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DOE OSTI2018

Polymorphous band structure model of gapping in the antiferromagnetic and paramagnetic phases of the Mott insulators MnO, FeO, CoO, and NiO

The existence of band gaps in both the antiferromagnetic (AFM) and paramagnetic (PM) phases of the classic NaCl-structure Mott insulators MnO, FeO, CoO, and NiO is traditionally viewed and taught as a manifestation of strong correlation whereby insulation results from electrons moving across the lattice forming states with doubly occupied d orbitals on certain atomic sites and empty d orbitals on other sites. Within such theories, the gap of the AFM and PM phases of these oxides emerges even in the absence of spatial symmetry breaking. The need for such a correlated picture is partially based on the known failure of the commonly used band models for the PM phase that assume for such a spin disordered state the macroscopically averaged NaCl structure, where all transition metal (TM) sites are symmetry-equivalent (a monomorphous description), producing a gapless PM state with zero magnetic moments, in sharp conflict with experiment. Here, we seek to understand the minimum theoretical description needed to capture the leading descriptors of ground state Mott insulation in the classic, 3d monoxide Mott systems—gapping and moment formation in the AFM and PM phase. As noted by previous authors, the spin-ordered AFM phase in these materials already shows in band theory a significant band gap when one doubles the NaCl unit cell by permitting different potentials for transition-metal atoms with different spins. For the spin-disordered PM phase, we allow analogously larger NaCl-type supercells where each TM site can have different spin direction and local bonding environments (i.e., disordered), yet the total spin is zero. Such a polymorphous description has the flexibility to acquire symmetry-breaking energy-lowering patterns that can lift the degeneracy of the d orbitals and develop large on-site magnetic moments without violating the global, averaged NaCl symmetry. Electrons are exchanged between spin-up and spin-down bands to create closed-shell insulating configurations that lend themselves to a single determinental description. It turns out that such a polymorphous description of the structure within the single-determinant, mean-field, Bloch periodic band structure approach (based on DFT+U) allows large on-site magnetic moments to develop spontaneously, leading to significant (1–3 eV) band gaps and large local moments in the AFM and PM phases of the classic NaCl-structure Mott insulators MnO, FeO, CoO, and NiO in agreement with experiment. We adapt to the spin disordered polymorphous configurations the “special quasirandom structure” (SQS) construct known from the theory of disordered substitutional alloys whereby supercell approximants which represent the best random configuration average (not individual snapshots) for finite (64, 216 atoms, or larger) supercells of a given lattice symmetry are constructed. We conclude that the basic features of these paradigmatic Mott insulators can be approximated by the physics included in energy-lowering symmetry broken DFT.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Modeling and Simulation of Fuel Dispersal During the Loss-of-Coolant Accident

This document is the compilation of the milestone portion to a larger end of project NEUP report. The executive summary of the modeling portion is provided below: In the event of cladding rupture during a postulated LOCA in a pressurized water reactor, fuel particles, along with fission gases, can be expelled into the reactor core from the fractured fuel rod, a phenomenon referred to as fuel dispersal. The initial stage of fuel dispersal is strongly influenced by the high-pressure ejection of fuel fragments, the size and geometry of the ruptured cladding, and the depressurization history of the fuel rod during the postulated LOCA transient. Depending on the location of the burst orifice relative to the quench front, the dispersal event represents an intricate three-phase flow and heat transfer phenomenon, where high-temperature fuel particles carried by the fission gases interact with the coolant within the narrow subchannels of the fuel assemblies, inducing localized phase change. Given the unique multiphysics nature of this phenomena, the current study develops a dedicated computational framework to predict the mass distribution and cooling of dispersing fuel particles, facilitating post-accident assessment and management of the fuel assemblies. Considering the scale of nuclear reactor applications, a continuum three-fluid model is proposed for simulating the transport of solids within the reactor core. With high-temperature fuel fragments within the liquid media, nucleation sites inducing phase changes are dispersed within the flow domain. Coupled with the fact that the transient dispersal event occurs on different time scales than other three-phase flow applications, this study derives a time-averaged three-fluid flow model without losing generality. The assumptions regarding the continuum treatment of the solid phase and the modeling of fuel dispersal behavior are incorporated to simplify the governing equations and derive applicable closure relations. The computational validation of the model was conducted using adiabatic experimental results obtained from ongoing research at Oregon State University, focusing on characterizing fuel dispersal behavior during simulated LOCA conditions. Settlement characteristics of the solids, quantified by the probability distribution of equivalent particles, closely matched the probability density functions reported in experimental studies. The transport of fuel particles within a scaled 5 × 5 lattice of a pressurized-water reactor rod bundle geometry was modeled through a two-fluid Eulerian framework. The required boundary conditions were evaluated from the fuel performance code BISON in a postulated large-break LOCA scenario. The modeling framework considered solid fuel particles as granular matter, interacting with the gaseous dry steam phase and fission gases through the governing interfacial momentum exchange between the participating fluids. The simulation results provided the volume fraction of the solids obtained at the bottom surface of the enclosing tank geometry. Postulated LOCA leading to fuel dispersal phenomena involves the strong coupling between fuel thermomechanics, cladding deformation, thermal-hydraulics, and fuel particle transport. Incorporation of such a strong coupling in numerical simulation is performed by coupling the multiphysics solvers. In the case of fuel dispersal, a strong coupled simulation can be performed by coupling the BISON code for fuel performance, the TRACE code for system-level thermal hydraulics, and fuel particle transport in Multiphysics Object-Oriented Simulation Environment (MOOSE). For such intricate infrastructure, the MOOSE Framework eases the data transfer between codes. The recent version of MOOSE has incorporated the Navier-Stokes module for the fluid flow. An exploratory exercise was done to gain familiarity with finite volume capabilities in the MOOSE framework to incorporate the Spalart-Allmaras (SA) turbulence model. New finite-volume and auxiliary kernels were introduced to assemble the SA transport equation, compute turbulent viscosity, and evaluate wall distance and diagnostic turbulence terms, fully integrated with existing Navier-Stokes modules. A turbulent lid-driven cavity at a Reynolds number of approximately 10,000 is used for verification. MOOSE shows the robust solver convergence and produces the turbulent features. But it underpredicts the velocity profile and turbulent quantities, emphasizing the need to develop improved SA near-wall treatments (e.g., low-Re corrections or wall functions) as a key direction for future work.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2019

