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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Preliminary Monte Carlo and Thermal Hydraulic Analysis using a Hybrid ETF-Corrected-Diffusion Prediction Block

This paper builds upon previous work to accelerate the Picard iteration (PI) method typically applied for coupled Monte Carlo-Thermal hydraulic (MC-TH) solutions. Previously, the use of the generalized transfer functions (GTFs) to predict variation in macroscopic cross sections following a perturbation in TH properties was demonstrated for a subset of simple 3D problems. In addition, the reduced-order transport prediction block relied on the first order perturbation (FOP) method, which was shown to have computational overheads. Recent work replaced the FOP block with a 1-group nodal diffusion solver to eliminate these overheads. While the use of diffusion is desirable for large-scale problems, the new solver introduces significant homogenization error. This work aims to address this issue by using the Jacobian-Free Newton Krylov (JFNK) method to generate a set of super homogenization (SPH) factors to improve the accuracy of the diffusion solution. The SPH factors will be used in conjunction with an improved cross section prediction method – the expanded transfer function (ETF) method – to produce a highly accurate flux prediction for an axial 1D boiling water reactor (BWR) pincell following a large perturbation in moderator density. The ETF-corrected diffusion (ETF-CD) block is shown to be highly accurate for the 1D test case. Future work will investigate the accuracy of the method for a realistic 3D pressurized water reactor core.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

An Improved Model For Determining Salinity Recharge Time for Deep Borehole Disposal - 20405

In a previous publication (K. P. Travis, D. Burley and F. G. F. Gibb, WM2017 Conference, Phoenix Arizona paper no. 17480) we introduced a numerical model to estimate the time it would take for a pressure perturbation to subside following its creation from the construction of a deep geological borehole in water-saturated rock. The model was based on the notion of a point source of momentum - a solution of the time-dependent pressure-diffusion equation. Using the model, we estimated that it would take on the order of 10 k years for physical equilibrium to become re-established following the sinking of a 5 km borehole in granite. The significance of such a model is that it places an upper bound on the lifetime required of a borehole sealing system - a necessary input to a borehole post-closure safety case assessment. No engineered sealing system has ever been devised which is capable of retaining its sealing properties for 10 half-lives of long-lived radioisotopes in spent fuel or high-level waste. One of the key advantages of disposing of nuclear waste via Deep Borehole Disposal (DBD) is the natural sealing provided by density stratified groundwater. Upon sinking of a borehole, and subsequent filling with fresh water, brine or drilling mud, this natural barrier may be temporarily damaged. Over time, fresh brine from the far-field will flow towards or away from the hole (driven by a pressure gradient) and will eventually re-establish the original salinity gradient. It follows that the engineered seals need last only as long as the time required for this salinity gradient to reset itself. One of the limitations of our previous model was the use of a static boundary condition on the borehole wall. The model used a boundary pressure which varied quadratically with depth (arising from differences between the pressure of a column of fresh water in the borehole and that of a column of brine in the host rock). However as brine replaces fresh water in the borehole (driven by a pressure gradient), the boundary function must change with time. We now introduce an improved model which takes this time dependent boundary condition into account. The model also takes into account the time taken for a mixture of brine and fresh water to re-establish chemical equilibrium through the process of diffusion. The paper contains the mathematical details of our new iterative model as well as results showing the time taken to reach steady state, and concentration profiles for the components of the brine-filled borehole as a function of time together with a discussion on the implications of the results for developing a post-closure safety assessment for DBD. (authors)

