Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “TRANSPORT THEORY”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

235-F GoldSim Fate and Transport Model: Uncertainty Quantification

Building 235-F was configured with two missions in mind: Actinide Billet Line (ABL) and the fabrication of Pu-238 oxide for space program applications. ABL produced Np-237 billets for use in SRS reactors, whereas the design process, fabrication, and examination of Pu-238 oxide powder occurred within the following areas, respectively: Plutonium Experimental Facility (PEF), Plutonium Fuel Form (PuFF), and Old Metallography Lab (OML). By 1990 production ceased and by 2006 de-inventory occurred; however, assays have shown significant holdup remains within ABL and PuFF. As a result, 235-F is a Category 2 nuclear facility, with plans to undergo deactivation and decommission (D and D) via In-Situ Disposal (ISD). The purpose of this project is to ensure United States Environmental Protection Agency (USEPA) groundwater radiation maximum contaminant level (MCL) and dosage standards are met during the D and D of 235-F by quantifying uncertainty through probabilistic modeling and evaluation of various ISD alternatives. GoldSim is a dynamic modeling software package with a graphical, object-oriented interface capable of capturing the influence of complex system input variability on probabilistic system outcomes. A GoldSim stochastic fate and transport model for 235-F was developed and matched with a PORFLOW deterministic model to simulate probabilistic release and flow of radionuclides from ABL and PuFF into the vadose zone, the Upper Three Runs (UTR) Aquifer, and UTR Creek. The GoldSim model was used to probabilistically evaluate four ISD scenarios against USEPA groundwater radiation MCLs and dosage standards. The deterministic 235-F GoldSim fate and transport model continues to be refined to match the results of the PORFLOW deterministic model to ensure the model accurately represents radionuclide movement through the groundwater system. The stochastic variables that are utilized within the GoldSim model are founded on the most current data; a conservative perspective is taken where needed. Alignment with the PORFLOW deterministic model, coupled with input stochastic variability, allows the probabilistic 235-F GoldSim model to capture the conservative breadth of possible outcomes for radionuclide fate within this particular system. This ensures that the USEPA MCLs and dosage limits hold even in the worst case scenarios.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

A Perspective on the Successes of the NNSS Underground Test Area (UGTA) Activity - 20221

Between 1951 and 1992, 828 underground nuclear tests were performed at the Nevada National Security Site (NNSS). Underground testing was done in five major testing areas, which included (1) Frenchman Flat, (2) Rainier Mesa/Shoshone Mountain, (3) Yucca Flat/Climax Mine (4) Central Pahute Mesa, and (5) Western Pahute Mesa. About one third of the underground tests were detonated near, at or below the water table, and thus radioactive contamination was introduced to the groundwater system. The U.S. Department of Energy's Underground Test Area (UGTA) Activity was established in the late 1990's to address the fate and movement of residual radioactivity in groundwater, and characterize the risk that it may pose to NNSS workers and the offsite public. It has accomplished this goal through a process of iterative groundwater sampling and numerical groundwater flow and transport modeling, and long-term monitoring. The UGTA Activity draws on the expertise of scientists in the fields of geology, hydrology, radiochemistry, and risk assessment from the U.S. DOE staff, the lead contractor (currently Navarro) and many other organizations, in cooperation with the governing regulatory body, the State of Nevada's Division of Environmental Protection (NDEP). Los Alamos National Laboratory (LANL) is one of the participating research organizations involved with the UGTA Activity. Under the direction of DOE and the lead contractor, LANL's role in UGTA has evolved over time from an initial focus on geologic characterization, to conducting field and laboratory experiments, and finally to its current role of providing modeling and geochemistry expertise to characterize the rates and directions of groundwater and radionuclide movement. In its current role, LANL has either developed or provided the numerical tools for developing flow and transport models in each of the four major testing areas. In addition, LANL has provided an independent assessment of future groundwater flow and transport behavior through the analysis of naturally-occurring geochemical and isotopic tracers in groundwater. The five major testing areas are now in different stages of investigation or closure: (1) Frenchman Flat is in its fifth year of post closure modeling; (2) The Rainier Mesa/Shoshone Mountain Closure Report has been submitted to NDEP and is awaiting approval; (3) The Yucca Flat/Climax Mine Closure Report is under development; and (4) Central and (5) Western Pahute Mesa is still undergoing investigation and flow and transport model development. The success of the UGTA Activity in reaching or approaching closure in three of the five major testing areas is primarily due to the DoE's focus on regulatory closure requirements, but also is in part attributable to a rigorous internal review process and the involvement of NDEP and Nye County water professionals as participants and observers in the reviews. County and state involvement in the internal review process has promoted trust that the U.S. DOE is deeply committed to ensuring the present and future safely of NNSS workers and the surrounding communities. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Calibration and Uncertainty Estimation Using the Ensemble Kalman Filter with a Large Subsurface Flow and Transport Model - 20321

