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All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

Stochastic Reductions for Inertial Fluid-Structure Interactions Subject to Thermal Fluctuations

We explore the dynamics of elastic microstructures within a fluid that are subjected to thermal fluctuations. We perform analysis to obtain systematically simplified descriptions of the mechanics in the limiting regimes when (i) the coupling forces that transfer momentum between the fluid and microstructures are strong, (ii) the mass of the microstructures is small relative to the displaced mass of the fluid, and (iii) the response to stresses results in hydrodynamics that relax rapidly to a quasi-steady-state relative to the motions of the microstructure. Furthermore, we derive effective equations using a singular perturbation analysis of the backward Kolmogorov equations of the stochastic process. Our continuum mechanics description is based on the stochastic Eulerian--Lagrangian method which provides a framework for approximation of the fluid-structure interactions when subject to thermal fluctuations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Physics-Informed Learning Machines for Multiscale and Multiphysics Problems (PHILMS) (Technical Report)

The research work at University of California Santa Barbara (UCSB) resulted in several new developments in the areas of scientific machine learning, numerical analysis, and practical methods for data-driven modeling, prediction, reductions, and simulation. Many of the projects were carried out in collaboration with members of the national laboratories at Sandia National Laboratories (SNL), Pacific Northwestern National Laboratories (PNNL), and other institutions. Results included developing new scientific machine learning methods, related theory and mathematical frameworks for analysis and training, data-driven numerical solvers, and related tools and software for scientific computation. During the support period, over 16+ papers were submitted for publication, and 4 open-source software packages were developed and released (available at http://atzberger.org/). In addition, 7+ students and 2 post-docs were mentored in collaboration with the laboratory staff for future careers in academia, government labs, and industry.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2004

Chemical Reaction and Flow Modeling in Fullerene and Nanotube Production

The development of processes to produce fullerenes and carbon nanotubes has largely been empirical. Fullerenes were first discovered in the soot produced by laser ablation of graphite [1]and then in the soot of electric arc evaporated carbon. Techniques and conditions for producing larger and larger quantities of fullerenes depended mainly on trial and error empirical variations of these processes, with attempts to scale them up by using larger electrodes and targets and higher power. Various concepts of how fullerenes and carbon nanotubes were formed were put forth, but very little was done based on chemical kinetics of the reactions. This was mainly due to the complex mixture of species and complex nature of conditions in the reactors. Temperatures in the reactors varied from several thousand degrees Kelvin down to near room temperature. There are hundreds of species possible, ranging from atomic carbon to large clusters of carbonaceous soot, and metallic catalyst atoms to metal clusters, to complexes of metals and carbon. Most of the chemical kinetics of the reactions and the thermodynamic properties of clusters and complexes have only been approximated. In addition, flow conditions in the reactors are transient or unsteady, and three dimensional, with steep spatial gradients of temperature and species concentrations. All these factors make computational simulations of reactors very complex and challenging. This article addresses the development of the chemical reaction involved in fullerene production and extends this to production of carbon nanotubes by the laser ablation/oven process and by the electric arc evaporation process. In addition, the high-pressure carbon monoxide (HiPco) process is discussed. The article is in several parts. The first one addresses the thermochemical aspects of modeling; and considers the development of chemical rate equations, estimates of reaction rates, and thermodynamic properties where they are available. The second part addresses modeling of the arc process for fullerene and carbon nanotube production using O-D, 1-D and 2-D fluid flow models. The third part addresses simulations of the pulsed laser ablation process using time-dependent techniques in 2-D, and a steady state 2-D simulation of a continuous laser ablation process. The fourth part addresses steady state modeling in O-D and 2-D of the HiPco process. In each of the simulations, there is a variety of simplifications that are made that enable one to concentrate on one aspect or another of the process. There are simplifications that can be made to the chemical reaction models , e.g. reduction in number of species by lumping some of them together in a representative species. Other simulations are carried out by eliminating the chemistry altogether in order to concentrate on the fluid dynamics. When solving problems with a large number of species in more than one spatial dimension, it is almost imperative that the problem be decoupled by solving for the fluid dynamics to find the fluid motion and temperature history of "particles" of fluid moving through a reactor. Then one can solve the chemical rate equations with complex chemistry following the temperature and pressure history. One difficulty is that often mixing with an ambient gas is involved. Therefore, one needs to take dilution and mixing into account. This changes the ratio of carbon species to background gas. Commercially available codes may have no provision for including dilution as part of the input. One must the write special solvers for including dilution in decoupled problems. The article addresses both ful1erene production and single-walled carbon nanotube (SWNT) production. There are at least two schemes or concepts of SWNT growth. This article will only address growth in the gas phase by carbon and catalyst cluster growth and SW T formation by the addition of carbon. There are other models that conceive of SWNT growth as a phase separation process from clusters me up carbon and metal catalyst, with the carbon precipitating from the cluster as it cools. We will not deal with that concept in this article. Further research is needed to determine the rates at which these composite clusters form, evaporate, and segregate.