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

Temporal Analysis and Scene Change Detection in Multispectral Overhead Imagery

Scene change detection can be a tedious and time consuming process especially when concerning large geographical areas, and the process can be even more cumbersome when analyzing changes in an area over large spans of time. Developing a useful way to help analysts recognize at what points in time significant changes to a scene have occurred can allow them to better focus their efforts in characterizing events. Applications include: Facility monitoring, Construction chronology, Monitoring of vehicle/aircraft activity, Characterization of larger sequences of events. In large areas exceeding hundreds to thousands of square kilometers in size, it can be difficult localizing when scene changes have occurred. Analysts can spend hours going through imagery to try to identify new construction, monitor facility activities, monitor vehicle movement, etc. where the object of interest may only be a few square meters. Our goal is to help cut down this time by giving analysts change maps with hot spots of change, allowing them to focus on regions that have experienced actual change in time frames they're interested in. Additionally, by combining these change maps into layers within a data cube, analysts can examine the change maps from a temporal perspective, allowing events to be characterized over spans of time. By opening the data cube in an imaging software capable of separating the layers, we can analyze the change maps sequentially, allowing us to examine scene changes occurring over time. As an example, we examined overhead imagery from Planet Labs of what appears to be a parking lot on Fort Irwin over the course of a year using ENVI, a geospatial satellite imagery analysis software. Using ENVI, we generate a graph of changes over time, and notice a particular segment near the end of our analysis window where no changes are detected. Examination of the actual satellite imagery reveals that during this time span, the parking lot was empty. This could be due to facility shutdown for maintenance or upgrades, or possibly even total workforce/vehicle fleet movement. Information like this could help analysts better characterize events, as well as to help create clearer timelines in larger sequences of events. Workflow steps: - Collect multiple maps of the same AOI (Area of Interest) during a time span of interest; - Generate change maps from AOI maps; - Generate data cube from change maps. An analyst can use the data cube to help inspect an AOI for activities within a time span of interest. If an event of interest is discovered, the analyst can then refer to the maps corresponding to the appropriate dates and times in the data cube to see precisely what is transpiring. The biggest objective being worked on is improving the change detection methodology employed. We currently use PCA-EM (Principal Component Analysis with Expectation Maximization), but we are currently focusing on implementing IR-MAD (Iteratively Reweighted Multivariate Alteration Detection) to be used in conjunction with PCA-EM in an effort to decrease false positivity and noise in the change maps we generate.

42 ENGINEERING↗
DOE OSTI2020

Lessons Learned in the Development of Industry Guidance - 20279

The availability of industry guidance on different aspects of waste management forms a valuable reference for waste practitioners. The guidance typically details the principles, processes and practices that should be consulted during each stage of the relevant activities. It also includes relevant regulatory and international requirements, appropriate case studies and examples of best practices to illustrate technical concepts and make the information available to the reader in an accessible manner. Over recent years Wood have developed (or are developing) a number of industry guidance documents on a range of topics including Solid Waste Characterization, Routine Water Quality Monitoring on Nuclear Sites: Pipeline Characterization: Determining Background Radioactivity for Land Quality Assessment: Interim Storage and Aqueous Waste Management. This talk provides an overview of lessons learned along the way including: - the importance of stakeholder engagement through the process: - how to identify 'good practice'; - the importance of iterative development; and - the selection of illustrative and informative case studies. (authors)

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

Defining a Metric to Assess Leachability of Contaminants from Cementitious Waste Forms in Lab Testing Related to Hanford - 20478

This paper reports on the determination of performance metrics for the release of four contaminants (technetium, iodine, nitrate, and chromium) from a theoretical supplemental low-activity waste (LAW) inventory of grout in the Hanford Integrated Disposal Facility (IDF). The performance metric was defined as a retardation factor, R, that can be used to quantify a waste form's ability to retain one contaminant compared with an un-retarded species (e.g., sodium). By setting the target R value at the magnitude required to maintain concentrations of the contaminants below the drinking water standard at the point of compliance for the IDF, a bar for grout leach performance can be established for screening laboratory leach test data. The R can be converted to a corresponding laboratory-observed diffusivity value against which to assess leach test data. The individual performance metrics were determined through an iterative set of simulations using a variable saturation and transport flow model of a grout waste form inventory in the IDF to calculate the resulting concentration-based requirements at the point of compliance. (authors)

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

Fourier analysis of continuous fractional diffusion synthetic acceleration schemes in slab geometry

We propose two fractional extensions of continuous diffusion synthetic acceleration (DSA) with fractional derivative order α varying over the interval 2 ≥ α ≥ 1 . We investigate the spectral properties of the corresponding continuous families of fractional preconditioners by performing Fourier analysis for a model infinite homogeneous medium problem in slab geometry. The first family results in a fractional acceleration scheme, FrDSAo, that reduces to traditional DSA for .α = 2 and scattering ratio c limiting to a unit value (c → 1) but is otherwise optimized via the Fourier analysis, to obtain the smallest possible spectral radius, for c < 1 and 2 ≥ α ≥ 1. The second family corresponds to a fractional acceleration scheme, FrDSAs, that reduces to traditional DSA for α = 2 for all values of c. The latter scheme is not optimized but has the advantage of lending itself to a more straightforward implementation. For high values of c, the results of the Fourier analysis point to the existence of an interval 2 > α > ∼1.8 where both FrDSAo and FrDSAs can achieve a lower spectral radius than DSA. For example, DSA has a spectral radius of ∼0.2246 for c = 0.9999 while FrDSAo produces a value of ∼0.1616 at α = 1.92 and FrDSAs results in ∼0.2116 at α =1.93. (author)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Investigating the AGN-201M research reactor's unique dominance ratio

