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DOE OSTI2020

Physics-Informed Deep Neural Networks for Learning Parameters and Constitutive Relationships in Subsurface Flow Problems

In this paper, we present a physics informed deep neural network (DNN) method for estimating parameters and unknown physics (constitutive relationships) in partial differential equation (PDE) models. We use PDEs in addition to measurements to train DNNs to approximate unknown parameters and constitutive relationships as well as states. The proposed approach increases the accuracy of DNN approximations of partially known functions when a limited number of measurements is available and allows for training DNNs when no direct measurements of the functions of interest are available. We employ physics informed DNNs to estimate the unknown space-dependent diffusion coefficient in a linear diffusion equation and an unknown constitutive relationship in a non-linear diffusion equation. For the parameter estimation problem, we assume that partial measurements of the coefficient and states are available and demonstrate that under these conditions, the proposed method is more accurate than state-of-the-art methods. For the non-linear diffusion PDE model with a fully unknown constitutive relationship (i.e., no measurements of constitutive relationship are available), the physics informed DNN method can accurately estimate the non-linear constitutive relationship based on state measurements only. Finally, we demonstrate that the proposed method remains accurate in the presence of measurement noise.

42 ENGINEERING↗

DOE OSTI2026

Intrinsic kinetics of water-inhibited ultra-lean methane oxidation over PtPd-Mg/ θ -Al 2 O 3 catalyst

Here, this study develops intrinsic methane oxidation kinetics for ultra-lean methane conditions in the presence of water over a highly active and stable PtPd–Mg/θ-Al 2 O 3 catalyst. Comprehensive laboratory experiments were conducted over a wide range of methane concentrations (150–1200 ppm CH 4 ), water contents (1–5% H 2 O), and industrially relevant space velocities (80,000 ≤ GHSV ≤ 160,000 h -1 ). These systematic experiments informed a two-dimensional, axisymmetric, multiscale reactor model that was used to develop and validate methane oxidation kinetics under practically relevant conditions, including non-isothermal operation and high conversion regimes. Combined experimental and modeling results revealed significant intraparticle diffusion resistance and transport-induced reaction exotherm at elevated temperatures, which limited catalyst utilization despite high intrinsic activity. These transport effects were explicitly incorporated into the reactor model, enabling accurate estimation of intrinsic kinetic parameters without reliance on conventional effectiveness-factor corrections. The resulting kinetic model successfully captured both kinetically controlled and mass-transfer-limited regimes and reliably predicted CH 4 conversion across broad ranges of temperature, methane concentration, and water content

Heat and mass transfer limitations↗

DOE OSTI2017

Surface transport processes in charged porous media

Surface transport processes are important in chemistry, colloidal sciences, engineering, biology, and geophysics. Natural or externally produced charges on surfaces create electrical double layers (EDLs) at the solid-liquid interface. The existence of the EDLs produces several complex processes including bulk and surface transport of ions. In this work, a model is presented to simulate bulk and transport processes in homogeneous porous media comprising big pores. It is based on a theory for capacitive charging by ideally polarizable porous electrodes without Faradaic reactions or specific adsorption of ions. A volume averaging technique is used to derive the averaged transport equations in the limit of thin electrical double layers. Description of the EDL between the electrolyte solution and the charged wall is accomplished using the Gouy-Chapman-Stern (GCS) model. The surface transport terms enter into the average equations due to the use of boundary conditions for diffuse interfaces. Two extra surface transports terms appear in the closed average equations. One is a surface diffusion term equivalent to the transport process in non-charged porous media. The second surface transport term is a migration term unique to charged porous media. The effective bulk and transport parameters for isotropic porous media are calculated solving the corresponding closure problems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1972

Dispersive waves in a seeded MHD generator.

