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A moment-based kinetic theory model for polydisperse gas–particle flows

Starting from a generalized population balance equation and the Boltzmann–Enskog collision model for hard spheres, a kinetic theory model for polydisperse gas–particle flows is introduced. Here, polydispersity results from spherical particles with the same material density but different diameters. The particle size distribution (PSD) of the particles is allowed to evolve in space and time due to physical processes such as mixing. In order to treat a continuous PSD, the particle-phase model is formulated in terms of the moments of the PSD, and velocity moments conditioned on the particle size. Velocity moments up to second order are included, resulting in transport equations for the mass, momentum and granular temperature, all conditioned on the particle size. In the numerical implementation, the PSD is represented using quadrature-based moment methods (QBMM). With QBMM, a continuous PSD can be treated using a relatively small number of moments as compared to class or sectional methods. In this work, a realizable numerical algorithm for solving the moment system in a finite-volume code is proposed, valid for dilute systems wherein frictional forces are negligible. The ability of the proposed model to describe polydisperse gas–particle systems is demonstrated using cluster-induced turbulence and riser flow.

42 ENGINEERING↗

Poincaré beams from a free electron laser

Poincaré beams are light beams that have spatially inhomogeneous polarization structure that spans a finite portion of the Poincaré sphere. This feature bestows the beams with intriguing topological properties and has led to a surge in research on their fundamental characteristics, their controlled generation and on emerging applications. Here we present an experimental demonstration of a Poincaré beam generated in the extreme ultraviolet (16.7 nm) at the FERMI free electron laser (FEL). The ‘star’ type Poincaré beam is generated by exploiting the phase and intensity structure intrinsic to FEL radiation without relying on optical elements. Here, we controlled the spatial polarization distribution through a precise overlap and power balance between two FEL pulses, each with different transverse phase distributions and orthogonal circular polarizations. The spatial polarization structure was mapped in detail and shows extensive coverage of the Poincaré sphere, in agreement with analytic predictions. This method of in situ Poincaré beam production in FELs enables straightforward flexibility in the orientation and balance of polarization states, and can readily be extended to other vector beams and to shorter wavelengths enabling novel science applications in modern light sources.

Morgan, Jenny [SLAC National Accelerator Laborator↗

Brittle failure analysis and modeling of high-burnup PWR fuel cladding alloys

The aim of this research is the development of methods for predicting mechanical behavior and identification of limiting conditions to prevent brittle failure of high-burnup (HBU) pressure water reactor (PWR) fuel cladding alloys. A finite element (FE) model of the ring compression test (RCT) was created to analyze the failure behavior of zirconium-based alloys with radial hydrides during the RCT. An elastic-plastic material model describes the zirconium alloy. The stress-strain curve needed for the elastic-plastic material model was derived by inverse finite element analyses. Cohesive zone modeling is used to reproduce sudden load drops during RCT loading. Based on the failure mechanism in non-irradiated ZIRLO (R) claddings, a micro-mechanical model was developed that distinguishes between brittle failure along hydrides and ductile failure of the zirconium matrix. Two different cohesive laws representing these types of failure are present in the same cohesive interface. The key differences between these constitutive laws are the cohesive strength, the stress at which damage initiates, and the cohesive energy, which is the damage energy dissipated by the cohesive zone. Statistically generated matrix-hydride distributions were mapped onto the cohesive elements and simulations with focus on the first load drop were performed. Computational results are in good agreement with the RCT results conducted on high-burnup M5 (R) samples. It could be shown that crack initiation and propagation strongly depend on the specific configuration of hydrides and matrix material in the fracture area.

Simbruner, Kai↗

Sierra/RKPM: Current State and Applications

The Reproducing Kernel Particle Method (RKPM), a meshfree method, has been implemented in Sandia's Sierra/Solid Mechanics in a collaboration between Sandia and the University of California San Diego's Center for Extreme Events Research (UCSD/CEER). Meshfree methods, like RKPM, have an advantage over mesh-based methods, like the Finite Element Method (FEM), in applications where achieving or maintaining a quality mesh becomes burdensome or impractical. For example, using FEM for problems with very large deformations will result in poor element Jacobians which causes problems with the parametric mapping. RKPM constructs the approximation functions in the physical domain, circumventing the parametric mapping issue. Also, reconstructing the approximation functions at very large deformations is straight-forward. RKPM has an advantage over traditional meshfree methods such as Smoothed-Particle Hydrodynamics (SPH) due to its ability to reproduce linear or higher-order functions exactly. This removes the tensile instabilities that are present in SPH and allows preservation of angular momentum. The point of this memo is to explore the capabilities and limitations of the current implementation by testing it on three different applications: 1) a quasi-static ductile shearing problem 2) a dynamic concrete panel perforation problem and 3) a set of dynamic metal panel perforation problems. In summary, areas where RKPM appears to be a promising alternative to current methods have been identified. Also, outstanding inefficiencies and issues (bugs) with code are noted, ways to improve the capabilities using material from literature are mentioned and areas deserving of new research are highlighted.

