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Additive Manufacturing Model-Based Process Metrics: Reduced Order Modeling of the Laser Powder Bed Fusion Process

The multi-scale and complex process of printing additively manufactured (AM) parts can have unexpected, but predictable, build conditions that result in material microstructure variability. In this work, we describe a fully parallel reduced order modeling approach that has been developed to evaluate the evolution of AM processes, termed the AM moment measure method. This method couples the known sequence of the AM process with a physically informed nearest neighbors’ calculation to map the conditions of a part-scale build. The result is a map of the build that is derived directly from build files or in-situ process monitoring sensors. The methodology and terminology of the approach will be described, and computed build maps will be calculated and compared for various laser powder bed fusion (LPBF) builds of Ti-6Al-4V. Such comparative results develop understanding of how the sequential process actions can affect the LPBF-AM build quality and microstructure variability.

Laser Powder Bed Fusion↗

DOE OSTI2021

Quantifying multipoint ordering in alloys

A central problem in multicomponent lattice systems is to systematically quantify multipoint ordering. Ordering in such systems is often described in terms of pairs, even though this is not sufficient when three-point and higher-order interactions are included in the Hamiltonian. Current models and parameters for multipoint ordering are often only applicable for very specific cases or require approximating a subset of correlated occupational variables on a lattice as being uncorrelated. In this paper, cluster order parameters are introduced to systematically quantify arbitrary multipoint ordering motifs in substitutional systems through direct calculations of normalized cluster probabilities. These parameters can describe multipoint chemical ordering in crystal systems with multiple sublattices, multiple components, and systems with reduced symmetry. These are defined in this paper and applied to quantify four-point chemical ordering motifs in platinum/palladium alloy nanoparticles that are of practical interest to the synthesis of catalytic nanocages. Impacts of chemical ordering on nanocage stability are discussed. It is demonstrated that approximating four-point probabilities from superpositions of lower-order pair probabilities is not sufficient in cases where three- and four-body terms are included in the energy expression. Furthermore, conclusions about the formation mechanisms of nanocages may change significantly when using common pair approximations.

36 MATERIALS SCIENCE↗

DOE OSTI2019

A semi-Lagrangian direct-interaction closure of the spectra of isotropic variable-density turbulence

A study of variable-density homogeneous stationary isotropic turbulence based on the sparse direct-interaction perturbation (SDIP) and supporting direct numerical simulations (DNS) is presented. The non-solenoidal flow considered here is an example of turbulent mixing of gases with different densities. The spectral statistics of this type of flow are substantially more difficult to understand theoretically than those of the similar solenoidal flows. In the approach described here, the nonlinearly coupled velocity and scalar (which determine the density of the fluid) equations are expanded in terms of a normalised density ratio parameter. A new set of coupled integro-differential SDIP equations are derived and then solved numerically for the first-order correction to the incompressible equations in the variable-density expansion parameter. By adopting a regular expansion approach, one obtains leading-order corrections that are universal and therefore interesting in their own right. The predictions are then compared with DNS of forced variable-density flow with different density contrasts. It is found that the velocity spectrum owing to variable density is indistinguishable from that of constant-density turbulence, as it is supported by a wealth of indirect experimental evidence, but the scalar spectra show significant deviations, and even loss of monotonicity, as a function of the type and strength of the large-scale source of the mixing. Furthermore, the analysis helps clarify what may be the proper approach to interpret the power spectrum of variable-density turbulence.