The equations giving the response of a slightly ionized plasma with monatomic components to sinusoidal perturbations have been formulated. Included in the model equations were the electron Hall effect, electron thermal diffusion, radiation, and electron-atom rate processes. Plasma conditions were limited to those where viscous effects, the induced magnetic field, ion slip, and atom-atom inelastic processes can be neglected. Presented are results of numerical calculations for MHD generators with a working fluid of potassium seeded argon.

Harstad, K. G.↗

NASA NTRS1998

Contactless Growth of ZnSe Single Crystals by Physical Vapor Transport

ZnSe crystals were grown by self-seeded physical vapor transport (PVT) technique in the horizontal configuration. The source materials were heat treated by H2 reduction to remove the oxide followed by baking under dynamic vacuum to adjust the source composition toward that of congruent sublimation. Contactless growth of ZnSe single crystals have been performed consistently using three different source materials. The crystals grew away from the wall during the later stage of the growth with large (110) facets tend to align parallel to the gravity direction. The Scanning Electron Micrography (SEM) micrographs and the Atomic Force Microscope (AFM) images showed that large (110) terraces and steps dominate the as-grown facets. The measured residual gas pressures in the processed ampoules agree well among various source materials and the major components were CO and H2. No preferred growth direction was found. The one-dimensional diffusion model on the mass flux of a multi-species PVT system was employed to analyze the conditions for contactless growth. The calculated thermal profile for supersaturation is very close to the thermal profile measured inside the empty furnace bore in the region of contactless growth. The effects of convective flows in the vapor phase inside the ampoule on the growth processes are discussed.

Su, Ching-Hua↗

DOE OSTI2016

Atomistic modeling of dropwise condensation

The basic aim of the atomistic modeling of condensation of water is to determine the size of the stable cluster and connect phenomena occurring at atomic scale to the macroscale. In this paper, a population balance model is described in terms of the rate equations to obtain the number density distribution of the resulting clusters. The residence time is taken to be large enough so that sufficient time is available for all the adatoms existing in vapor-phase to loose their latent heat and get condensed. The simulation assumes clusters of a given size to be formed from clusters of smaller sizes, but not by the disintegration of the larger clusters. The largest stable cluster size in the number density distribution is taken to be representative of the minimum drop radius formed in a dropwise condensation process. A numerical confirmation of this result against predictions based on a thermodynamic model has been obtained. Results show that the number density distribution is sensitive to the surface diffusion coefficient and the rate of vapor flux impinging on the substrate. The minimum drop radius increases with the diffusion coefficient and the impinging vapor flux; however, the dependence is weak. The minimum drop radius predicted from thermodynamic considerations matches the prediction of the cluster model, though the former does not take into account the effect of the surface properties on the nucleation phenomena. For a chemically passive surface, the diffusion coefficient and the residence time are dependent on the surface texture via the coefficient of friction. Thus, physical texturing provides a means of changing, within limits, the minimum drop radius. The study reveals that surface texturing at the scale of the minimum drop radius does not provide controllability of the macro-scale dropwise condensation at large timescales when a dynamic steady-state is reached.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Simulating Uranium(VI) Diffusion in Sodium-Montmorillonite as a Function of Chemical Solution Conditions