At routinely monitored groundwater contamination sites, periodically measured environmental conditions such as groundwater levels and contaminant concentrations are used to inform and confirm a conceptual site model (CSM) and guide the development and calibration of a numerical groundwater flow and transport model. The calibration of groundwater flow and transport models after each measurement (sampling) event can illuminate deficiencies in a CSM, identify areas where additional monitoring is warranted, and predict the behavior of the system to guide decision making. However, manual and automated (e.g. PEST) model calibration tools can be time-consuming and computationally expensive to implement after each sampling event. Perhaps as a result, such calibration tools generally utilize all available monitoring data simultaneously rather than sequentially assimilating monitoring data one sampling event at a time as the results from sampling become available. A more real-time data assimilation approach may reduce parameter uncertainty, quantify the value of additional monitoring data, and produce a usable model more quickly and with less effort. To mitigate the potential time-consuming aspects of manual and widely applied automated calibration techniques, a data assimilation algorithm called the ensemble Kalman filter (EnKF) was evaluated as a relatively efficient method of model calibration and uncertainty assessment via the sequential integration of monitoring data into a model. The EnKF was able to successfully and efficiently assimilate monitoring and modeling data to calibrate a complex flow and transport model at a real-world site with significant subsurface heterogeneity, uncertainty, and 12 years of monitoring data (over 4,000 individual measurements of groundwater levels and over 2,500 measurements of contaminant concentrations). Starting with an uncalibrated model data from annual sampling events were sequentially assimilated, and the resultant predication errors and estimated parameter uncertainties were tracked. After all monitoring data were assimilated, both flow and transport residuals at the end of the EnKF process were comparable to those produced via a concurrent PEST calibration effort but required fewer model simulations. Both uncertainty and prediction errors decreased over time. In a real-time application, the adequacy of the model could be assessed after each sampling event. The benefits of such a real-time approach to utilizing monitoring data include reduced costs (in the form of model updates or site characterization efforts), early flagging of possible errors in the CSM, and a reduced risk of overfitting and corresponding increased confidence in model predictions. This tool may be particularly useful compared to other calibration techniques (e.g. manual, PEST) when model runtimes are long, calibration parameters are many, or parameter uncertainty is large. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Contaminant Transport Modeling for Technology Evaluation and Long-Term Monitoring in the Tims Branch Testbed, SC - 20343