Scott, Carl D.↗
DOE OSTI2019

Reduction Kinetics of Perovskite Oxides for Selective Hydrogen Combustion in the Context of Olefin Production

Chemical looping represents a novel approach for generating light olefins in which thermal cracking or catalytic dehydrogenation is coupled with selective hydrogen combustion (SHC) by a metal oxide redox catalyst, which enables autothermal operation, increased per-pass conversion, and greater-than-equilibrium yields. Recent studies indicate that Na 2 WO 4 -promoted perovskite oxides are effective redox catalysts with high olefin selectivity. Herein, kinetic parameters, rates, and reaction models for the reduction of unpromoted and Na 2 WO 4 -promoted CaMnO 3 redox catalysts by H 2 , C 2 H 4 , and C 2 H 6 , is reported. Reduction rates of CaMnO 3 under ethylene and ethane are significantly lower than under H 2 . Additionally, model fitting of reduction kinetics show good agreement with reaction order–controlled models for CaMnO 3 reduction and predict greater oxygen site dependence and higher activation energy for CaMnO 3 reduction by C 2 H 4 as compared with H 2 . Avrami–Erofe'ev nucleation and growth models provide the best fit to the reduction of Na 2 WO 4 /CaMnO 3 in H 2 and in C 2 H 4 . After Na 2 WO 4 promotion, the reduction rate of CaMnO 3 is three orders of magnitude lower in ethylene in comparison to hydrogen, consistent with its superior selectivity to hydrogen combustion. The models developed can be applied toward reactor design and optimization in the context of enhanced olefin production via SHC under a cyclic redox scheme.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1991

Air oxidation of hydrazine. 1. Reaction kinetics on natural kaolinites, halloysites, and model substituent layers with varying iron and titanium oxide and O- center contents

Air oxidation of hydrazine was studied by using a group of kaolinites, halloysites, and substituent oxides as models for the tetrahedral and octahedral sheets. The rate was found to be linear with oxygen. The stoichiometry showed that oxygen was the primary oxidant and that dinitrogen was the only important nitrogen-containing product. The rates on kaolinites were strongly inhibited by water. Those on three-dimensional silica and gibbsite appeared not to be. That on a supposedly layered silica formed from a natural kaolinite by acid leaching showed transitional behavior--slowed relative to that expected from a second-order reaction relative to that on the gibbsite and silica but faster than those on the kaolinites. The most striking result of the reaction was the marked increase in the rate of reaction of a constant amount of hydrazine as the amount of clay was increased. The increase was apparent (in spite of the water inhibition at high conversions) over a 2 order of magnitude variation of the clay weight. The weight dependence was taken to indicate that the role of the clay is very important, that the number of reactive centers is very small, or that they may be deactivated over the course of the reaction. In contrast to the strong dependence on overall amount of clay, the variation of amounts of putative oxidizing centers, such as structural Fe(III), admixed TiO2 or Fe2O3, or O- centers, did not result in alteration of the rate commensurate with the degree of variation of the entity in question. Surface iron does play some role, however, as samples that were pretreated with a reducing agent were less active as catalysts than the parent material. These results were taken to indicate either that the various centers interact to such a degree that they cannot be considered independently or that the reaction might proceed by way of surface complexation, rather than single electron transfers.