42 ENGINEERING↗

Modeling Nonlinear Energy Dissipation of the Ministack Assembly

An assessment of two methodologies used at Sandia National Laboratories to model mechanical interfaces is performed on the Ministack finite element model. One method uses solid mechanics models to model contacting surfaces with Coulomb frictional contact to capture the physics. The other, termed the structural dynamics reduced order model, models the interface with a simplified whole joint model using four-parameter Iwan elements. The solid mechanics model resolves local kinematics at the interface while the simplified structural dynamics model is significantly faster to simulate. One of the current challenges to using the whole joint model is that it requires calibration to data. A novel approach is developed to calibrate the reduced structural dynamics model using data from the solid mechanics model to match the global dynamics of the system. This is achieved by calibrating to amplitude dependent frequency and damping of the system modes, which are estimated using three different approaches.

42 ENGINEERING↗

[Presentation Slides] Code-to-Code Benchmark Study for Thermal Stress Modeling and Preliminary Analysis of the High-temperature Single Heat-Pipe Experiment

In the heat-pipe-cooled microreactor, heat pipes remove heat from the reactor core as a passive heat-transfer device, so the fluid circulation is not required for cooling, which can substantially simplify the overall reactor design. However, given the extremely high temperatures in the core region and potentially large temperature gradients across the structure materials, thermal stresses need to be well-analyzed to ensure structural integrity during normal operations and accident scenarios. This presentation slides discuss finite element method-based thermal-stress analysis for the high-temperature single heat-pipe test article in the Single Primary Heat Extraction and Removal Emulator (SPHERE) facility at Idaho National Laboratory (INL), using two commercial software packages, Abaqus and Star-CCM+. A code-to-code benchmark study was performed to crosscheck the model setup and capability of each code and to gain preliminary insights into the potential thermal stress concerns from the current experimental setup. It is observed the significant thermal stresses happen at the inner surface of the heat pipe hole surrounded by electric heaters where the largest temperature gradients appear. The temperature fields have good agreements between Abaqus and Star-CCM+, while the induced thermal stresses show modest deviations probably due to differences of meshing engines used in these two codes. It is found that the local maximum thermal stresses may reach close to the ultimate tensile strength and yield strength of structural material depending on the heater power. Ultimately, the coupled thermal-structural analysis will help guide the current experimental plan and ensure the facility safety for future experimental study.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

A Multi-Scale Computational Platform for Predictive Modeling of Corrosion in Al-Steel Joints (Final Report)