Simulation of site and topographic effects on ground motion in Los Alamos, NM mesas

Mesas, which consist of an elevated area of land with a flat top and steep cliffs at the sides, are one of the common geological formations present in the Los Alamos region. Previous research has shown that geological formations such as sedimentary canyons can amplify soil response during earthquakes. There have also been parametric studies to understand the response of an idealized and isolated mountain/canyon under inclined plane waves. In this study, a 2-D linear anelastic soil domain, with topography modelled after the Los Alamos region with many mesas and canyons, is considered to understand site-specific topographic effects in the presence of non-isolated topographical features. Various earthquake sources configurations ranging from point sources to finite faults with varying rupture length, dip angles and spatial slip distributions are considered. To isolate the effect of topography, three other soil domains—a homogeneous half-space, homogeneous half-space with mesas and canyons, and a computational domain with just the soil properties from the Los Alamos region on a flat soil domain is also considered. 2-D site-response analyses of these soil domains under earthquake excitation show that the free-field response of the soil can be amplified or de-amplified depending on the topography of the region and the location of the station relative to the fault. These studies also show that even relatively small mesas with height less than 100 m can significantly amplify the response (by a factor of 2 or more), which differ from the much smaller amplification factors (≤1.2) specified by standard building codes such as Eurocode-8 (2000) for topographical features with a similar slope. De-amplifications are also fairly common, especially close to the canyons. The results from this study agree qualitatively with those from the ambient vibration study conducted by Stolte et al. on a mesa from the Los Alamos region. Furthermore, such site-specific studies provide important insights into the variability of the topographic amplification factors within a region of interest. Such knowledge is important in the design of safety-related critical infrastructure located within that region.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

A physics-informed and hierarchically regularized data-driven model for predicting fluid flow through porous media

This paper presents a new deep learning data-driven model for predicting structure dependent pore-fluid velocity fields in rock. The model is based on a Convolutional Auto-Encoder (CAE) artificial neural network capable of learning from image data generated by direct numerical simulations of fluid flow through pore-structures, such as by Lattice Boltzmann or molecular dynamics methods. The main novelty of the model in comparison to previous CAE-based data-driven approaches consists of three parts. The first is a methodology for decomposing the full-domain of the porous media into sub-regions, or “sub-domains”, in order to reduce the overall size of the CAE, batch process the sub-domains in parallel, and enable the CAE to learn local and generalizable nonlinear mappings of pore-fluid velocities. The second consists of embedding the finite difference solutions of the incompressible Navier-Stokes and continuity equations into convolutional layers prior to the CAE in order to provide the CAE with knowledge of fluid dynamics physics (PhyFlow). The third main novelty is that the training of the CAE is regularized with a hierarchical loss function that encourages the learning of fluid flow patterns (in a way similar to ranked modes in principal component analysis), ranking from most to least important. This is shown to increase the stability in learning, reduce over-fitting, and promote interpretability of the CAE neural network layers (HierCAE). The comprehensive new data-driven model, which we call the PhyFlow-HierCAE model, is shown to exhibit improved accuracy and generalizability of flow field predictions over conventional CAE models, attributable to the embedded physical knowledge and the hierarchical regularization, as well as realize orders of magnitude speed-ups in computation times as a surrogate for the direct numerical simulations. Examples of training and forward predictions on unseen pore-structures are provided and evaluated for data from Lattice Boltzmann and molecular dynamics simulations of pore-fluid flow. The model is shown to be a fast and accurate emulator (or “surrogate”) for predicting effective permeability of unseen pore-structures based on learning from relatively small direct numerical simulation datasets.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2016