NASA Discipline Number 52-20↗
DOE OSTI2022

Polyakov model in ’t Hooft flux background: a quantum mechanical reduction with memory

We construct a compactification of Polyakov model on T 2 × $\mathbb{R}$ down to quantum mechanics which remembers non-perturbative aspects of field theory even at an arbitrarily small area. Standard compactification on small T 2 × $\mathbb{R}$ possesses a unique perturbative vacuum (zero magnetic flux state), separated parametrically from higher flux states, and the instanton effects do not survive in the Born-Oppenheimer approximation. By turning on a background magnetic GNO flux in co-weight lattice corresponding to a non-zero ’t Hooft flux, we show that N-degenerate vacua appear at small torus, and there are N - 1 types of flux changing instantons between them. We construct QM instantons starting with QFT instantons using the method of replicas. For example, SU(2) gauge theory with flux reduces to the double-well potential where each well is a fractional flux state. Despite the absence of a mixed anomaly, the vacuum structure of QFT and the one of QM are continuously connected. We also compare the quantum mechanical reduction of the Polyakov model with the deformed Yang-Mills, by coupling both theories to TQFTs. In particular, we compare the mass spectrum for dual photons and energy spectrum in the QM limit. We give a detailed description of critical points at infinity in the semi-classical expansion, and their role in resurgence structure.

nonperturbative effects↗
DOE OSTI2014

Adaptive h -refinement for reduced-order models: ADAPTIVE h -refinement for reduced-order models

Our work presents a method to adaptively refine reduced-order models a posteriori without requiring additional full-order-model solves. The technique is analogous to mesh-adaptive h-refinement: it enriches the reduced-basis space online by ‘splitting’ a given basis vector into several vectors with disjoint support. The splitting scheme is defined by a tree structure constructed offline via recursive k-means clustering of the state variables using snapshot data. This method identifies the vectors to split online using a dual-weighted-residual approach that aims to reduce error in an output quantity of interest. The resulting method generates a hierarchy of subspaces online without requiring large-scale operations or full-order-model solves. Furthermore, it enables the reduced-order model to satisfy any prescribed error tolerance regardless of its original fidelity, as a completely refined reduced-order model is mathematically equivalent to the original full-order model. Experiments on a parameterized inviscid Burgers equation highlight the ability of the method to capture phenomena (e.g., moving shocks) not contained in the span of the original reduced basis.

42 ENGINEERING↗
DOE OSTI2023

Operator inference with roll outs for learning reduced models from scarce and low-quality data

Data-driven modeling has become a key building block in computational science and engineering. However, data that are available in science and engineering are typically scarce, often polluted with noise and affected by measurement errors and other perturbations, which makes learning the dynamics of systems challenging. Here, in this work, we propose to combine data-driven modeling via operator inference with the dynamic training via roll outs of neural ordinary differential equations. Operator inference with roll outs inherits interpretability, scalability, and structure preservation of traditional operator inference while leveraging the dynamic training via roll outs over multiple time steps to increase stability and robustness for learning from low-quality and noisy data. Numerical experiments with data describing shallow water waves and surface quasi-geostrophic dynamics demonstrate that operator inference with roll outs provides predictive models from training trajectories even if data are sampled sparsely in time and polluted with noise of up to 10%.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Machine-learning error models for approximate solutions to parameterized systems of nonlinear equations

Here, this work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of an iterative method, a lower-fidelity model, or a projection-based reduced-order model, for example. The proposed statistical model comprises the sum of a deterministic regression-function model and a stochastic noise model. The method constructs the regression-function model by applying regression techniques from machine learning (e.g., support vector regression, artificial neural networks) to map features (i.e., error indicators such as sampled elements of the residual) to a prediction of the approximate-solution error. The method constructs the noise model as a mean-zero Gaussian random variable whose variance is computed as the sample variance of the approximate-solution error on a test set; this variance can be interpreted as the epistemic uncertainty introduced by the approximate solution. This work considers a wide range of feature-engineering methods, data-set-construction techniques, and regression techniques that aim to ensure that (1) the features are cheaply computable, (2) the noise model exhibits low variance (i.e., low epistemic uncertainty introduced), and (3) the regression model generalizes to independent test data. Finally, numerical experiments performed on several computational-mechanics problems and types of approximate solutions demonstrate the ability of the method to generate statistical models of the error that satisfy these criteria and significantly outperform more commonly adopted approaches for error modeling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