The research team proposed to develop innovative multi-scale models to predict corrosion and the resulting mechanical performances in aluminum-steel joints. The methods of joining considered are resistance spot welding, self-piercing riveting, and rivet-welding, all suitable for mass production applications. The multi-scale models integrate high throughput first-principle calculations based on density functional theory (DFT), high throughput calculation of phase diagrams (CALPHAD) modeling, and finite element method (FEM) simulations. These models are to be validated through laboratory experiments. Furthermore, the models are available as open source so as to enable scientists and engineers in the community to adapt and contribute to the development and application. The approaches rely on the research team’s extensive experience on the prediction of properties of individual phases at finite temperatures and variable compositions through DFT calculations, and our broad expertise on dissimilar material joining and their corrosion. The proposed computational framework enables high throughput computations for improved predictions of corrosion and the associated mechanical performance in dissimilar material joints, resulting in significant reduction in computational time needed by the current state-of-the-art methods. With the participation of researchers from three universities, an auto manufacturer, two manufacturing technology/equipment suppliers, and a software developer/vendor, the interdisciplinary research team applies the technical development on both phase-based modeling and laboratory experiments into the automobile body joining processes for validation and technology demonstration. The global cost of corrosion was estimated at about 3.4% of the global GDP in 2013. By using available corrosion control practices, it is estimated a saving between 15-35% of the cost of corrosion. In the U.S., more than $276 billion is spent repairing corrosion damage. Prediction of the corrosion and its impact on performance of the dissimilar material joints is critical for reducing the massive number of the current corrosion-based recalls for automobiles. Thus, the project goal is to develop models to enable predictive maintenance and end-of-life planning of multi-metal joints with risk of corrosion under different conditions such as exposure to high temperatures in summer and salt solutions in winter, quantified through its pH. An academia-industry consortium led by the University of Michigan and including Pennsylvania State University, University of Illinois Urbana-Champaign, University of Georgia, General Motors Company, Livermore Software Technology Corporation, and Optimal Process Technologies, LLC. created multi-scale models for prediction of corrosion in aluminum-steel joint structures such of them used in vehicle subassemblies – chassis and transmission systems. Starting from the first principle calculations, the team developed mathematical and data-driven models to predict the metallic components, which are formed during joining of two metals, for example aluminum and steel - a lightweight multilateral system which is currently used in more than 60% car bodies. These models were used for simulating chemical reactions that are happening when the joining metallic components are exposed to high temperatures and different pH values. The team was able to predict how the corrosion installs on the metallic components and how they lead to a sudden failure of components in cars. Newly developed machine learning algorithms combining Science, Technology, Engineering and Math disciplines, advanced finite element simulation and experimental validations have been integrated in a platform for prediction of the corrosion evolution and prediction the failure of joints under mechanical loadings and fatigue. Moreover, based on machine learning and inverse analysis, the team proposed solutions for designing new metallic alloys less susceptible to corrosion when joining multi-material assembles. An average of 4% error compared with experiments was achieved for the most common joints that are used in vehicle subassemblies.

36 MATERIALS SCIENCE↗

Thermal stitching: Combining the advantages of different quantum fermion solvers

For quantum fermion problems, many accurate solvers are limited by the temperature regime in which they can be usefully applied. The Mermin theorem implies the uniqueness of an effective potential from which both the exact density and free energy at a target temperature can be found, via a calculation at a different, reference temperature. We derive exact expressions for both the potential and the free energy in such a calculation and introduce three controllable approximations that reduce the cost of such calculations. In conclusion, we illustrate the effective potential and its free energy, and test the approximations, on the asymmetric two-site Hubbard model at finite temperature.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Assessing the reliability of fast Fourier transform-based crystal plasticity simulations of a polycrystalline material near a crack tip

Crystal plasticity simulations enable a physically-based description of the micromechanical fields associated with microstructural attributes in polycrystalline materials. Fast Fourier transforms implementation of crystal plasticity (CP-FFT) in periodic unit cells offers increased computational efficiency compared to traditional finite element methods (CP-FEM). Albeit, questions may arise concerning the accuracy of the CP-FFT approach given its underlying spectral framework, specifically in regards to: potential artifacts due to violating the traction-free conditions at internal free surface within the unit cell, Gibbs phenomenon near regions with sharp changes in local mechanical properties, and representation of free surfaces under the constraints imposed by the requirement of periodicity of the unit cell. This paper presents a custom massively parallelized implementation of CP-FFT. A direct comparison of simulation results for polycrystalline deformation near a crack in a Ti55531 alloy is presented between CP-FEM and CP-FFT. The micromechanical fields and slip system level values are quantified and are similar between the two methods. Up to 10% difference in the stress fields is reported at the crack tip and this value dissipates moving away from the crack tip after 5 voxels (7 µm). In conclusion, the results point towards the reliable use of CP-FFT simulations to model polycrystalline deformation with caveats based on the treatment of the discussed artifacts.

36 MATERIALS SCIENCE↗

Energy density matrix formalism for interacting quantum systems: a quantum Monte Carlo study

We develop an energy density matrix that parallels the one-body reduced density matrix (1RDM) for many-body quantum systems. Just as the density matrix gives access to the number density and occupation numbers, the energy density matrix yields the energy density and orbital occupation energies. The eigenvectors of the matrix provide a natural orbital partitioning of the energy density while the eigenvalues comprise a single particle energy spectrum obeying a total energy sum rule. For mean-field systems the energy density matrix recovers the exact spectrum. When correlation becomes important, the occupation energies resemble quasiparticle energies in some respects. We explore the occupation energy spectrum for the finite 3D homogeneous electron gas in the metallic regime and an isolated oxygen atom with ground state quantum Monte Carlo techniques imple- mented in the QMCPACK simulation code. The occupation energy spectrum for the homogeneous electron gas can be described by an effective mass below the Fermi level. Above the Fermi level evanescent behavior in the occupation energies is observed in similar fashion to the occupation numbers of the 1RDM. A direct comparison with total energy differences demonstrates a quantita- tive connection between the occupation energies and electron addition and removal energies for the electron gas. For the oxygen atom, the association between the ground state occupation energies and particle addition and removal energies becomes only qualitative. The energy density matrix provides a new avenue for describing energetics with quantum Monte Carlo methods which have traditionally been limited to total energies.