Studies conducted at U.S. DOE sites have shown the presence of heavy metals, radionuclides, and volatile organic compounds in surface water, groundwater, and soil as a result of nuclear activity in the Cold War era. Since the 1990's, innovative cleanup methods have been implemented in the Tims Branch watershed at Savannah River Site (SRS) to limit the contaminant flux to the stream that have reduced the contaminant concentrations to acceptable regulatory levels in the dissolved phase. A tin-based treatment which effectively eliminated all local anthropogenic mercury inputs to this ecosystem resulted in a known step function addition of inert tin oxide particles which now serve as a potential tracer for sedimentation and particle transport processes in the stream. The long-term effectiveness of this and other remediation techniques and the potential for remobilization of adsorbed contaminant in sediment during extreme hydrologic conditions however remains unclear. It is therefore important to understand not only the fate and transport of dissolved contaminants, but also the movement of sediment and the relevant interactions with dissolved contaminant. To narrow this knowledge gap, a study is being conducted using the Tims Branch watershed as a stream-scale ecosystem test-bed to identify the primary transport processes of major contaminants of concern (such as mercury, nickel and uranium) with an emphasis on interactions with sediment transport. This involves the development of a fully distributed hydrologic watershed model of the Tims Branch watershed to predict streamflow under extreme weather conditions, as well as the development of a comprehensive contaminant transport model that can properly account for coupled contaminant and sediment transport. Review of relevant research reports and peer-reviewed journals revealed that aside from advection-dispersion transport of dissolved contaminants, adsorption and desorption with suspended solids and bed sediment also play an important role in the transport of those contaminants of concern. To develop the fully distributed hydrologic watershed model, the MIKE SHE 2-dimensional (2D) land surface/3D groundwater model that simulates surface/subsurface hydrologic processes (such as overland flow, evapotranspiration, and infiltration) was coupled with a 1D streamflow model that accounts for stream water hydraulics (such as hydraulic structures, cross-sections, and network). To model contaminant transport, the MIKE 11 streamflow component was coupled with the MIKE 11 AD module that simulates solute transport through advection and dispersion, and MIKE ECO Lab module that accounts for both sediment transport and interactions with dissolved contaminant. At this stage, the development and optimization of the fully distributed hydrologic model has been completed, achieving satisfactory statistical results between observed and predicted discharge as indicated by a root mean square error (RMSE) of 0.039 cms and a Nash-Sutcliffe efficiency coefficient (NSE) of 0.764. The ongoing development of the contaminant transport model has also yielded realistic results from preliminary tests. Results from this study are a key to evaluating the effectiveness of tin (II)-based mercury treatment of wetlands at the SRS site, and are also relevant to evaluating the potential of using this type of novel remediation technology in other mercury-contaminated stream systems. Knowledge acquired from this research will also support interpretation of historical data on the trends of contaminant concentration distribution in Tims Branch, particularly considering the effect of extreme hydrological events on the stream flow and pollutant transport. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Probabilistic Groundwater Modeling of the RDX Plume at Los Alamos National Laboratory to Support Risk Assessment - 20359

A plume of the contaminant hexahydro-1,3,5-trinitro-1,3,5-triazine (RDX) with concentrations greater than the New Mexico tap water drinking standard (9.66 ppb) is present in the regional aquifer near the southwestern boundary of Los Alamos National Laboratory (LANL). A risk assessment is performed for exposure to regional aquifer groundwater, with long-term predictions of RDX concentrations provided by a calibrated, probabilistic, numerical fate and transport model. The structure of the model is hierarchical, with the RDX Regional Aquifer (RA) groundwater model acting as the primary tool for analysis of downgradient RDX concentrations. The RA model is deeply informed by the conceptual site model (CSM) and is calibrated using site RDX concentration data and hydraulic head measurements, along with other analyses. The model is calibrated using data through December 2019. Where data are scarce other lines of evidence are used to inform inputs, including the multiphase RDX Vadose Zone (VZ) model and Pipe and Disk analytical screening tool. Model inputs are described with informative prior distributions using a robust approach to development that incorporates all available lines of evidence for every parameter used as an input to the RA model. Calibration is performed using a classical nonlinear optimization routine, which is then used to initialize a Bayesian calibration. The Bayesian calibration constrains the uncertainty in the classical calibration, ultimately providing posterior distributions for all model parameters. The challenges of the calibration include high-dimensional parameter space, including spatially heterogeneous hydraulic conductivities, comparatively sparse data, and low RDX concentrations. Posterior parameter distributions developed in the calibration process are then used for stochastic predictive model runs into the future. The result of the forward runs is spatially and temporally explicit estimates of head and concentration with uncertainty at all points in space and time. The probabilistic modeling approach presented here includes innovative computational and statistical methods that leverage high-performance computing (HPC) resources. It makes use of prior modeling work performed at the chromium plume site in the central LANL area, with extensive updates. The risk assessment will ultimately be used to support decision-making at the site, using multiple appropriately weighted sources of information, as well as uncertainty, sensitivity, and value-of-information analyses. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Choosing the Best Modeling Platform for Radiological Risk Assessment Models - 20468