Mechanics↗

DOE OSTI2020

Forecasting Remote Atmospheric Responses to Decadal Kuroshio Stability Transitions

Based on observational estimates and global ocean eddy-resolving coupled retrospective initialized predictions, we show that Kuroshio Extension variability affects rainfall variability along the west coast of North America. We show that the teleconnection between the current undulations and downstream rainfall can lead to improved subseasonal to seasonal predictions of precipitation over California, and we demonstrate that capturing these teleconnections requires coupled systems with sufficient ocean resolution (i.e., eddy-resolving), especially over time scales longer than one season. The improved forecast skill is diagnosed in terms of 35 years of retrospective initialized ensemble forecasts with an ocean eddy-resolving and an ocean eddy-parameterized coupled model. Not only does the ocean eddy-resolving model show sensitivity to Kuroshio Extension variability in terms of western North America precipitation, but the ocean eddy-resolving forecasts also show improved forecast skill compared to the ocean eddy-parameterized model. Additionally, the ocean eddy-parameterized coupled model shows no sensitivity to Kuroshio Extension variability. We also find near-decadal variability associated with a progression of a lower-tropospheric height dipole around the North Pacific and how these height anomalies lead to wind-driven Rossby waves that affect the eddy activity in the Kuroshio Extension with a time lag on the order of four years. This decadal-scale variability (~10 years) opens the possibility of multiyear predictability of western North American rainfall.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2020

The role of blocking circulation and emerging open water feedbacks on Greenland cold‐season air temperature variability over the last century

Substantial marine, terrestrial, and atmospheric changes have occurred over the Greenland region during the last century. Several studies have documented record‐levels of Greenland Ice Sheet (GrIS) summer melt extent during the 2000s and 2010s, but relatively little work has been carried out to assess regional climatic changes in other seasons. Here, we focus on the less studied cold‐season (i.e., autumn and winter) climate, tracing the long‐term (1873–2013) variability of Greenland's air temperatures through analyses of coastal observations and model‐derived outlet glacier series and their linkages with North Atlantic sea ice, sea surface temperature (SST), and atmospheric circulation indices. Through a statistical framework, large amounts of west and south Greenland temperature variance (up to r^2~50%) can be explained by the seasonally‐contemporaneous combination of the Greenland Blocking Index (GBI) and the North Atlantic Oscillation (NAO; hereafter the combination of GBI and NAO is termed GBI). Lagged and concomitant regional sea‐ice concentration (SIC) and the Atlantic Multidecadal Oscillation (AMO) seasonal indices account for small amounts of residual air temperature variance (r^2<~10%) relative to the GBI. The correlations between GBI and cold‐season temperatures are predominantly positive and statistically‐significant through time, while regional SIC conditions emerge as a significant covariate from the mid‐20th century through the conclusion of the study period. The inclusion of the cold‐season Pacific Decadal Oscillation (PDO) in multivariate analyses bolsters the air temperature variance explained by the North Atlantic regional predictors, suggesting the remote, background climate state is important to long‐term Greenland temperature variability. These findings imply that large‐scale tropospheric circulation has a strong control on surface temperature over Greenland through dynamic and thermodynamic impacts and stress the importance of understanding the evolving two‐way linkages between the North Atlantic marine and atmospheric environment in order to more accurately predict Greenland seasonal climate variability and change through the 21st century.

air temperatures↗

DOE OSTI2017

Demonstration of reduced-order urban scale building energy models

The aim of this study is to demonstrate a developed framework to rapidly create urban scale reduced-order building energy models using a systematic summary of the simplifications required for the representation of building exterior and thermal zones. These urban scale reduced-order models rely on the contribution of influential variables to the internal, external, and system thermal loads. OpenStudio Application Programming Interface (API) serves as a tool to automate the process of model creation and demonstrate the developed framework. The results of this study show that the accuracy of the developed reduced-order building energy models varies only up to 10% with the selection of different thermal zones. In addition, to assess complexity of the developed reduced-order building energy models, this study develops a novel framework to quantify complexity of the building energy models. Consequently, this study empowers the building energy modelers to quantify their building energy model systematically in order to report the model complexity alongside the building energy model accuracy. An exhaustive analysis on four university campuses suggests that the urban neighborhood buildings lend themselves to simplified typical shapes. Specifically, building energy modelers can utilize the developed typical shapes to represent more than 80% of the U.S. buildings documented in the CBECS database. One main benefits of this developed framework is the opportunity for different models including airflow and solar radiation models to share the same exterior representation, allowing a unifying exchange data. Altogether, the results of this study have implications for a large-scale modeling of buildings in support of urban energy consumption analyses or assessment of a large number of alternative solutions in support of retrofit decision-making in the building industry.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