A reduced multicomponent diffusion model

Here, the diffusion models for multicomponent mixtures are investigated in planar premixed flames, counterflow diffusion flames, and ignition of droplet flames. Discernable discrepancies were observed in the simulated flames with the mixture-averaged and multicomponent diffusion models, respectively, while the computational cost of the multicomponent model is significantly higher than that of the mixture-averaged model. A systematic strategy is proposed to reduce the cost of the multicomponent diffusion model by accurately accounting for the species whose diffusivity is important to the global responses of the combustion systems, and approximating those of less importance. The important species in the reduced model are identified with sensitivity analysis, and are found to be typically among those in high concentrations with exception of a few radicals, e.g. H and OH, that are known to participate in critical reactions. The reduced model is validated in simulating the propagation of planar premixed flames, extinction of counterflow non-premixed flames and ignition of droplet flames. The reduced model was shown to feature similar accuracy to that of the multicomponent model while the computational cost was reduced by a factor of approximately 5 for an n -heptane mechanism with 88 species.

42 ENGINEERING↗
DOE OSTI2019

Accounting for uncertainty in RCCE species selection

A framework is presented to quantify, based on Bayesian evidence, the relative plausibility of species se- lection options in rate-controlled constrained equilibrium (RCCE) reduced chemical models, accounting for uncertainty in the kinetic parameters and experimental data used to refine them. This approach bal- ances the joint goals of matching available data and avoiding overfitting, which is well-understood to limit extrapolative capacity for true prediction. The methodology is applied to homogeneous autoigni- tion, where predictions are known to be particularly sensitive to chemical model details, specially at low temperatures. It is first introduced for hydrogen–air autoignition using an established mechanism, then demonstrated in two applications of methane–air autoignition using the larger GRI-1.2 mechanism. This larger mechanism significantly increases the computational cost of model selection (though not of the subsequent application in predictions), which is alleviated with a time-scale-guided pre-sorting strategy. Uses and extensions of this new formulation are discussed.

08 HYDROGEN↗
DOE OSTI2022

Dendrite-resolved, full-melt-pool phase-field simulations to reveal non-steady-state effects and to test an approximate model

In this report we study the epitaxial, columnar growth of (multiply oriented) dendrites/cells for a spot melt in a polycrystalline Al–Cu substrate using two-dimensional, phase-field, direct numerical simulations (DNS) at the full-melt-pool scale. Our main objective is to compare the expensive DNS model to a much cheaper but approximate “line” model in which a single-crystal phase-field simulation is confined to a narrow rectangular geometry. To perform this comparison, we develop algorithms that automatically extract quantities of interest (QoIs) from both DNS and line models. These QoIs allow us to quantitatively assess the assumptions in the line model and help us analyze its discrepancy with the DNS model. We consider four sets of heat source parameters, mimicking welding and additive manufacturing conditions, that create a combination shallow and deep melt pools. Our largest DNS simulation used 16K x 14K grid points in space. Our main findings can be summarized as follows. Under AM conditions, the QoIs of line models are in excellent agreement with the full DNS results for both shallow and deep melt pools. Under welding conditions, the primary spacing of the DNS model is smaller than the prediction of line model. We identify a geometric crowding effect that accounts for the discrepancies between the DNS and line models. We propose two potential mechanisms that determine the response of the microstructure to geometric crowding.