Most nuclear waste disposal options include compacted bentonite, predominately consisting of montmorillonite clay, as part of a barrier system to minimize contaminant mobility. Uranium (U) is the primary element in spent nuclear fuel, and a potential contaminant of water resources. Uranium sorption onto clay and its slow diffusive transport away from waste canisters are expected to limit U(VI) mobility in these systems. However, their prediction is complicated by the complex mineralogical structure of montmorillonite clay, leading to two types of surface sites and clay porosities, and by the dependence of U(VI) solution speciation on chemical conditions. For instance, depending on pH and ionic strength, U(VI) may sorb onto montmorillonite due to weak ion exchange reactions or the formation of stable surface complexes. Furthermore, at the high degrees of clay compaction expected in future barrier systems, the ability of U(VI) species to access small, highly negatively charged interlayer spaces may ultimately control diffusive fluxes. In this modeling study, we investigate how the charge of U(VI) solution species affects U(VI) sorption and diffusion behavior. For this purpose, we simplified complex chemical solution speciation diagrams to charge speciation diagrams. Furthermore, we coupled an existing U(VI) sorption model (in PHREEQC) with U(VI) diffusion calculations (in GLE) to simulate U(VI) mobility in lab-scale through-diffusion experiments over various chemical conditions. Our results suggest that there are two important parameters that govern U(VI) diffusion in these systems. Uranium(VI) surface complexation on clay edge surfaces leads to contaminant retardation, while the access of U(VI) solution species to diffuse layers in clay interlayer spaces controls diffusive fluxes. Hence on the field scale, these parameters will determine how early a plume may cross site boundaries and pose risks to drinking water resources, and the levels of U(VI) concentrations to be expected in contaminated waters.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1996

Measurements and Modeling of Soot Formation and Radiation in Microgravity Jet Diffusion Flames

This is a computational and experimental study for soot formation and radiative heat transfer in jet diffusion flames under normal gravity (1-g) and microgravity (0-g) conditions. Instantaneous soot volume fraction maps are measured using a full-field imaging absorption technique developed by the authors. A compact, self-contained drop rig is used for microgravity experiments in the 2.2-second drop tower facility at NASA Lewis Research Center. On modeling, we have coupled flame structure and soot formation models with detailed radiation transfer calculations. Favre-averaged boundary layer equations with a k-e-g turbulence model are used to predict the flow field, and a conserved scalar approach with an assumed Beta-pdf are used to predict gaseous species mole fraction. Scalar transport equations are used to describe soot volume fraction and number density distributions, with formation and oxidation terms modeled by one-step rate equations and thermophoretic effects included. An energy equation is included to couple flame structure and radiation analyses through iterations, neglecting turbulence-radiation interactions. The YIX solution for a finite cylindrical enclosure is used for radiative heat transfer calculations. The spectral absorption coefficient for soot aggregates is calculated from the Rayleigh solution using complex refractive index data from a Drude- Lorentz model. The exponential-wide-band model is used to calculate the spectral absorption coefficient for H20 and C02. It is shown that when compared to results from true spectral integration, the Rosseland mean absorption coefficient can provide reasonably accurate predictions for the type of flames studied. The soot formation model proposed by Moss, Syed, and Stewart seems to produce better fits to experimental data and more physically sound than the simpler model by Khan et al. Predicted soot volume fraction and temperature results agree well with published data for a normal gravity co-flow laminar flames and turbulent jet flames. Predicted soot volume fraction results also agree with our data for 1-g and 0-g laminar jet names as well as 1-g turbulent jet flames.

Ku, Jerry C.↗

DOE OSTI2018

Helium diffusivity in oxide nuclear fuel: Critical data analysis and new correlations

Helium is relevant in determining nuclear fuel behaviour. It affects the performance of nuclear fuel both in reactor and in storage conditions. Helium becomes important in reactor conditions when high burnups are targeted or MOX fuel is used, whereas for storage conditions it can represent a threat to the fuel rods integrity. The accurate knowledge of helium behaviour combined with predictive model capabilities is fundamental for the safe management of nuclear fuel, with helium diffusivity being a critical property. For this reason, a considerable number of separate effect experiments in the last fifty years investigated helium diffusivity in nuclear fuel. The aim of this work is to critically review and assess the experimental results concerning the helium diffusivity. Experimental results are critically analysed in terms of the helium introduction technique used (either infusion, implantation or doping) and of sample characteristics (single crystal, poly-crystal or powder). Accordingly, we derived two different correlations for the diffusivity. Clearly, each of the new correlations corresponds to a limited range of application conditions, depending on the experimental data used to derive it. We provide recommendations regarding the proper application conditions for each correlation (e.g., in reactor or storage conditions).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2017