NASA NTRS1983

On the joint bimodality of temperature and moisture near stratocumulus cloud tops

The observed distributions of the thermodynamic variables near stratocumulus top are highly bimodal. Two simple models of sub-grid fractional cloudiness motivated by this observed bimodality are examined. In both models, certain low order moments of two independent, moist-conservative thermodynamic variables are assumed to be known. The first model is based on the assumption of two discrete populations of parcels: a warm-day population and a cool-moist population. If only the first and second moments are assumed to be known, the number of unknowns exceeds the number of independent equations. If the third moments are assumed to be known as well, the number of independent equations exceeds the number of unknowns. The second model is based on the assumption of a continuous joint bimodal distribution of parcels, obtained as the weighted sum of two binormal distributions. For this model, the third moments are used to obtain 9 independent nonlinear algebraic equations in 11 unknowns. Two additional equations are needed to determine the covariance within the two subpopulations. In case these two internal covariance vanish, the system of equations can be solved analytically.

Randall, D. A.↗

NASA NTRS1993

The structure of the broad-line region in the Seyfert galaxy Markarian 590

We have undertaken a nine-month study of continuum and emission-line variability in the Seyfert galaxy Mrk 590 in order to determine the structure of the broad-line region. The H-beta variations are found to lag behind those of the optical continuum by about 19 days. We apply a maximum entropy method to solve for the transfer function which relates the line and continuum variability. This analysis suggests that there is a deficit of emission-line response due to gas along the line of sight to the continuum source, as in the case of NGC 5548, although these data do not allow us to reject with confidence models with significant line-of-sight response. We also show that the H-beta line variability is apparently confined to the core of the emission line, as suggested previously by Ferland, Korista, and Peterson (1990).

Peterson, Bradley M.↗

NASA NTRS1993

Modeling of topographic effects on Antarctic sea ice using multivariate adaptive regression splines

The role of seafloor topography in the spatial variations of the southern ocean sea ice cover as observed (every other day) by the Nimbus 7 scanning multichannel microwave radiometer satellite in the years 1980, 1983, and 1984 is studied. Bottom bathymetry can affect sea ice surface characteristics because of the basically barotropic circulation of the ocean south of the Antarctic Circumpolar current. The main statistical tool used to quantify this effect is a local nonparametric regression model of sea ice concentration as a function of the depth and its first two derivatives in both meridional and zonal directions. First, we model the relationship of bathymetry to sea ice concentration in two sudy areas, one over the Maud Rise and the other over the Ross Sea shelf region. The multiple correlation coefficient is found to average 44% in the Maud Rise study area and 62% in the Ross Sea study area over the years 1980, 1983, and 1984. Second, a strategy of dividing the entire Antarctic region into an overlapping mosaic of small areas, or windows is considered. Keeping the windows small reduces the correlation of bathymetry with other factors such as wind, sea temperature, and distance to the continent. We find that although the form of the model varies from window to window due to the changing role of other relevant environmental variables, we are left with a spatially consistent ordering of the relative importance of the topographic predictors. For a set of three representative days in the Austral winter of 1980, the analysis shows that an average of 54% of the spatial variation in sea ice concentration over the entire ice cover can be attributed to topographic variables. The results thus support the hypothesis that there is a sea ice to bottom bathymetry link. However this should not undermine the considerable influence of wind, current, and temperature which affect the ice distribution directly and are partly responsible for the observed bathymetric effects.