The AGN-201M reactor is a small, thermal spectrum reactor located at the University of New Mexico (UNM). It is moderated by polyethylene, reflected by graphite, with fuel comprised of uranium microspheres embedded in polyethylene plates that are separated by an aluminum baffle. The dominance ratio of a multiplying system is the ratio of the first higher-mode eigenvalue to the fundamental, k{sub 1}/k{sub 0}. It is a key parameter in characterizing the rate of convergence, analyzing system stability, and determining how tightly coupled the system's neutron fission is. The purpose of this paper is to investigate the system's unusually low dominance ratio of 0.632. This investigation varied the reactor's physical parameters, such as the fuel geometry, fuel density, and reflector thickness, and examined their impact on the reactor's dominance ratio. Additionally, this study examined neutronically similar systems in hopes of identifying common causes for systems with low dominance ratios. The reason why the dominance ratio of the reactor is small compared to larger thermal reactors was determined to be because of its significantly smaller geometry and the composition of the fuel plates. The reflector's effect on the dominance ratio is small in comparison to the other factors, but was found to have a non-zero effect. Furthermore, the AGN-201M was found to have a significantly lower dominance ratio than systems in which it shares a very high (c{sub k} >95%) degree of neutronic similarity.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2024

Angular Distribution of Dimuons from Drell-Yan Production in p+Fe Interactions at 120 GeV Beam Energy

In the E906/SeaQuest Fermilab experiment, we report a measurement of the angular distributions by measuring the angular parameters $\lambda$, $\mu$, and $\nu$ of Drell-Yan dimuons produced using a 120 GeV proton beam incident on an iron target. The angular distribution in the naive Drell-Yan model does not show any $\cos2\phi$ dependency, where $\phi$ denotes the azimuthal angle of dimuons in the Collins-Soper frame. However, pion-induced Drell-Yan experiments, such as NA10 and E615, have observed a significant dependence on $\cos2\phi$. The Boer–Mulders function, a transverse momentum-dependent distribution function, represents the correlation between the transverse spin and the transverse momentum of the quark. A non-zero Boer-Mulders function or an improved higher-order Drell-Yan model considering QCD effects can produce a $\cos 2\phi$ modulation in the Drell-Yan angular distribution. To measure the angular distributions, we have used an event mixing method to construct the combin atorial background, which was then subtracted from the data to isolate the Drell-Yan signal. Following this, we corrected the detector, trigger, and reconstruction efficiencies using a doubly-iterative Bayesian Unfolding method. This iterative unfolding technique improves the response matrix based on the results of the previous unfolding step, ensuring robust convergence without exaggeration of uncertainties. The angular distributions of the dimuons were measured over the invariant mass range $5.0 < M_{\mu^+ \mu^-} < 8.0$ $GeV/c^2$, with dimuon transverse momentum $P_T < 2$ GeV/c and Feynman-x $-0.18 < x_F < 0.9$. The measured angular distributions are then compared with the QCD calculations for $p + \text{Fe}$ interactions, and proton-induced angular distribution measurements from other experiments. We have observed weak $\cos 2\phi$ modulations as a function of $P_T$. For $P_T > 1.0 \, \text{GeV}/c$, the predicted NNLO perturbative QCD value of $\nu$ is larger than what we have me asured at E906/SeaQuest. Moreover, we have not observed a strong dependence of $\nu$ on the kinematic variables, such as dimuon mass $M_{\mu^+ \mu^-}$ and Bjorken-$x$. The spin alignment of the virtual photon, $\lambda$, measured from the SeaQuest Drell-Yan $p+\text{Fe}$ data, is found to be strongly dependent on $P_T$, decreasing as $P_T$ increases. $\lambda$ also holds to the upper bound condition $\lambda < 1.0$ within the statistical uncertainty, showing a trend similar to that predicted by NNLO perturbative QCD. However, for $1.0 < P_T < 2.0 \, \text{GeV}/c$, the extracted $\lambda$ value from SeaQuest is smaller than that predicted by perturbative QCD at NNLO.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Preliminary Study on TRISO Fuel Cross Section Generation