Generalized Fluid System Simulation Program, Version 6.0

The Generalized Fluid System Simulation Program (GFSSP) is a general purpose computer program for analyzing steady state and time-dependent flow rates, pressures, temperatures, and concentrations in a complex flow network. The program is capable of modeling real fluids with phase changes, compressibility, mixture thermodynamics, conjugate heat transfer between solid and fluid, fluid transients, pumps, compressors, and external body forces such as gravity and centrifugal. The thermofluid system to be analyzed is discretized into nodes, branches, and conductors. The scalar properties such as pressure, temperature, and concentrations are calculated at nodes. Mass flow rates and heat transfer rates are computed in branches and conductors. The graphical user interface allows users to build their models using the 'point, drag, and click' method; the users can also run their models and post-process the results in the same environment. Two thermodynamic property programs (GASP/WASP and GASPAK) provide required thermodynamic and thermophysical properties for 36 fluids: helium, methane, neon, nitrogen, carbon monoxide, oxygen, argon, carbon dioxide, fluorine, hydrogen, parahydrogen, water, kerosene (RP-1), isobutene, butane, deuterium, ethane, ethylene, hydrogen sulfide, krypton, propane, xenon, R-11, R-12, R-22, R-32, R-123, R-124, R-125, R-134A, R-152A, nitrogen trifluoride, ammonia, hydrogen peroxide, and air. The program also provides the options of using any incompressible fluid with constant density and viscosity or ideal gas. The users can also supply property tables for fluids that are not in the library. Twenty-four different resistance/source options are provided for modeling momentum sources or sinks in the branches. These options include pipe flow, flow through a restriction, noncircular duct, pipe flow with entrance and/or exit losses, thin sharp orifice, thick orifice, square edge reduction, square edge expansion, rotating annular duct, rotating radial duct, labyrinth seal, parallel plates, common fittings and valves, pump characteristics, pump power, valve with a given loss coefficient, Joule-Thompson device, control valve, heat exchanger core, parallel tube, and compressible orifice. The program has the provision of including additional resistance options through User Subroutines. GFSSP employs a finite volume formulation of mass, momentum, and energy conservation equations in conjunction with the thermodynamic equations of state for real fluids as well as energy conservation equations for the solid. The system of equations describing the fluid network is solved by a hybrid numerical method that is a combination of the Newton-Raphson and successive substitution methods. The application and verification of the code has been demonstrated through 30 example problems.

Majumdar, A. K.↗

DOE OSTI2019

Characterization of Creep-Fatigue Crack Growth in Alloy 709 and Prediction of Service Lives in Nuclear Reactor Components (Final Report)

This final report summarizes the activities and results that were obtained by the research team working on the project “Characterization of Creep-Fatigue Crack Growth in Alloy 709 and Prediction of Service Lives in Nuclear Reactor Components”, DOE-NEUP Project 15-8623. This project was mainly concerned with the creep-fatigue crack growth characterization of austenitic stainless-steel Fe-20Cr-25Ni (Alloy 709). For this purpose, an array of experimental and computational activities was performed. The main goal of these activities was to describe and predict the crack growth behavior in Alloy 709 under different conditions of applied loading and temperature. Alloy 709 specimens were tested to describe both the uniaxial creep behavior and creep-fatigue crack growth rates at temperatures between 550°C and 700°C. Microstructure and fracture surface analysis was performed using several experimental techniques, and the defining features of crack growth propagation were identified and described. Thermodynamic and diffusion simulations were performed to understand the microstructure evolution of Alloy 709 at elevated temperatures, and to establish an aging schedule relevant for in-service conditions over extended periods. Experimental testing was performed on both as-received and aged Alloy 709 specimens. Two computational methods were developed to predict crack growth rates and remaining lives in specimens loaded under either fatigue of creep-fatigue. The first computational technique was the finite element method, while the second was strip-yield modeling. Both methods relied on the prediction of crack growth rates using the concept of plasticity-induced crack closure. Crack-tip opening loads were computed and used to perform crack growth rate predictions. The computational predictions matched well with the experimental results. The strip-yield model was shown to be an excellent predictive tool not only for crack growth in austenitic SS Alloy 709, but also in 316 SS, martensitic Cr-Mo steels, Ni-based alloys and Al-based alloys. The main conclusion of this study is that Alloy 709 exhibits excellent creep crack growth resistance at temperatures between 550°C and 700°C. In fact, the crack growth resistance of this alloy appears to be higher than that of 316 SS in similar testing conditions. Moreover, when creep loading with hold (dwell) times of 60s or 600s were intercalated every fatigue cycle, the crack growth rates did not change significantly. The conclusion is that the tests performed revealed that the crack growth is insignificant during the creep portion of a loading cycle, as compared with the crack growth during the fatigue portion of the cycle. In general, Alloy 709 shows excellent resistance to creep deformations and creep crack growth up to 700°C.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRSDate not supplied