De Veaux, Richard D.↗

DOE OSTI2019

Leapfrog Time-Stepping for Hermite Methods

We introduce here Hermite-leapfrog methods for first order linear wave systems. The new Hermite-leapfrog methods pair leapfrog time-stepping with the Hermite methods of Goodrich and co-authors et al. (Math Comput 75(254):595–630, 2006). The new schemes stagger field variables in both time and space and are high-order accurate for equations with smooth solutions and coefficients. We provide a detailed description of the method and demonstrate that the method conserves variable quantities. Higher dimensional versions of the method are constructed via tensor products. Numerical evidence and rigorous analysis in one space dimension establish stability and high-order convergence. Experiments demonstrating efficient implementations on a graphics processing unit are also presented.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1997

Spherical Harmonics Analysis of the ECMWF Global Wind Fields at the 10-Meter Height Level During 1985: A Collection of Figures Illustrating Results

Half-daily global wind speeds in the east-west (u) and north-south (v) directions at the 10-meter height level were obtained from the European Centre for Medium Range Weather Forecasts (ECMWF) data set of global analyses. The data set covered the period 1985 January to 1995 January. A spherical harmonic expansion to degree and order 50 was used to perform harmonic analysis of the east-west (u) and north-south (v) velocity field components. The resulting wind field is displayed, as well as the residual of the fit, at a particular time. The contribution of particular coefficients is shown. The time variability of the coefficients up to degree and order 3 is presented. Corresponding power spectrum plots are given. Time series analyses were applied also to the power associated with degrees 0-10; the results are included.

Sanchez, Braulio V.↗

NASA NTRS1997

Comparison of Several Numerical Methods for Simulation of Compressible Shear Layers

An investigation is conducted on several numerical schemes for use in the computation of two-dimensional, spatially evolving, laminar variable-density compressible shear layers. Schemes with various temporal accuracies and arbitrary spatial accuracy for both inviscid and viscous terms are presented and analyzed. All integration schemes use explicit or compact finite-difference derivative operators. Three classes of schemes are considered: an extension of MacCormack's original second-order temporally accurate method, a new third-order variant of the schemes proposed by Rusanov and by Kutier, Lomax, and Warming (RKLW), and third- and fourth-order Runge-Kutta schemes. In each scheme, stability and formal accuracy are considered for the interior operators on the convection-diffusion equation U(sub t) + aU(sub x) = alpha U(sub xx). Accuracy is also verified on the nonlinear problem, U(sub t) + F(sub x) = 0. Numerical treatments of various orders of accuracy are chosen and evaluated for asymptotic stability. Formally accurate boundary conditions are derived for several sixth- and eighth-order central-difference schemes. Damping of high wave-number data is accomplished with explicit filters of arbitrary order. Several schemes are used to compute variable-density compressible shear layers, where regions of large gradients exist.

Kennedy, Christopher A.↗

NASA NTRS1995

Extensional flow convecting a reactant undergoing a first order homogeneous reaction and diffusional mass transfer from a sphere at low to intermediate Peclet and Damkohler numbers

Forced convective diffusion-reaction is considered for viscous axisymmetric extensional convecting velocity in the neighborhood of a sphere. For Peclet numbers in the range 0.1 less than or equal to Pe less than or equal to 500 and for Damkohler numbers increasing with increasing Pe but in the overall range 0.02 less than or equal to Da less than or equal to 10, average and local Sherwood numbers have been computed. By introducing the eigenfunction expansion c(r, Theta) = Sum of c(n)(r)P(n)(cos Theta) into the forced convective diffusion equation for the concentration of a chemical species undergoing a first order homogeneous reaction and by using properties of the Legendre functions Pn(cos Theta), the variable coefficient PDE can be reduced to a system of N + 1 second order ODEs for the radial functions c(sub n)(r), n = 0, 1, 2,..., N. The adaptive grid algorithm of Pereyra and Lentini can be used to solve the corresponding 2(N + 1) first order differential equations as a two-point boundary value problem on 1 less than or equal to r less than or equal to r(sub infinity). Convergence of the expansion for a specific value of N can thus be established and provides 'spectral' behavior as well as the full concentration field c(r, Theta).