Cross section self-shielding methodologies for TRISO fuel were assessed to provide accurate multigroup cross sections for a high-fidelity reactor physics code so that the code is able to accurately model and simulate advanced reactors with TRISO fuel. Initially, the two existing methodologies (the SCALE method and the Sanchez-Pomraning method) were studied and implemented to MC2-3 for detailed performance tests. Additionally, a new spatial self-shielding method, named the iterative local spatial self-shielding (ILSS) method, for particulate fuels was developed based on the disadvantage factor and implemented to MC2-3 as well. The new method approximately accounts for the effect of randomly distributed particles on the particle shadowing effect using a homogenized compact region surrounding a particle of interest at the center. The self-shielded cross sections of the particle at the center are determined iteratively since the cross sections of the homogenized compact region are calculated using them. For the energy range above 100 keV where the fuel-to-moderator ratio is more important than the random distribution of particles, a single particle unit-cell model is used by preserving the average amount of moderator per fuel particle in the system. The three self-shielding methods implemented in MC2-3 were tested using numerical benchmark problems made based on fuel compact problems of a prismatic-type very high temperature reactor. Test results indicated that the ILSS method produced slightly better results than the SCALE and Sanchez-Pomraning methods, compared to the Serpent-2 Monte Carlo results obtained with 25 independent random particle configurations. The SCALE and Sanchez-Pomraning methods tend to underestimate the heterogeneity effect by 150 and 100 pcm, respectively, while the new ILSS method overestimates the heterogeneity effect by 70 pcm. In future, the new self-shielding method will be extended to perform pebble calculations and compare results with those from the SCALE and Sanchez-Pomraning methods. Furthermore, the new method will be optimized for practical applications to on-the-fly resonance treatment for lattice or whole-core calculations for advanced reactors.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1986

Simultaneous iterations algorithm for general eigenvalue problems on parallel processors

The method of simultaneous iteration with shift is extended to extraction of m-eigenpairs of a general eigenvalue problem of large order n in a parallel processing environment. The algorithm combines the power method and the Jacobi technique, and reduces to performing four basic operations. Parallel implementation of the algorithm is discussed in detail. The analysis accounts for computation and communication costs, and utilizes a parallel processing architecture of the ensemble type. Expressions for the computational efficiency and speedup are defined as a function of the problem and hardware parameters. Selected representative problems exhibit efficiencies ranging from 60 to 98 percent.

Utku, S.↗
DOE OSTI2025

SymProp: Scaling Sparse Symmetric Tucker Decomposition via Symmetry Propagation

Sparse symmetric tensors are an important class of tensors, and their decompositions serve as powerful tools for revealing low-rank structures. This paper introduces SymProp, a novel approach for scaling sparse symmetric Tucker decomposition by propagating symmetry through intermediate computations. SymProp optimizes two key computational kernels: Sparse Symmetric Tensor Times Same Matrix chain (S3 TTMc) for Higher-Order Orthogonal Iteration (HOOI) and Sparse Symmetric Tensor Times Same Matrix chain Times Core (S3 TTMcTC) for Higher-Order QR Iteration (HOQRI). Our method employs a metaprogramming-based index iteration approach to efficiently handle the upper triangular parts of intermediate dense symmetric tensors. SymProp achieves up to 50.9× speedup over SPLATT and up to 360.8× over Compressed Sparse Symmetric (CSS) format on the S3 TTMc operation. Moreover, our S3 TTMc and S3 TTMcTC implementations support tensor orders four levels higher than state-of-the-art methods. Our HOQRI demonstrates superior scalability and up to a 33.6× speedup over optimized HOOI. By enabling more scalable Tucker decompositions for higher orders, decomposition ranks, and dimension sizes, SymProp opens new possibilities for analyzing complex hypergraph structures in fields such as network science, data mining, and machine learning.

Li, Zecheng [North Carolina State University]↗
NASA NTRS1992

Upper bounds for convergence rates of vector extrapolation methods on linear systems with initial iterations

The application of the minimal polynomial extrapolation (MPE) and the reduced rank extrapolation (RRE) to a vector sequence obtained by the linear iterative technique x(sub j) + 1 = Ax(sub j) = b,j = 1,2,..., is considered. Both methods produce a two dimensional array of approximations s(sub n,k) to the solution of the system (I - A)x = b. Here, s(sub n,k) is obtained from the vectors x(sub j), n is less than or equal to j is less than or equal to n + k + 1. It was observed in an earlier publication by the first author that the sequence s(sub n,k), k = 1,2,..., for n greater than 0, but fixed, possesses better convergence properties than the sequence s(sub 0,k), k = 1,2,.... A detailed theoretical explanation for this phenomenon is provided in the present work. This explanation is heavily based on approximations by incomplete polynomials. It is demonstrated by numerical examples when the matrix A is sparse that cycling with s(sub n,k) for n greater than 0, but fixed, produces better convergence rates and costs less computationally than cycling with s(sub 0,k). It is also illustrated numerically with a convection-diffusion problem that the former may produce excellent results where the latter may fail completely. As has been shown in an earlier publication, the results produced by s(sub 0,k) are identical to the corresponding results obtained by applying the Arnoldi method or generalized minimal residual scheme (GMRES) to the system (I - A)x = b.