Probability Bounds Analysis Applied to Multi-Purpose Crew Vehicle Nonlinearity

The Multi-Purpose Crew Vehicle (MPCV) Program Orion vehicle finite element model (FEM) was updated based on a modal test performed by Lockheed Martin. Due to nonlinearity observed in the test results, linear low force level (LL) and high force level (HL) FEMs were developed for use during various Space Launch System (SLS) flight regimes depending on expected forcing levels. Uncertainty models were derived for the combined MPCV and MPCV Stage Adaptor LL and HL Hurty/Craig-Bampton (HCB) components based on the MPCV structural test article Configuration 4 modal test-analysis correlation results. Subsequently, system-level uncertainty quantification analyses were performed using both models for various SLS flight configurations to determine the impact of the nonlinearity on important system metrics. The system metrics included both transfer functions associated with attitude control and dynamic loads associated with aerodynamic buffeting during ascent. In each case, an independent Monte Carlo (MC) analysis was performed, and no attempt was made to combine the results. The Hybrid Parametric Variation (HPV) method was used to develop the LL and HL MPCV HCB uncertainty models. The HPV method provides both parametric and non-parametric components of uncertainty. The non-parametric uncertainty accounts for the difference in model-form between the linearized analytical model and the corresponding linearized component test results in the form of mode shapes and frequencies at that force level. This linear model-form uncertainty is implemented in the HPV method using random matrix theory. However, the HPV uncertainty models developed for the linear LL and HL MPCV components do not account for the nonlinearity in the MPCV. With respect to the linearized models, this nonlinearity is also an uncertainty in model form, but in this case, it must be treated independently as an epistemic uncertainty. It represents a lack of knowledge, in contrast to an aleatory uncertainty due to the randomness of a variable. In the case of an epistemic variable, the true value is unknown, only the interval within which it lies is known. Epistemic uncertainty can be reduced with increased knowledge, while in general, aleatory uncertainty cannot. This work combines the epistemic uncertainty due to the MPCV nonlinearity with the parametric and non-parametric uncertainty within the HPV method using a second order propagation approach. The LL and HL test data is augmented with surrogate test data derived from a nonlinear MPCV representation. The impact of the MPCV nonlinearity on system response statistics is determined using a series of cumulative distribution functions in the form of a horsetail plot, or p-box. This results in an interval of probabilities for a specific response value, or an interval of response values at a specific probability.

Daniel C Kammer↗

DOE OSTI2021

Implicit highly-coupled single-ion Hall-MHD formulation for hybrid particle-in-cell codes

The rudiments of a particle-based single-fluid two-temperature magnetohydrodynamic (MHD) algorithm have been outlined in Thoma et al. (2013). The extension of this algorithm to include the effect of Hall physics is described in this paper. An implicit leapfrog version of the algorithm, which allows timesteps large compared to the resistive decay time and other relevant timescales, has recently been added to a hybrid particle-in-cell code. In standard MHD the Hall term in the generalized Ohm’s law can often be neglected when the Hall parameter is small. This term must, however, be retained in regimes where it is non-negligible. The retention of displacement current in Maxwell’s equations avoids the numerical difficulties associated with the whistler mode, which are encountered in standard explicit Hall-MHD codes, and allows the algorithm to be incorporated into hybrid particle-in-cell codes, for which particles may migrate from a kinetic to fluid to MHD description based upon local ambient plasma conditions. A highly-coupled implicit Hall-MHD formalism is presented, in which displacement current can either be retained or neglected. Even when displacement current is neglected, the highly-coupled implicit formalism avoids the restrictive timesteps for the whistler mode in explicit Hall-MHD codes. A comparison of numerical and analytic dispersion analysis demonstrates the feasibility of this approach and establishes relevant constraints to assure numerical stability. The implementation of the algorithm is described, and test simulation results in 1D and 2D in both linear and nonlinear regimes are presented.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Injection current dependences of electroluminescence transition energy in InGaN/GaN multiple quantum wells light emitting diodes under pulsed current conditions