Radiological risk assessments, in the form of performance or safety assessments, are often required under regulations or guidance for remediation of contaminated land, decommissioning of contaminated buildings or structures, and radioactive waste disposal. These risk assessments are usually supported by fate and transport models that address decay and ingrowth of radionuclides, as well as their movement through engineered systems and the natural environment. These models are often projected thousands, or more, years into the future, largely because the radioactive species change through decay and ingrowth, and hence the magnitude of the radioactive effect changes with time. There are many computer codes that are available to address this type of modeling. They range from addressing specific pathways or processes such as infiltration of water, groundwater, surface water, air, biota, diffusion and advection of water and gases, to those that try to couple all processes together to evaluate the impact of fate and transport through the entire system to places in space and time to which access is assumed. These different types of codes are sometimes separated with the monikers process-level and systems-level codes, although it is often not clear that this separation does justice to the capabilities of the many codes that are available to evaluate fate and transport of radionuclides. The focus of this paper is the latter group of modeling codes. Several systems level modeling codes exist and are used. There are differences between these codes in terms of utility, flexibility, complexity and cost. The purpose of this paper is to compare a few of these codes in the context of work currently being performed by the International Atomic Energy Agency (IAEA) Modeling and Data for Radiological Impact Assessments (MODARIA) II Working Group 1 (WG1). The MODARIA II WG1's main focus is how stakeholder engaged decision analysis can, or should, be applied to radiological contamination problems so that better, longstanding, sustainable, solutions are reached. However, the WG1 also recognizes the potential impact of the modeling tools that are chosen to address radiological risk, which is often a primary objective of decision making for radiological problems. Other objectives might also be important, such as constraining costs, obtaining financing, minimizing impact on ecosystems, saving cultural resources, saving jobs, farmland, environmental justice, etc., in a full decision analysis for a given radiological contamination problem, but none of these other objectives have the same types of complex modeling needs as minimize radiological dose. Consequently, a further focus of WG1 is to evaluate the potential impacts on decision making of the choice of fate and transport, and risk assessment, modeling codes that are used to support decision making. The WG1 will produce a report at the end of 2020 that will focus on an approach to effective decision making and stakeholder engagement. The report will also consider the role that performance assessment modeling should play in the decision-making process, including the impact of the choice of modeling tools or computer codes on risk-informed decision making. Several sites around the World have been made available by Member States for these model comparisons, and several modeling tools have been considered. However, the focus of this paper is on two of the sites, one in Belgium and one in Ukraine, and on three of the tools: NORMALYSA (NORM And Legacy Site Assessment); GoldSim{sup C}, and AMBER{sup C}. The final report from this working group will also cover other modeling tools, including RESRAD, and PC-Cream{sup R}. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Proceedings of the international conference on physics of reactors - Physor 2022

The theme for this year's conference is 'Making Virtual a Reality: Advancements in Reactor Physics to Leap Forward Reactor Operation and Deployment'. As we leap forward to the future of nuclear technology, micro-reactors, small modular reactors, advanced reactors, and high energy LWR fuel are at the forefront of the topics.The Physor 2022 will cover a broad range of topics in thirty standard and special sessions tracks, and ten panel sessions gathering more than 350 papers.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Anderson acceleration stability in NDA-accelerated k-eigenvalue problems

Anderson acceleration (AA) has been used to improve the stability and convergence rate of multiphysics iterative methods for reactor analysis. Most applications studied assume a tightly converged solution for the different physics problems, and AA is usually applied to state variables like temperature, density, and heat generation rate. In this paper, we study the theoretical performance of AA in NDA-accelerated k-eigenvalue problems. The problems and algorithms studied are simplified from the coupled iteration scheme adopted by MPACT and many other high-fidelity whole-core reactor codes. Compared to previous analyses of AA for these iteration schemes, we study the case with a partially converged neutronics solution and possibly partially converged nonlinear diffusion acceleration (NDA)/coarse mesh finite difference (CMFD) solutions. We observe that the performance of the iteration scheme with AA is very sensitive to the initial guess and is affected by the partially converged CMFD solutions. When the NDA solution is fully converged, using AA cannot achieve the optimal convergence rate in large-sized problems. Conversely, if the NDA solution is partially converged, the iteration scheme with AA can diverge or converge extremely slowly. It is found that the loss of robustness for AA is due to the fact that it is applied to the iterative subspace of state variables rather than the fundamental unknowns of the governing equations. To improve the robustness, the scalar flux should also be considered in the implementation of AA. After considering the residuals of flux, we observe that the stability is regardless of the partial convergence of NDA solutions. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Implementation of hybrid finite element method based transport solver in GRIFFIN