SUNSPOT AND STARSPOT LIFETIMES IN A TURBULENT EROSION MODEL

Quantitative models of sunspot and starspot decay predict the timescale of magnetic diffusion and may yield important constraints in stellar dynamo models. Motivated by recent measurements of starspot lifetimes, we investigate the disintegration of a magnetic flux tube by nonlinear diffusion. Previous theoretical studies are extended by considering two physically motivated functional forms for the nonlinear diffusion coefficient D : an inverse power-law dependence D ∝ B {sup −ν} and a step-function dependence of D on the magnetic field magnitude B . Analytical self-similar solutions are presented for the power-law case, including solutions exhibiting “super fast” diffusion. For the step-function case, the heat-balance integral method yields approximate solutions, valid for moderately suppressed diffusion in the spot. The accuracy of the resulting solutions is confirmed numerically, using a method which provides an accurate description of long-time evolution by imposing boundary conditions at infinite distance from the spot. The new models may allow insight into the differences and similarities between sunspots and starspots.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2015

Derivation of an Analytical Solution to a Reaction-Diffusion Model for Autocatalytic Degradation and Erosion in Polymer Microspheres

A mathematical reaction-diffusion model is defined to describe the gradual decomposition of polymer microspheres composed of poly(D,L-lactic-co-glycolic acid) (PLGA) that are used for pharmaceutical drug delivery over extended periods of time. The partial differential equation (PDE) model treats simultaneous first-order generation due to chemical reaction and diffusion of reaction products in spherical geometry to capture the microsphere-size dependent effects of autocatalysis on PLGA erosion that occurs when the microspheres are exposed to aqueous media such as biological fluids. The model is solved analytically for the concentration of the autocatalytic carboxylic acid end groups of the polymer chains that comprise the microspheres as a function of radial position and time. The analytical solution for the reaction and transport of the autocatalytic chemical species is useful for predicting the conditions under which drug release from PLGA microspheres transitions from diffusion-controlled to erosion-controlled release, for understanding the dynamic coupling between the PLGA degradation and erosion mechanisms, and for designing drug release particles. The model is the first to provide an analytical prediction for the dynamics and spatial heterogeneities of PLGA degradation and erosion within a spherical particle. The analytical solution is applicable to other spherical systems with simultaneous diffusive transport and first-order generation by reaction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1995

Detailed modeling analysis for soot formation and radiation in microgravity gas jet diffusion flames

Radiation heat transfer in combustion systems has been receiving increasing interest. In the case of hydrocarbon fuels, a significant portion of the radiation comes from soot particles, justifying the need for detailed soot formation model and radiation transfer calculations. For laminar gas jet diffusion flames, results from this project (4/1/91 8/22/95) and another NASA study show that flame shape, soot concentration, and radiation heat fluxes are substantially different under microgravity conditions. Our emphasis is on including detailed soot transport models and a detailed solution for radiation heat transfer, and on coupling them with the flame structure calculations. In this paper, we will discuss the following three specific areas: (1) Comparing two existing soot formation models, and identifying possible improvements; (2) A simple yet reasonably accurate approach to calculating total radiative properties and/or fluxes over the spectral range; and (3) Investigating the convergence of iterations between the flame structure solver and the radiation heat transfer solver.