Injection current dependences of electroluminescence transition energy in blue InGaN/GaN multiple quantum wells light emitting diodes (LEDs) with different quantum barrier thicknesses under pulsed current conditions have been analyzed taking into account the related effects including deformation caused by lattice strain, quantum confined Stark effects due to polarization field partly screened by carriers, band gap renormalization, Stokes-like shift due to compositional fluctuations which are supposed to be random alloy fluctuations in the sub-nanometer scale, band filling effect (Burstein-Moss shift), and quantum levels in finite triangular wells. The bandgap renormalization and band filling effect occurring at high concentrations oppose one another, however, the renormalization effect dominates in the concentration range studied, since the band filling effect arising from the filling in the tail states in the valence band of quantum wells is much smaller than the case in the bulk materials. In order to correlate the carrier densities with current densities, the nonradiative recombination rates were deduced experimentally by curve-fitting to the external quantum efficiencies. The transition energies in LEDs both with 15 nm quantum barriers and 5 nm quantum barriers, calculated using full strengths of theoretical macroscopic polarization given by Barnardini and Fiorentini [Phys. Status Solidi B 216, 391 (1999)] are in excellent accordance with experimental results. The LED with 5 nm barriers has been shown to exhibit a higher transition energy and a smaller blue shift than those of LED with 15 nm barriers, which is mainly caused by the smaller internal polarization field in the quantum wells.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Unsteady fluid flow in a slightly curved pipe: A comparative study of a matched asymptotic expansions solution with a single analytical solution

The present work is motivated by the fact that blood flow in the aorta and the main arteries is governed by large finite values of the Womersley number α and for such values of α there is not any analytical solution in the literature. The existing numerical solutions, although accurate, give limited information about the factors that affect the flow, whereas an analytical approach has an advantage in that it can provide physical insight to the flow mechanism. Having this in mind, we seek analytical solution to the equations of the fluid flow driven by a sinusoidal pressure gradient in a slightly curved pipe of circular cross section when the Womersley number varies from small finite to infinite values. Initially the equations of motion are expanded in terms of the curvature ratio δ and the resulting linearized equations are solved analytically in two ways. In the first, we match the solution for the main core to that for the Stokes boundary layer. This solution is valid for very large values of α. In the second, we derive a straightforward single solution valid to the entire flow region and for 8 ≤ α < ∞, a range which includes the values of α that refer to the physiological flows. Each solution contains expressions for the axial velocity, the stream function, and the wall stresses and is compared to the analogous forms presented in other studies. The two solutions give identical results to each other regarding the axial flow but differ in the secondary flow and the circumferential wall stress, due to the approximations employed in the matched asymptotic expansion process. The results on the stream function from the second solution are in agreement with analogous results from other numerical solutions. The second solution predicts that the atherosclerotic plaques may develop in any location around the cross section of the aortic wall unlike to the prescribed locations predicted by the first solution. In addition, it gives circumferential wall stresses augmented by approximately 100% with respect to the matched asymptotic expansions, a factor that may contribute jointly with other pathological factors to the faster aging of the arterial system and the possible malfunction of the aorta.

42 ENGINEERING↗

NASA NTRS1999

The Effect of Penetration Depth on Thermal Contrast of NDT by Thermography

Nondestructive evaluation by Thermography (TNDE) is generally classified into two categories, the passive approach and the active approach. The passive approach is usually performed by measuring the natural temperature difference between the ambient and the material or structure to be tested. The active approach, on the other hand, requires the application of an external energy source to stimulate the material for inspection. A laser, a heater, a hot air blower, a high power thermal pulse, mechanical, or electromagnetic energy may provide the energy sources. For the external heating method to inspect materials for defects and imperfection at ambient temperature, a very short burst of heat can be introduced to one of the surfaces or slow heating of the side opposite to the side being observed. Due to the interruption of the heat flow through the defects, the thermal images will reveal the defective area by contrasting against the surrounding good materials. This technique is called transient Thermography, pulse video Thermography, or thermal wave imaging. As an empirical rule, the radius of the smallest defect should be at least one to two times larger than its depth under the surface. Thermography is being used to inspect void, debond, impact damage, and porosity in composite materials. It has been shown that most of the defects and imperfection can be detected. However, the current method of inspection using thermographic technique is more of an art than a practical scientific and engineering approach. The success rate of determining the defect location and defect type is largely depend on the experience of the person who operates thermography system and performs the inspection. The operator has to try different type of heat source, different duration of its application time, as well as experimenting with the thermal image acquisition time and interval during the inspection process. Further-more, the complexity of the lay-up and structure of composites makes it more difficult to determine the optimal operating condition for revealing the defects. In order to develop an optimal thermography inspection procedure, we must understand the thermal behavior inside the material subjected to transient heat in order to interpret the thermal images correctly. Fabrication of finite element models of characteristic defects in composite materials subjected to transient heat will enable the development of appropriate procedure for thermography inspection. Design of phantom defects could be modeled and behavior characterized prior to physically building these test parts. Since production of phantom test parts can be very time consuming and laborious, it is important to design good representative defects.