Shah, N. Y.↗

NASA NTRS1997

Aircraft Pitch Control With Fixed Order LQ Compensators

This paper considers a given set of fixed order compensators for aircraft pitch control problem. By augmenting compensator variables to the original state equations of the aircraft, a new dynamic model is considered to seek a LQ controller. While the fixed order compensators can achieve a set of desired poles in a specified region, LQ formulation provides the inherent robustness properties. The time response for ride quality is significantly improved with a set of dynamic compensators.

Green, James↗

NASA NTRS1997

Aircraft Pitch Control with Fixed Order LQ Compensators

Green, James↗

NASA NTRS2009

The a(4) Scheme-A High Order Neutrally Stable CESE Solver

The CESE development is driven by a belief that a solver should (i) enforce conservation laws in both space and time, and (ii) be built from a nondissipative (i.e., neutrally stable) core scheme so that the numerical dissipation can be controlled effectively. To provide a solid foundation for a systematic CESE development of high order schemes, in this paper we describe a new high order (4-5th order) and neutrally stable CESE solver of a 1D advection equation with a constant advection speed a. The space-time stencil of this two-level explicit scheme is formed by one point at the upper time level and two points at the lower time level. Because it is associated with four independent mesh variables (the numerical analogues of the dependent variable and its first, second, and third-order spatial derivatives) and four equations per mesh point, the new scheme is referred to as the a(4) scheme. As in the case of other similar CESE neutrally stable solvers, the a(4) scheme enforces conservation laws in space-time locally and globally, and it has the basic, forward marching, and backward marching forms. Except for a singular case, these forms are equivalent and satisfy a space-time inversion (STI) invariant property which is shared by the advection equation. Based on the concept of STI invariance, a set of algebraic relations is developed and used to prove the a(4) scheme must be neutrally stable when it is stable. Numerically, it has been established that the scheme is stable if the value of the Courant number is less than 1/3

Chang, Sin-Chung↗

DOE OSTI2017

Pendulum Systems with Dynamical Symmetry

In this paper, we consider a class of oscillatory mechanical systems described by nonlinear second-order differential equations that contain parameters with variable dissipation and possess the property of dynamic symmetry. We study properties of mathematical models of such systems depending on parameters. Special attention is paid to bifurcations and reconstructions of phase portraits and the appearance and disappearance of cycles that envelope the phase cylinder or lie entirely on its covering. We present a complete parametric analysis of system with position-viscous friction and four parameters, where the force action linearly depends on the speed. The space of parameters is split into domains in which the topological behavior of the system is preserved. For some classes of pendulum systems whose right-hand sides depend on smooth functions, a qualitative analysis is performed, i.e., the space of systems considered is split into domains of different behavior of trajectories on the phase cylinder of quasi-velocities. We also perform a systematic analysis of the problem on an aerodynamic pendulum and detect periodic modes unknown earlier; these modes correspond to cycles in the mathematical model.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Atomistically-informed modeling of point defect clustering and evolution in irradiated ThO 2

A cluster dynamics (CD) model has been developed to investigate the nucleation and growth of point defect clusters, i.e., interstitial prismatic loops and nanoscale and sub-nanoscale voids, in ThO 2 during irradiation by energetic particles. The model considers cluster off-stoichiometry due to the asymmetry of point defect generation on the O and Th sublattices under irradiation, as well as the point defect diffusivities and the defect binding energies to clusters. The energies were established using detailed molecular dynamics simulations considering the statistical variability of cluster configuration. A high-order adaptive time-integration has been used to solve the model. The predicted loop density and their average size is in good agreement with reported experimental observations for proton irradiated ThO 2 at 600°C. In conclusion, the model did not predict void evolution due to the sluggish kinetics of cation vacancies, explaining the absence of voids in proton irradiated ThO 2 (and other oxides) at relatively low temperatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