Ku, Jerry C.↗

NASA NTRS1990

A scaling law of radial gas distribution in disk galaxies

Based on the idea that local conditions within a galactic disk largely determine the region's evolution time scale, researchers built a theoretical model to take into account molecular cloud and star formations in the disk evolution process. Despite some variations that may be caused by spiral arms and central bulge masses, they found that many late-type galaxies show consistency with the model in their radial atomic and molecular gas profiles. In particular, researchers propose that a scaling law be used to generalize the gas distribution characteristics. This scaling law may be useful in helping to understand the observed gas contents in many galaxies. Their model assumes an exponential mass distribution with disk radius. Most of the mass are in atomic gas state at the beginning of the evolution. Molecular clouds form through a modified Schmidt Law which takes into account gravitational instabilities in a possible three-phase structure of diffuse interstellar medium (McKee and Ostriker, 1977; Balbus and Cowie, 1985); whereas star formation proceeds presumably unaffected by the environmental conditions outside of molecular clouds (Young, 1987). In such a model both atomic and molecular gas profiles in a typical galactic disk (as a result of the evolution) can be fitted simultaneously by adjusting the efficiency constants. Galaxies of different sizes and masses, on the other hand, can be compared with the model by simply scaling their characteristic length scales and shifting their radial ranges to match the assumed disk total mass profile sigma tot(r).

Wang, Zhong↗

DOE OSTI2022

Enhanced mobility of cations and anions in the redox state: The polaronium mechanism

Hugely enhanced slow-ion diffusivity has been widely observed under extreme redox conditions and for unclear reasons. Aided by first-principles calculations on model systems of ZrO 2 , CeO 2 , BaTiO 3 and Li 4/3 Mn 2/3 O 2 , here we successfully explained the intriguing phenomenon by a polaronium mechanism. We found a polaronium, defined as a transitory complex of a polaronic electron or hole and a migrating counterion, becomes highly mobile when the counterion comes from a d 0 or f 0 cation (e.g., Zr 4+ , Ti 4+ and Ce 4 ) or a p 6 anion (e.g., O 2- ) in the host compound. Upon a redox reaction, the complex attains a d 1 /f 1 or p 5 configuration, which spontaneously forms because it is favored by an electron-phonon interaction (manifest as the Jahn-Teller effect in high symmetry systems) that enables local relaxation and lowers the system energy. Here our calculations found such interaction reaching its peak at the saddle point where the local environment is softest, so soft that it allows a reorientation of the anisotropic d/f/p orbital to minimize the electron repulsion locally. Since the complex may dissolve after a successful ion-migration event, the redox electron/hole can be recycled to form another free-radical-like polaronium elsewhere, thereby enhancing ion migration repeatedly. The proposed polaronium mechanism, which also operates in ceramics doped with mixed-valence cations, is most relevant under dynamic and extreme thermal/field/irradiation conditions where extra electrons/holes are abundantly generated by non-equilibrium redox reactions. For such operations, some with emerging applications, our diffusion-enhancing mechanism may provide new theoretical insight to help understand their material/microstructure stability and performance.

36 MATERIALS SCIENCE↗

NASA NTRS1992

Model atmospheres and radiation of magnetic neutron stars. I - The fully ionized case

Model neutron star atmospheres are calculated for typical cooling stars with a strong magnetic field and effective temperatures of 10 exp 5 to 10 exp 6 K. The effect of anisotropic photon diffusion in two normal modes are examined under the assumption that the opacity is due solely to the bremsstrahlung and Thomson scattering processes under conditions of LTE that are expected to prevail at the temperatures and densities obtained. The main aspects of anisotropic photon diffusion, and an original procedure for calculating model atmospheres and emitted spectra are discussed. Representative calculated spectra are given, and it is found that the hard spectral excess characterizing the nonmagnetic case, while still present, becomes less prominent in the presence of magnetic fields in the range of 10 exp 11 to 10 exp 13 G.

Shibanov, Iu. A.↗

DOE OSTI2014

A DNS evaluation of mixing models for transported PDF modelling of turbulent nonpremixed flames