A new transport solver option based on the hybrid FEM (HFEM) was implemented in GRIFFIN, the MOOSE-based reactor analysis code, as an effort to support routine core design calculations for advanced reactor applications. The HFEM formulation with P{sub N} (spherical harmonics expansion), akin to the variational nodal method, is effective for solving a spatially homogenized problem with strong transport effect. The residual and Jacobian evaluations of the HFEM weak form were derived and successfully implemented in GRIFFIN, having the diffusion and the PN options available in the new HFEM based transport solver. The performance was tested with the simplified ABTR benchmark problems. The results indicate that the HFEM-based transport solver is a feasible option for solving problems with spatially homogenized and strong streaming by providing superior accuracy with a proper p-refinement. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

New modelling capabilities in IDT

This work concerns the enhanced modelling capabilities of the discrete ordinates transport solver IDT. The novelties introduced allow for modelling unstructured geometries composed by a collection of X/Y segments and circles, and the use of reciprocity and conservation relations reduce the memory imprint as well as the computational cost of the method. IDT decomposes geometries in modular Cartesian patterns, which are the so-called Heterogeneous Cartesian Cells (HCCs), containing a chunk of the original unstructured geometries. Each HCC can be then discretized by superimposing a XY grid to refine locally the HCC. Unlike the most popular MOC, IDT performs the spatial sweeping by directional collision probabilities instead of trajectories. The sources and interface angular fluxes are expanded up to linear order. The accuracy of ray-tracing, the memory imprints together with the novel mesh refinement capabilities have been verified. A first set of preliminary results on PWR lattice problems will be presented in this paper.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

First-collision source treatment for ray effect mitigation in discrete-ordinate radiation transport solutions

Deterministic transport codes play a fundamental role in the modelling and simulation of neutron transport. One of the most common deterministic methods is the method of discrete ordinates, also known as the S method. While offering significant advantages over other deterministic methods or stochastic methods like Monte Carlo, the method of discrete ordinates suffers from non-physical artifacts in its local solution due to its discretization of angle. These artifacts, referred to as ray effects because of their ray-like appearance, tend to be worse in problems with small sources in areas with little scattering. Significant effort has gone into developing methods to mitigate ray effects, such as the first-collision source treatment, which separates the angular flux into the uncollided and collided fluxes and solving them using non-traditional techniques such as ray tracing. One such code capable of doing this is Lawrence Livermore National Laboratory's deterministic transport code ARDRA. Current ray tracing methods typically trace to a set of points inside a zone to compute an overall flux. However, this approach has significant drawbacks, such as a low order of convergence and not being conservative. Therefore, a new method has been developed that traces instead to a set of points on each of a zone's surfaces and computing the currents, before using these to obtain the flux. A comparison between these two ray tracing methods showed significant advantages to the new surface method, including inherent conservation, a higher convergence rate, and an increase in calculable information like leakage. This work performed under the auspices of the U.S. Department of Energy by Lawrence Liver- more National Laboratory under Contract DE-AC52-07NA27344. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

3D spherical functional expansion tallies in Serpent 2 Monte Carlo code

This work extends the application of functional expansion tallies to 3D spherical geometries. The 3D Zernike polynomials are set as an orthonormal polynomials basis for the functional reconstruction. The study describes the construction of the complete set of polynomials, a natural expansion of the spherical harmonics polynomials where 3D Zernike moments can be evaluated as a linear combination of the geometrical moments. The 3D Zernike polynomials formulation and the computational approach implemented in Serpent 2 are presented and tested through the Godiva model from the ICSBEP criticality benchmark test cases. The implementation results are in agreement with a reference solution described in a fine-resolution mesh, enhancing also the performance and memory demand. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Particle transport in Markov stochastic mixtures with spatial gradients

