion (NTP) system simulated via the radiation transport code Griffin to simulate neutronics. Our goal is to develop a reduced-order (surrogate) model that can be rapidly sampled with perturbations to multiple input parameters. In this NTP system, reactivity and power feedback affect the rotation of control drums (CDs), which is itself controlled by a hybrid proportional-integral-derivative (PID) controller actuated by the power demand and reactivity feedback from the numerical model. This model uses reactor kinetic feedback (mean generation time [Λ] and effective delayed neutron fraction [ β eff ] from a transient Griffin simulation executed via Griffin’s improved quasi-static solver to provide the kinetic parameters) as inputs to functions that control the CD rotation angle. By investigating numerous stochastic approaches, we developed a dual-purpose surrogate model of the NTP system, using polynomial regression in the Multiphysics Object-Oriented Simulation Environment (MOOSE) Stochastic Tools Module (STM). The trained model can be rapidly sampled while simultaneously perturbing various input parameters, such as coefficients on the PID control or temperature (directly affecting the neutron cross section). The surrogate model delivers accurate (within 5%) results at speeds orders of magnitude faster (minutes, not days of computational time) than the base model. Once the surrogate model has been trained, distributions of the uncertain parameters can be changed at will to investigate the effects of perturbing multiple inputs as well as the effects of these inputs on the model output. For example, coefficients used in the PID control system may vary due to some type of physical interference, or uncertainty may exist in the temperature of the neutron cross sections in various regions of the reactor. A distribution can be placed on these parameters, and operational boundaries can be determined. The goal of this work is to support development of an advanced control system for operating CDs in a functioning NTP system. This work is a scoping study of the MOOSE STM.
21 - SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLAN↗
Utilization of ACE nuclear data file toolkit ACEtk to calculate relative sensitivity coefficients of point-kinetics parameters
Sensitivity and uncertainty methods are quintessential for nuclear criticality safety and experiment design. This type of analysis relies on calculations of sensitivity coefficients; sensitivity coefficients of the effective neutron multiplication factor with respect to some nuclear data are predominantly calculated and used. As a part of the Laboratory Directed Research & Development project EUCLID (Experiments Underpinned by Computational Learning for Improvements in nuclear Data) at Los Alamos National Laboratory, sensitivity coefficients of many radiation detector measurement responses with respect to nuclear data were investigated. Specifically, this paper outlines a method to calculate point-kinetics parameters relative sensitivity coefficients with respect to nuclear data. Point-kinetics parameters such as the prompt neutron decay constant, effective delayed neutron fraction, and neutron generation time are especially important to experimenters and reactor operators designing systems with dynamic neutron populations. This method couples capabilities of the ACE (A Compact ENDF) nuclear data file toolkit, ACEtk, with the ability to load cross sections into the radiation transport code Monte Carlo N-Particle (MCNP). In conclusion, key aspects of optimizing this method for a particular application and sensitivity profiles of the Jezebel criticality experiment are examined and discussed.
98 NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL P↗
Using Prompt Neutron Decay Constant Measurements to Obtain Additional Kinetics Information
Prompt neutron decay constant measurements are typically used to infer the prompt neutron lifetime in a chain-reacting system, but these measurements include much more information about the kinetics of the system. This work focuses specifically on the Rossi-α method of measuring the prompt neutron decay constant. The Rossi-α system of equations consists of five unknown parameters. With five unknowns and three equations, the system of equations solved by the Rossi-α measurement is under-determined. It has been postulated that a well posed problem can be formulated using independent measurement configurations on a single system. The external source strength, the effective delayed neutron fractions, and Diven’s parameter do not typically change for different configurations of a single experiment. If good detector geometry is chosen, the detector efficiency does not change for multiple measurements of a single experiment using Rossi-α measurements. By making these assumptions, there are only two unique variables. This knowledge can be used to solve for most of the unique parameters using two independent, unique Rossi-α measurements.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Effects of Uranium Impurities in Downblended HEU on HTGR Performance
Many advanced reactor designs require fuel enriched between 5% and 20% 235 U. To assist in producing fuel at these enrichment levels, government-owned inventories of highly enriched uranium can be downblended. However, fuel produced from these inventories contain uranium impurities that are not often found when enriching natural uranium or accounted for when modeling reactor cores. To address this concern, this work models reactor designs like the X-energy Xe-100 and the Ultra Safe Nuclear Company’s Micro Modular Reactor, and compares their performance with fuel from enriching natural uranium to fuel from downblended highly enriched uranium. This paper evaluates the models based on the effective neutron multiplication factor, k eff , effective delayed neutron fraction, β eff , and energy- and spatially dependent neutron flux, ϕ, as well as the fuel, coolant, moderator, and total reactivity temperature feedback coefficients, α F , α C , α M , and α T . The results show that the fuel from downblended highly enriched uranium inventories leads to differences in each of the metrics, especially in the keff values. In the Xe-100–like and Micro Modular Reactor–like models, k eff changes by about 1400 pcm and up to 1200 pcm, respectively. Total reactivity feedback coefficients α T are negative with the impure fuels and the keff values remain above 1 for each core configuration and fuel composition. These results show that the impure fuel compositions do not necessarily prevent achieving key design parameters, such as cycle length, or from operating in a safe condition.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Pile Oscillator Evaluation for Flattop [Poster]
Useful method for high-precision measurements of integral cross section in various samples. The availability of benchmark-quality effective delayed neutron fraction (ßeff) values for nuclear data and code validation remains limited.