Transported probability density function (TPDF) approaches are well suited to modelling turbulent, reacting, variable density flows. One of the main challenges to the successful deployment of TPDF methods is accurately modelling the unclosed molecular mixing term. This study examines three of the most widely used mixing models: the Interaction by Exchange with the Mean (IEM), Modified Curl (MC) and Euclidean Minimum Spanning Tree (EMST) models. Direct numerical simulation (DNS) data-sets were used to provide both initial conditions and inputs needed over the course of the runs, including the mean flow velocities, mixing frequency, and the turbulent diffusion coefficient. The same chemical mechanism and thermodynamic properties were used, allowing the study to focus on the mixing model. The simulation scenario was a one-dimensional, nonpremixed, turbulent jet flame burning either a syngas or ethylene fuel stream that featured extinction and reignition. This test scenario was selected because extinction and reignition phenomena are sensitive to the mixing model. Three DNS cases were considered for both the syngas and ethylene cases with a parametric variation of Reynolds and Damköhler numbers, respectively. Extinction events became more popular with increasing Reynolds number in the syngas cases and with decreasing Damköhler number in the ethylene cases. The model was first tested with the mixing frequency defined from the dissipation rate and variance of mixture fraction. With this definition, for the syngas cases this study finds that the TPDF method is successful at predicting flame extinction and reignition using all three mixing models for the relatively lower and intermediate Reynolds number cases, but that all models under-predict reignition in the relatively higher Reynolds number case. In the ethylene fuelled cases, only the EMST mixing model correctly predicts the reignition event for the two higher Damköhler number cases, yet, in the lowest Damköhler number case the EMST model over-predicts reignition and the IEM and MC models under-predict it. Mixing frequency was then modelled based on the turbulence frequency and a model constant $C_{\phi}$, the ratio of scalar to mechanical mixing rates. The DNS cases were reexamined with this definition and the findings suggested that the optimal value for $C_{\phi}$ is mixing model and case dependent. In particular, it was found in the ethylene case considered that reignition could be achieved with the IEM and MC models by adjusting the value of $C_{\phi}$.

42 ENGINEERING↗

DOE OSTI2015

Reduced order modeling of mechanical degradation induced performance decay in lithium-ion battery porous electrodes

In this paper, a one-dimensional computational framework is developed that can solve for the evolution of voltage and current in a lithium-ion battery electrode under different operating conditions. A reduced order model is specifically constructed to predict the growth of mechanical degradation within the active particles of the carbon anode as a function of particle size and C-rate. Using an effective diffusivity relation, the impact of microcracks on the diffusivity of the active particles has been captured. Reduction in capacity due to formation of microcracks within the negative electrode under different operating conditions (constant current discharge and constant current constant voltage charge) has been investigated. At the beginning of constant current discharge, mechanical damage to electrode particles predominantly occurs near the separator. As the reaction front shifts, mechanical damage spreads across the thickness of the negative electrode and becomes relatively uniform under multiple discharge/charge cycles. Mechanical degradation under different drive cycle conditions has been explored. It is observed that electrodes with larger particle sizes are prone to capacity fade due to microcrack formation. Finally, under drive cycle conditions, small particles close to the separator and large particles close to the current collector can help in reducing the capacity fade due to mechanical degradation.

25 ENERGY STORAGE↗

DOE OSTI2020

Heavy flavor quenching and flow: the roles of initial condition, pre-equilibrium evolution, and in-medium interaction

Within an advanced Langevin-hydrodynamics framework coupled to a hybrid fragmentation-coalescence hadronization model, we study heavy flavor quenching and flow in relativistic heavy-ion collisions. We investigate how the initial heavy quark spectrum, the in-medium energy loss and hadronization mechanisms of heavy quarks, the evolution profile of the pre-equilibrium stage, the medium flow, and the temperature dependence of heavy quark diffusion coefficients influence the suppression and elliptic flow of heavy mesons at the RHIC and the LHC. Our results show that the different modeling of initial conditions, pre-equilibrium evolution, and in-medium interactions can individually yield uncertainties of approximately 10-40% in D meson suppression and flow at a low transverse momentum. Furthermore, we also find that proper combinations of collisional versus radiative energy loss, coalescence versus fragmentation in hadronization, and the inclusion of medium flow are the most important factors for describing the suppression and elliptic flow of heavy mesons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