density matrix↗

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↗

Positivity Limiters for Filtered Spectral Approximations of Linear Kinetic Transport Equations

We analyze the properties and compare the performance of several positivity limiters for spectral approximations with respect to the angular variable of linear transport equations. It is well-known that spectral methods suffer from the occurrence of (unphysical) negative spatial particle concentrations due to the fact that the underlying polynomial approximations are not always positive at the kinetic level. Positivity limiters address this defect by enforcing positivity of the polynomial approximation on a finite set of preselected points. With a proper PDE solver, they ensure positivity of the particle concentration at each step in a time integration scheme. We review several known positivity limiters proposed in other contexts and also introduce a modification for one of them. We give error estimates for the consistency of the positive approximations produced by these limiters and compare the theoretical estimates to numerical results. We then solve two benchmark problems with these limiters, make qualitative and quantitative observations about the solutions, and then compare the efficiency of the different limiters.

97 MATHEMATICS AND COMPUTING↗

Application of scanning angle Raman spectroscopy for determining the location of buried polymer interfaces with tens of nanometer precision

In this study, near-infrared scanning angle (SA) Raman spectroscopy was utilized to determine the interface location in bilayer films (a stack of two polymer layers) of polystyrene (PS) and polycarbonate (PC). Finite-difference-time-domain (FDTD) calculations of the sum square electric field (SSEF) for films with total bilayer thicknesses of 1200–3600 nm were used to construct models for simultaneously measuring the film thickness and the location of the buried interface between the PS and PC layers. Samples with total thicknesses of 1320, 1890, 2300, and 2750 nm and varying PS/PC interface locations were analyzed using SA Raman spectroscopy. Comparing SA Raman spectroscopy and optical profilometry measurements, the average percent difference in the total bilayer thickness was 2.0% for films less than ~2300 nm thick. The average percent difference in the thickness of the PS layer, which reflects the interface location, was 2.5% when the PS layer was less than ~1800 nm. SA Raman spectroscopy has been shown to be a viable, non-destructive method capable of determining the total bilayer thickness and buried interface location for bilayer samples consisting of thin polymer films with comparable indices of refraction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Performance analysis of a finite radon transform in OFDM system under different channel models

In this paper, a class of discrete Radon transforms namely Finite Radon Transform (FRAT) was proposed as a modulation technique in the realization of Orthogonal Frequency Division Multiplexing (OFDM). The proposed FRAT operates as a data mapper in the OFDM transceiver instead of the conventional phase shift mapping and quadrature amplitude mapping that are usually used with the standard OFDM based on Fast Fourier Transform (FFT), by the way that ensure increasing the orthogonality of the system. The Fourier domain approach was found here to be the more suitable way for obtaining the forward and inverse FRAT. This structure resulted in a more suitable realization of conventional FFT- OFDM. It was shown that this application increases the orthogonality significantly in this case due to the use of Inverse Fast Fourier Transform (IFFT) twice, namely, in the data mapping and in the sub-carrier modulation also due to the use of an efficient algorithm in determining the FRAT coefficients called the optimal ordering method. The proposed approach was tested and compared with conventional OFDM, for additive white Gaussian noise (AWGN) channel, flat fading channel, and multi-path frequency selective fading channel. The obtained results showed that the proposed system has improved the bit error rate (BER) performance by reducing inter-symbol interference (ISI) and inter-carrier interference (ICI), comparing with conventional OFDM system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Frequency- and Time-Domain Methods in Soil-Structure Interaction Analysis

Soil-structure interaction (SSI) analysis in the nuclear industry is currently performed using linear codes that function in the frequency domain. There is a consensus that these frequency-domain codes give reasonably accurate results for low-intensity ground motions that result in almost linear response. For higher intensity ground motions, which may result in nonlinear response in the soil, structure or at the vicinity of the foundation, the adequacy of frequency-domain codes is unproven. Nonlinear analysis, which is only possible in the time domain, is theoretically more appropriate in such cases. These methods are available but are rarely used due to the large computational requirements and a lack of experience with analysts and regulators. This paper presents an assessment of the linear frequency-domain code, SASSI, which is widely used in the nuclear industry, and the time-domain commercial finite-element code, LS-DYNA, for SSI analysis. The assessment involves benchmarking the SSI analysis procedure in LS-DYNA against SASSI for linearly elastic models. After affirming that SASSI and LS-DYNA result in almost identical responses for these models, they are used to perform nonlinear SSI analyses of two structures founded on soft soil. An examination of the results shows that, in spite of using identical material properties, the predictions of frequency- and time-domain codes are significantly different in the presence of nonlinear behavior such as gapping and sliding of the foundation.