Sidi, Avram↗
NASA NTRS1987

Development of generalized block correction procedures for the solution of discretized Navier-Stokes equations

Effort is directed towards developing a solution method which combines advantages of both the iterative and the direct methods. It involves iterative solution on the fine grid, convergence of which is enhanced by a direct solution for correction quantities on a coarse grid. The proposed block correction procedure was applied to compute recirculating flow in a driven cavity.

Kelkar, Kanchan M.↗
NASA NTRS1998

Progressive content-based retrieval of image and video with adaptive and iterative refinement

A method and apparatus for minimizing the time required to obtain results for a content based query in a data base. More specifically, with this invention, the data base is partitioned into a plurality of groups. Then, a schedule or sequence of groups is assigned to each of the operations of the query, where the schedule represents the order in which an operation of the query will be applied to the groups in the schedule. Each schedule is arranged so that each application of the operation operates on the group which will yield intermediate results that are closest to final results.

Li, Chung-Sheng↗
NASA NTRS1997

Computational Issues in Damping Identification for Large Scale Problems

Two damping identification methods are tested for efficiency in large-scale applications. One is an iterative routine, and the other a least squares method. Numerical simulations have been performed on multiple degree-of-freedom models to test the effectiveness of the algorithm and the usefulness of parallel computation for the problems. High Performance Fortran is used to parallelize the algorithm. Tests were performed using the IBM-SP2 at NASA Ames Research Center. The least squares method tested incurs high communication costs, which reduces the benefit of high performance computing. This method's memory requirement grows at a very rapid rate meaning that larger problems can quickly exceed available computer memory. The iterative method's memory requirement grows at a much slower pace and is able to handle problems with 500+ degrees of freedom on a single processor. This method benefits from parallelization, and significant speedup can he seen for problems of 100+ degrees-of-freedom.

Pilkey, Deborah L.↗
DOE OSTI2025

An eigenvalue-based method for computing the relaxed pressure in compressible multiphase flow with N phases

The modeling of compressible multiphase flows is a decades-old area of study with many applications across various fields. Many of these application areas use stiff pressure relaxation. This process involves the solution of a nonlinear system with N + 1 equations and N + 1 unknowns, where N is the number of phases. The resolution of this system with general equations of state (EOSs) is difficult. Furthermore, nonlinear systems can admit multiple solutions, and current solution methods do not address this possibility. Very recently, a thermodynamic relaxation method was introduced, which effectively maps a relatively simple predictor equation of state onto a more complex target equation of state. In this context, the target EOSs are the chosen EOSs for the thermodynamic model. Furthermore, this thermodynamic relaxation has the benefit of simplifying the stiff pressure relaxation system of equations. In this article, we show this system reduces to a polynomial of degree N, which can be recast as an eigenvalue problem through the use of the associated companion matrix. We show that although this eigenvalue method is generally less efficient than Newton–Raphson iteration, it does not suffer from convergence issues and finds all N roots of the polynomial. Hence, the method provides a fail-safe for root-finding iterative methods and a way to address the issue of multiple solutions to the nonlinear system of equations in stiff pressure relaxation.

Eigenvalue algorithm↗
NASA NTRS1978

Finite elements and finite differences for transonic flow calculations

The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

Hafez, M. M.↗
NASA NTRS1993

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

In this study involving advanced fluid flow codes, an incremental iterative formulation (also known as the delta or correction form) together with the well-known spatially-split approximate factorization algorithm, is presented for solving the very large sparse systems of linear equations which are associated with aerodynamic sensitivity analysis. For smaller 2D problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. Iterative methods are needed for larger 2D and future 3D applications, however, because direct methods require much more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioning of the coefficient matrix; this problem can be overcome when these equations are cast in the incremental form. These and other benefits are discussed. The methodology is successfully implemented and tested in 2D using an upwind, cell-centered, finite volume formulation applied to the thin-layer Navier-Stokes equations. Results are presented for two sample airfoil problems: (1) subsonic low Reynolds number laminar flow; and (2) transonic high Reynolds number turbulent flow.

Taylor, Arthur C., III↗