MCNP↗
PERTRAN - A transport-perturbation program
Computer programs for determining neutron lifetime, effective delayed neutron fraction, and reactivity contributions
Anderson, J. L.↗
Multi-Physics Investigation of a Natural Circulation Molten Salt Micro-Reactor that Utilizes an Experimental In-Pile Device to Improve Core Physics and System Thermal-Hydraulic Performance.
INL employee PhD Dissertation - The Molten Salt Reactor (MSR) concept is a rapidly evolving Generation IV design that has recently attracted favorable attention due to the potential for reducing waste generation, realizing passive safety features, and seizing on the opportunity for cost effective economics. This thesis investigates the performance benefit of a new device invented by the doctoral candidate. The device is referred to as a Wrapped Helix around an Inclined Plane or WHIP. The WHIP is protected under a provisional patent filed with the USA Patent Office on 28 September 2021 under application number 63/261,776, BEA docket number BA-1254. The WHIP device can be located in-core or near-core to promoted enhanced thermal-hydraulics and neutronics performance. While the WHIP can be employed in a variety of solid or liquid fuel designs, this thesis investigates the device’s benefit in the application of a natural-circulation, micro-molten salt nuclear battery concept (MsNB). This thesis will specifically investigate the temperature coefficient of the MsNB fuel (FLiNaK) using novel temperature sensitivity techniques unique to Serpent particle transport code, evaluate the WHIP’s thermal-hydraulic and neutronic performance effects using both established (STAR-CCM+) and novel (Python code developed to estimate the circulation effective delayed neutron fraction, ßef f ) analytical and numerical methods, evaluate the neutron noise behavior of the MsNB and how the WHIP may alter the character of the MsNB’s transfer function, and how the WHIP affects the autonomous, load-following performance under transient power conditions using Python code developed by the candidate. The sum body of this work, in part, has been published in three journal articles as the timing of the provisional patent process has allowed. Results show that creative utilization of WHIP engineering design and function reduces reactor system volume, fuel loading, control/stability in the buoyant regime
buoyant flow↗
Validation of KENO Delayed Neutron Fraction Capabilities
The delayed neutron fraction, which is necessary for the safe operation of reactors, varies by fissionable material and neutron spectrum. A prompt fission neutron spectrum has been included in the SCALE 6.2 release to account for the removal of delayed neutrons from precursor materials from the neutron balance. This paper describes how experimental measurements from criticality safety benchmarks were used to validate the SCALE calculational procedure for the delayed neutron fraction. Additionally, the effect of nuclear data uncertainty on the KENO calculation of β eff was examined with the SAMPLER sequence.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Dynamics modeling of molten salt reactor with reduced and expanded representations of delayed neutron precursors
Molten salt reactors (MSRs) present unique challenges in dynamic behavior due to the mobility of their fuel. In these reactors, delayed neutron precursors (DNPs) drift with the fuel circulation through the primary loop. As a result, a fraction of DNPs decays outside the core, effectively reducing the available delayed neutron population for reactivity control. Consequently, precise modeling of the distribution and behavior of DNPs is critical for accurate reactor dynamics simulations. In this study, the System Dynamics Analysis Tool (SDAT) was used to simulate a thermal-spectrum MSR under steady-state conditions and following transients. The effects of using reduced and expanded representations of DNPs with fewer or more groups than the conventional 6-group model were investigated. Their impact on the simulated distribution of precursors in the primary loop, reactivity loss value, and reactor response to transients was analyzed. Simulation results showed that reduced models lead to the loss of the actual DNPs distribution data, resulting in less accurate estimates of reactivity loss. Reactor power predictions using these reduced models showed significant deviations compared to those using the conventional 6-group model in transient simulations. Expanded models offered a more accurate representation of the distribution of DNPs and reactivity loss estimates. Reactor power predictions using expanded models showed minimal deviation from the conventional 6-group model during the simulated transients.
analysis↗
Investigation of the OECD/NEA PWR MOX/UO{sub 2} core transient benchmark using a coupled whole core pin-by-pin route in WIMS
This paper investigates the new CAMELOT coupling route developed in WIMS, which uses prepared tabulated cross-sections combined with the flux solver MERLIN module and the integrated sub-channel thermal hydraulics solver ARTHUR module to solve for the coupled core state. This coupling route is applied to the OECD/NEA pressurized water reactor (PWR) core transient benchmark exercise, involving 3-D neutronics and thermal-hydraulics analysis of a full-sized PWR core featuring MOX fuel at various core states, as well as simulating a control rod ejection transient. Analysis of the results for each part of the benchmark demonstrate that the high-resolution pin-by-pin analysis used in WIMS closely matches the other participants in the benchmark, with differences of between 20-200 pcm for k-effective, 1-2.5% RMS difference for assembly-averaged powers, 2-8% difference in rod worth calculations, < 200 ppm for calculations of critical boron concentration, zero difference in delayed neutron fraction calculation and a very close match for power response to the rod ejection transient. This is the first application of the WIMS-CAMELOT approach for the transient analysis of a full-sized reactor and as such further improvements such as reducing computational cost through parallelization, optimisation and memory reduction, are currently in active development. This paper demonstrates the accuracy and flexibility of the CAMELOT coupling route, providing a straightforward and consistent user image that can be easily used for a variety of modelling problems involving coupled neutronics and thermal-hydraulics. (authors)
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