Markov geometries are a prototype class of stochastic media that are widely used to model complex disordered systems. In a series of recent works, we have shown that spatially homogeneous (but possibly non-isotropic) Poisson tessellations can be conveniently used in order to generate three-dimensional realizations of Markov media and thus characterize the features of particle transport e.g. in fragmented fuel elements following severe nuclear accidents or Rayleigh-Taylor turbulent mixing for inertial confinement fusion. In this paper we show that Poisson tessellations can be extended to take into account the presence of spatial gradients, which commonly occur in real-world applications due to material stratification. For this purpose, we will provide an explicit construction of spatially-non-homogeneous Poisson tessellations, fully characterize their statistical properties, and finally illustrate the behaviour of particle transport in such random media. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Linear source method of characteristics in HELIOS2

The Studsvik Scandpower code HELIOS2 is a fast lattice transport code that has gained wide use for reactor fuel cycle analysis in commercial, regulatory, and research environments. It contains two transport solvers - Collision Probabilities (CP) and Method of Characteristics (MoC) - with a general geometry ability and generalized depletion for a variety of fuel types, experimental facilities, and isotope production applications. The HELIOS2 lattice code has been extended with the development of a linear source MoC option. The linear source equations are derived within the scope of the HELIOS2 general geometry and non-cyclic ray tracing. The implementation was tested for fine and coarse spatial mesh models of the 2D C5G7 MOX computational benchmark, which provides a pure and extreme test of a transport solver. The linear source yields at least comparable accuracy with reduced computational resource requirements relative to the flat-source approximation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Performance enhancement of planar MOC calculation in hexagonal geometries by assembly-wise domain decomposition

The parallelization of planar Method of Characteristics (MOC) calculation with the higher order scattering in the hexagonal version of the nTRACER direct whole core calculation code is enhanced by adopting assembly-wise domain decomposition and other techniques. In order to augment the hexagonal domain decomposition, the three-color scheme, the angular decomposition, and the angular flux storage scheme are examined. The parallel performance assessed for the VVER benchmark problems demonstrates that the hexagonal assembly-wise domain decomposition significantly reduces the computing time in ray tracing by up to 64 %. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Variance reduction techniques for Monte Carlo neutron noise simulations

The small fluctuations of the neutron flux caused by small perturbations of the macroscopic cross-sections take the name of neutron noise. Advanced Monte Carlo methods have been recently proposed in order to solve the neutron noise equations in the frequency domain, which allows establishing reference solutions to validate faster but approximate deterministic solvers. Due to the presence of particles carrying two statistical weights (for the real and imaginary components of the noise field), both of which may be positive or negative, Monte-Carlo simulations of neutron noise pose distinct challenges in terms of variance reduction. In this work we investigate two variance-reduction techniques, namely branchless collisions and weight cancellation, and probe their effectiveness for a benchmark con- figuration concerning the noise field induced by a pin with oscillating cross sections in a fuel assembly.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Analytical benchmark solution for 1-D neutron transport coupled with thermal conduction and material expansion

In this work we present fully analytical solutions for a class of finite, homogeneous, 1-D slab benchmark problems with nonlinear temperature feedback effects. The proposed class of benchmarks include multiplicative 1-D neutron transport (limited to quasistatic S{sub 2} with μ = ±1) coupled with thermal conduction, convection, Doppler broadening, and expansion effects along the length of the slab. This class of benchmark models, along with the corresponding analytical solutions, are valuable for validating multiphysics analysis frameworks that support coupled neutronics/thermal/structural calculations. Analytical solutions for the benchmarks are obtained by introducing an ansatz that the equilibrium flux and temperature distributions in the slab have the same shape. Specific values for the total microscopic cross section, σ{sub t,0}, and conductive heat transfer coefficient, h, that satisfy the assumed ansatz are then determined. A discussion of the procedure for generating benchmark models and analytical solutions is provided, along with numerical results for an example set of model parameters and thoughts on practical applications of the benchmarks for multiphysics code validation. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

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↗