Chu, Tsuchin Philip↗

DOE OSTI2021

A solution framework for linear PDE-constrained mixed-integer problems

Abstract We present a general numerical solution method for control problems with state variables defined by a linear PDE over a finite set of binary or continuous control variables. We show empirically that a naive approach that applies a numerical discretization scheme to the PDEs to derive constraints for a mixed-integer linear program (MILP) leads to systems that are too large to be solved with state-of-the-art solvers for MILPs, especially if we desire an accurate approximation of the state variables. Our framework comprises two techniques to mitigate the rise of computation times with increasing discretization level: First, the linear system is solved for a basis of the control space in a preprocessing step. Second, certain constraints are just imposed on demand via the IBM ILOG CPLEX feature of a lazy constraint callback. These techniques are compared with an approach where the relations obtained by the discretization of the continuous constraints are directly included in the MILP. We demonstrate our approach on two examples: modeling of the spread of wildfire and the mitigation of water contamination. In both examples the computational results demonstrate that the solution time is significantly reduced by our methods. In particular, the dependence of the computation time on the size of the spatial discretization of the PDE is significantly reduced.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

SAM Plug-in Development (Phase I Final Report)

The DOE Office of Nuclear Energy (NE) has created an extensive set of advanced modeling and simulation tools for nuclear engineering analysis. The advanced capabilities of these newer analysis codes require more in-depth training, skills, and knowledge in order to effectively utilize them for the design, analysis, and licensing of advanced nuclear systems and experiments. A high learning curve for inexperienced users may deter organizations from incorporating these tools into their internal processes. This project involved development of a plug-in to the Symbolic Nuclear Analysis Package (SNAP) for the System Analysis Module (SAM) tool. SAM is an advanced system analysis tool for reactor transient analyses being developed at Argonne National Laboratory under the U.S. DOE Office of Nuclear Energy’s Nuclear Energy Advanced Modeling and Simulation (NEAMS) program. SAM utilizes an object-oriented application framework (MOOSE), and its underlying meshing and finite-element library (libMesh) and linear and non-linear solvers (PETSc), to leverage modern advanced software environments and numerical methods. SNAP provides a highly flexible framework for creating, modifying and documenting input for engineering analysis codes such as SAM as well as extensive functionality for submitting, monitoring, and interacting with the codes through an intuitive graphical user interface (GUI). The common user interface provided by SNAP minimizes the learning curve for engineers starting with a new analysis code and provides an intuitive framework for transitioning between different analysis codes. SNAP provides a powerful but intuitive interface to facilitate access to advanced modeling and simulation tools for inexperienced users. Unlike many “form based” GUI’s, SNAP maps each engineering code’s component input to an internal database which manages all component input parameters along with component interconnections. This level of abstraction permits SNAP to support several advanced capabilities such as renodalization, model validation and consistency checks, embedded documentation, model notebook generation, data ownership and reviewer tracking, and variable assignment for inputs to name a few. SNAP includes a built-in Python interpreter and is interfaced to several commercial and open source packages including CPython, MATLAB/OCTAVE, Microsoft Office, Open Office, and SANDIA’s DAKOTA package which provides Uncertainty Quantification analysis through the SNAP plug-ins. Phase I of this project involved development a fully functional basic SAM plug-in to SNAP. This plug-in provides the ability to import existing models, graphically construct, edit and submit models using SNAP’s extensive functionality.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2016

Surface and finite size effects impact on the phase diagrams, polar, and dielectric properties of (Sr,Bi)Ta{sub 2}O{sub 9} ferroelectric nanoparticles