42 ENGINEERING↗

Molecular dynamics study on the effect of boundary heating rate on the phase change characteristics of thin film liquid

In this study, theoretical investigation of thin film liquid phase change phenomena under different boundary heating rates has been conducted with the help of molecular dynamics simulation. To do this, the case of argon boiling over a platinum surface has been considered. The study has been conducted to get a better understanding of the nano-scale physics of evaporation/boiling for a three phase system with particular emphasis on the effect of boundary heating rate. The simulation domain consisted of liquid and vapor argon atoms placed over a platinum wall. Initially the whole system was brought to an equilibrium state at 90 K with the help of equilibrium molecular dynamics and then the temperature of the bottom wall was increased to a higher temperature (250 K/130 K) over a finite heating period. Depending on the heating period, the boundary heating rate has been varied in the range of 1600×10{sup 9} K/s to 8×10{sup 9} K/s. The variations of argon region temperature, pressure, net evaporation number with respect to time under different boundary heating rates have been determined and discussed. The heat fluxes normal to platinum wall for different cases were also calculated and compared with theoretical upper limit of maximum possible heat transfer to elucidate the effect of boundary heating rate.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Multi-scale Material Parameter Identification Using LS-DYNA® and LS-OPT®

Ever-tightening regulations on fuel economy, and the likely future regulation of carbon emissions, demand persistent innovation in vehicle design to reduce vehicle mass. Classical methods for computational mass reduction include sizing, shape and topology optimization. One of the few remaining options for weight reduction can be found in materials engineering and material design optimization. Apart from considering different types of materials, by adding material diversity and composite materials, an appealing option in automotive design is to engineer steel alloys for the purpose of reducing plate thickness while retaining sufficient strength and ductility required for durability and safety. A project to develop computational material models for advanced high strength steel is currently being executed under the auspices of the United States Automotive Materials Partnership (USAMP) funded by the US Department of Energy. Under this program, new Third Generation Advanced High Strength Steel (i.e., 3GAHSS) are being designed, tested and integrated with the remaining design variables of a benchmark vehicle Finite Element model. The objectives of the project are to integrate atomistic, microstructural, forming and performance models to create an integrated computational materials engineering (ICME) toolkit for 3GAHSS. The mechanical properties of Advanced High Strength Steels (AHSS) are controlled by many factors, including phase composition and distribution in the overall microstructure, volume fraction, size and morphology of phase constituents as well as stability of the metastable retained austenite phase. The complex phase transformation and deformation mechanisms in these steels make the well-established traditional techniques obsolete, and a multi-scale microstructure-based modeling approach following the ICME [0]strategy was therefore chosen in this project. Multi-scale modeling as a major area of research and development is an outgrowth of the Comprehensive Test Ban Treaty of 1996 which banned surface testing of nuclear devices [1]. This had the effect that experimental work was reduced from large scale tests to multiscale experiments to provide material models with validation at different length scales. In the subsequent years industry realized that multi-scale modeling and simulation-based design were transferable to the design optimization of any structural system. Horstemeyer [1] lists a number of advantages of the use of multiscale modeling. Among these are: the reduction of product development time by alleviating costly trial-and-error iterations as well as the reduction of product costs through innovations in material, product and process designs. Multi-scale modeling can reduce the number of costly large scale experiments and can increase product quality by providing more accurate predictions. Research tends to be focussed on each particular length scale, which enhances accuracy in the long term. This paper serves as an introduction to the LS-OPT and LS-DYNA methodology for multi-scale modeling. It mainly focuses on an approach to integrate material identification using material models of different length scales. As an example, a multi-scale material identification strategy, consisting of a Crystal Plasticity (CP) material model and a homogenized State Variable (SV) model, is discussed and the parameter identification of the individual material models of different length scales is demonstrated. The paper concludes with thoughts on integrating the multi-scale methodology into the overall vehicle design.

Stander, Nielen↗