36 MATERIALS SCIENCE↗
DOE OSTI2017

A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials

Since the beginning of the industrial age, material performance and design have been in the midst of innovation of many disruptive technologies. Today's electronics, space, medical, transportation, and other industries are enriched by development, design and deployment of composite, heterogeneous and multifunctional materials. As a result, materials innovation is now considerably outpaced by other aspects from component design to product cycle. In this article, we review predictive nonlinear theories for multiscale modeling of heterogeneous materials. Deeper attention is given to multiscale modeling in space and to computational homogenization in addressing challenging materials science questions. Moreover, we discuss a state-of-the-art platform in predictive image-based, multiscale modeling with co-designed simulations and experiments that executes on the world's largest supercomputers. Such a modeling framework consists of experimental tools, computational methods, and digital data strategies. Once fully completed, this collaborative and interdisciplinary framework can be the basis of Virtual Materials Testing standards and aids in the development of new material formulations. Moreover, it will decrease the time to market of innovative products.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Constraint energy minimizing generalized multiscale finite element method for multi-continuum Richards equations

In fluid flow simulation, the multi-continuum model is a useful strategy. When the heterogeneity and contrast of coefficients are high, the system becomes multiscale, and some kinds of reduced order methods are demanded. Combining these techniques with nonlinearity, we will consider in this paper a dual-continuum model which is generalized as a multi-continuum model for a coupled system of nonlinear Richards equations as unsaturated flows, in complex heterogeneous fractured porous media; and we will solve it by a novel multiscale approach utilizing the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM). In particular, such a nonlinear system will be discretized in time and then linearized by Picard iteration (whose global convergence is proved theoretically). Subsequently, we tackle the resulting linearized equations by the CEM-GMsFEM and obtain proper offline multiscale basis functions to span the multiscale space (which contains the pressure solution). More specifically, we first introduce two new sources of samples, and the GMsFEM is used over each coarse block to build local auxiliary multiscale basis functions via solving local spectral problems, that are crucial for detecting high-contrast channels. Second, per oversampled coarse region, local multiscale basis functions are created through the CEM as constrainedly minimizing an energy functional. Various numerical tests for our approach reveal that the error converges with the coarse-grid size and that only few oversampling layers as well as basis functions are needed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A long short-term memory embedding for hybrid uplifted reduced order models

In this paper, we introduce an uplifted reduced order modeling (UROM) approach through the integration of standard projection based methods with long short-term memory (LSTM) embedding. Our approach has three modeling layers or components. In the first layer, we utilize an intrusive projection approach to model dynamics represented by the largest modes. The second layer consists of an LSTM model to account for residuals beyond this truncation. This closure layer refers to the process of including the residual effect of the discarded modes into the dynamics of the largest scales. However, the feasibility of generating a low rank approximation tails off for higher Kolmogorov n -width systems due to the underlying nonlinear processes. The third uplifting layer, called super-resolution, addresses this limited representation issue by expanding the span into a larger number of modes utilizing the versatility of LSTM. Therefore, our model integrates a physics-based projection model with a memory embedded LSTM closure and an LSTM based super-resolution model. In several applications, we exploit the use of Grassmann manifold to construct UROM for unseen conditions. We performed numerical experiments by using the Burgers and Navier-Stokes equations with quadratic nonlinearity. Finally, our results show robustness of the proposed approach in building reduced order models for parameterized systems and confirm the improved trade-off between accuracy and efficiency.

42 ENGINEERING↗
DOE OSTI2013

Thermal stability and lifetime estimates of a high temperature epoxy by T g reduction

Thermal degradation of a high temperature epoxy network is studied in terms glass transition temperature (T g ) reduction over a temperature window encompassing the T g of the network. The T g is shown to decrease as the network is thermally aged at elevated temperatures in air and in argon. The duration of the aging experiments is extended to long time such that the absolute T g reduction approaches a long time reduction plateau. Degradation is dominated by non-oxidative pyrolysis with a small contribution from diffusion limited thermal oxidative degradation at the surface. A time–temperature superposition is constructed from the extent of T g reduction of samples aged in air and the thermal shift factors are shown to have Arrhenius scaling behavior. An activation energy is extracted that agrees with previous activation energy measurements derived from other property measurements of the same network aged under similar conditions. The agreement of the activation energy with past results shows that T g reduction is controlled by the same degradation mechanism and may be used as an observable for lifetime estimates when thermal degradation is pyrolytic in nature. The extent of T g reduction is modeled with an autocatalytic rate expression and compared to previous property measurements to show the difference in sensitivity of observable material properties on degradation.

36 MATERIALS SCIENCE↗