In the framework of the thermodynamic approach Landau-Ginzburg-Devonshire (LGD) combined with the equations of electrostatics, we investigated the effect of polarization surface screening on finite size effects of the phase diagrams, polar, and dielectric properties of ferroelectric nanoparticles of different shapes. We obtained and analyzed the analytical results for the dependences of the ferroelectric phase transition temperature, critical size, spontaneous polarization, and thermodynamic coercive field on the shape and size of the nanoparticles. The pronounced size effect of these characteristics on the scaling parameter, the ratio of the particle characteristic size to the length of the surface screening, was revealed. Also our modeling predicts a significant impact of the flexo-chemical effect (that is a joint action of flexoelectric effect and chemical pressure) on the temperature of phase transition, polar, and dielectric properties of nanoparticles when their chemical composition deviates from the stoichiometric one. We showed on the example of the stoichiometric nanosized SrBi{sub 2}Ta{sub 2}O{sub 9} particles that except the vicinity of the critical size, where the system splitting into domains has an important role, results of analytical calculation of the spontaneous polarization have a little difference from the numerical ones. We revealed a strong impact of the flexo-chemical effect on the phase transition temperature, polar, and dielectric properties of Sr{sub y}Bi{sub 2+x}Ta{sub 2}O{sub 9} nanoparticles when the ratio Sr/Bi deviates from the stoichiometric value of 0.5 within the range from 0.35 to 0.65. From the analysis of experimental data, we derived the parameters of the theory, namely, the coefficients of expansion of the LGD functional, the contribution of flexo-chemical effect, and the length of the surface screening.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Pin-by-Pin Core Calculation with an NEM-Based Two-Level Hybrid CMFD Algorithm

In the near future, systematic pin-by-pin core calculations are expected to provide a high level of accuracy. These are being developed in pursuit of high-fidelity tools for analyzing the reactor configurations. One such tool that has recently gained significant attention is the pin-by-pin core calculation via local-global iteration using nonlinear acceleration scheme, such as the One-Node CMFD (Coarse-Mesh Finite Difference) nonlinear algorithm. The One-Node CMFD method uses two correction factors to preserve the interface current, in contrast to the one correction term employed by conventional nonlinear iterative methods such as that proposed by Kord. S. Smith. These correction factors are updated with surface flux and net current which are obtained from a high order local problem. With two correction factors, One-Node CMFD can reduce computing time of local FMFD (Fine-Mesh Finite Difference) as it nonlinearly couples the CMFD and FMFD methods in global-local iterations. Nonetheless, very small mesh size is still required and it consequently requires long computing time for high accuracy. As such, a more flexible approach is needed to address this challenge. This paper presents one such possible approach named the hCMFD (Hybrid CMFD) method. In this method, One-Node CMFD is used to solve the global problem, while Two-Node NEM (Nodal Expansion Method) CMFD replaces FMFD as the solver for the local problem. In this paper, two kinds of CMFD methods has been simultaneously implemented for a global-local nonlinear iteration in order to do pin-by-pin heterogeneous reactor calculations. The global problem is solved by a one-node CMFD which uses two correction factors, while the local fixed-source problem is solved by the conventional two-node NEM CMFD which use one correction factor on a surface. From solution of the global eigenvalue problem, incoming partial current is obtained and it is used as boundary condition of the local fixed-source problems. It has been shown that over 99% of the whole calculations can be done in parallel with the new CMFD method for 2-D problems and the algorithm can be easily parallelized by using the OpenMP parallel scheme. The hCMFD method will enable an efficient pin-by-pin reactor analysis since a very efficient parallel calculation is possible with the hCMFD method. In future works, the hCMFD method will be extended to three-dimensional reactor problem. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2019

Stratified manifold of quantum states, actions of the complex special linear group

We review the geometry of the space of quantum states S(H) of a finite-level quantum system with Hilbert space H from a group-theoretical point of view. This space carries two stratifications generated by the action of two different Lie groups, namely, the special unitary group SU(H) and its complexification SL(H), the complex special linear group. A stratum of the stratification generated by SU(H) is composed of isospectral states, that is, density operators with the same spectrum. A stratum of the stratification generated by SL(H) is composed of quantum states with the same rank. We prove that on every submanifold of isospectral quantum states there is also a canonical left action of SL(H) which is related with the canonical Kähler structure on isospectral quantum states. The fundamental vector fields of this SL(H)-action are divided into Hamiltonian and gradient vector fields. The former give rise to invertible maps on S that preserve the von Neumann entropy and the convex structure of S(H), while the latter give rise to invertible maps on S(H) that preserve the von Neumann entropy but not the convex structure of S(H). A similar decomposition is given for the fundamental vector fields of the SL(H)-action generating the stratification of S(H) into manifolds of quantum states with the same rank. However, in this case, the gradient vector fields preserve the rank but do not preserve entropy. Finally, some comments on multipartite quantum systems are made, and it is proved that the sets of product states of a multipartite quantum system are homogeneous manifolds for the local action of the complex special linear group associated with the partition.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Determination of crystal growth rates during rapid solidification of polycrystalline aluminum by nano-scale spatio-temporal resolution in situ transmission electron microscopy

In situ investigations of rapid solidification in polycrystalline Al thin films were conducted using nano-scale spatio-temporal resolution dynamic transmission electron microscopy. Differences in crystal growth rates and asymmetries in melt pool development were observed as the heat extraction geometry was varied by controlling the proximity of the laser-pulse irradiation and the associated induced melt pools to the edge of the transmission electron microscopy support grid, which acts as a large heat sink. Experimental parameters have been established to maximize the reproducibility of the material response to the laser-pulse-related heating and to ensure that observations of the dynamical behavior of the metal are free from artifacts, leading to accurate interpretations and quantifiable measurements with improved precision. Interface migration rate measurements revealed solidification velocities that increased consistently from ∼1.3 m s{sup −1} to ∼2.5 m s{sup −1} during the rapid solidification process of the Al thin films. Under the influence of an additional large heat sink, increased crystal growth rates as high as 3.3 m s{sup −1} have been measured. The in situ experiments also provided evidence for development of a partially melted, two-phase region prior to the onset of rapid solidification facilitated crystal growth. Using the experimental observations and associated measurements as benchmarks, finite-element modeling based calculations of the melt pool evolution after pulsed laser irradiation have been performed to obtain estimates of the temperature evolution in the thin films.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Time-dependent THMC properties and microstructural evolution of damaged rocks in excavation damage zone

Modeling coupled thermo-hydro-mechanical-chemical (THMC) processes in host rocks near high-level nuclear waste (HLW) repositories at various time scales is an extremely challenging task. The current study integrates experimental, theoretical, and numerical methods in assessing the evolution of excavation damage zone (EDZ) over time and its implication on the long-term migration of hazardous species. Argillite and rock salt and are the focus of this study. The first part of the report presents a novel time-dependent directional microcrack damage theory for generic brittle rocks. It features detailed statistical description of the microcracks within a damaged solid, permitting a direct upscaling of microscale processes such as crack growth kinetics, crack closure/opening, sliding friction to explain the macroscopic creep, nonlinear elasticity, shear dilation, and loading-unloading hysteresis. This provides a basic platform for describing the anisotropic mechanical and transport properties of damaged rocks during excavation and subsequent THMC loadings. The model is validated and numerically implemented to Finite Element (FE) package ABAQUS through the user-defined material (UMAT) interface and have demonstrated great potential in resolving the time-dependent and anisotropic evolution of damage in the EDZ. The second part of the report presents a multi-scale experimental effort in characterizing the thermal, hydraulic, and mechanical properties of Mancos shale and Avery Island salt. For the Mancos shale, triaxial compression tests are performed at different confining pressures and temperatures to probe its thermomechanical properties relevant to HLW repositories. The obtained stress-strain data are interpreted using the proposed directional damage theory. Post-test specimens are subjected to gas permeability tests to reveal the correlation between permeability and the degree of microcracking. At microscale, temperature-controlled nanoindentation tests are performed and found a linear correlation between fracture toughness and elastic modulus from 25°C to 300°C. For Avery Island salt, we have designed and manufactured a novel relative-humidity controlled uniaxial creep device. Long-term creep tests at low stresses (< 5 MPa) are performed at different levels of relative humidity (RH). Besides confirming the much higher creep rates as one would expect through extrapolating the high-stress creep data, the results reveal that the steady-state creep rate of rock salt is strongly dependent on the ambient RH, an aspect that is often neglected in the literature. Both behaviors can be attributed to the pressure-solution creep mechanism which dominates at low stress and high RH levels. The third part of the report explores a set of numerical strategies in modeling the THMC behavior of porous geomaterials. A fully implicit, monolithic FE solution that can flexibly interface with different material models and coupling mechanisms for THMC problems is developed and verified through the ABAQUS user-defined element (UEL) interface. The scheme is used to study the THM response of a hypothetical HLW storage site with reference to an existing in-situ heater test. Strategies for integrating the UEL and the microcrack UMAT are suggested. Another numerical endeavor of this study is to implement a higher-order asymptotic homogenization method to account for the heterogeneous porous structures. The same method is then extended to perform microstructure-informed thermo-mechanical modeling of generalized continua. The above outcomes of this project provide a strong thrust towards enhancing the fundamental understanding and modeling capability of the long-term evolution of host rocks in EDZ, thus helping achieve the design goal of 1-million-year isolation of high-level nuclear wastes.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