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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Turbulence theories and statistical closure approaches

When discussing research in physics and in science more generally, it is common to ascribe equal importance to the three components of the scientific trinity: theoretical, experimental, and computational studies. This review will explore the future of modern turbulence theory by tracing its history, which began in earnest with Kolmogorov’s 1941 analysis of turbulence cascade and inertial range [A.N. Kolmogorov, Dokl. Akad. Nauk SSSR, 30, 299, (1941); 32, 19, (1941)]. The 80th Anniversary of Kolmogorov’s landmark study is a welcome opportunity to survey the achievements and evaluate the future of the theoretical approach of turbulence research. Over the years, turbulence theories have been critically important in laying the foundation of our understanding of the nature of turbulent flows. In particular, the Direct Interaction Approximation (DIA) [R.H. Kraichnan, J. Fluid Mech., 5, 497 (1959)] and its subsequent development, known as the statistical closure approach, can be identified as perhaps the most profound single advancement. The remarkable success of the statistical closure has furnished a platform to study such essential concepts as the energy transfer process and interacting scales, and the roles of the straining and sweeping motions. More recently, the quasi-Lagrangian formulation of V. L’vov & I. Procaccia and Kraichnan’s solvable passive scalar model provided powerful ways to explore another fundamental aspect of turbulent flows, the phenomena of intermittency, and the associated anomalous scaling exponents. In the meantime, the theory of fluid equilibria has been developed to describe the large-scale structures that can emerge from turbulent cascades of two-dimensional and geophysical flows at a later time. And yet, despite all these successes, analytical treatments suffer from mathematical complexities. As a result, the utility of theoretical approaches has been limited to relatively idealized flows. On the other hand, in recent decades, computational abilities and experimental facilities have reached an unprecedented scale. Looking beyond the horizon, the imminent deployment of exascale supercomputers will generate complete datasets of the entire flow field of key benchmark flows, allowing researchers to extract additional measurements concerning fully developed, complex turbulent flow fields far beyond those available from the statistical closure theories. Some other developments that could potentially influence the future course of turbulence theories include the advancement of machine learning, artificial intelligence, and data science; likely disruptions arising from the advent of quantum computation; and the increasingly prominent role of turbulence research in providing more accurate climate scientific data. Finally, turbulence theorists can leverage these developments by asking the right questions and developing advanced, sophisticated frameworks that will be able to predict and correlate vast amounts of data from the other two components of the trinity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Closures and Simulation for Thermal Radiation Transport in Stochastic Media with Nonlinear Temperature Dependence

Because of the practical challenge of rendering very complex realistic spatial structures for numerical work, it is common practice to resort to characterizing such media as stochastic mixtures of materials, ideally parametrized with low order statistics such as the mean, variance, and correlation functions of the now random material properties. This enables realizations of the medium to be repeatedly generated and radiation transport computations to, in principle, be performed for a large ensemble of these realizations to obtain a statistically well-characterized radiation field. Statistical post-processing yields desired quantities such as conditional and unconditional mean radiation flux and probability distributions of transmitted radiation. However, such computations prove expensive for all but the simplest stochastic geometries and are most suited for benchmarking approximate models. The most common approximations lead to homogenized media so that transport computations are required only on a single medium realization but by construct provide only limited statistical information on the radiation field. Almost all approximate approaches to this problem attempt to develop equations for low order moments of the radiation intensity (mean, second moment, correlation function) but inevitably encounter a closure problem: the equation for any statistical moment will contain terms depending on unknown higher-order moments. Thus, the challenge shifts to one of developing closure relations that relate the unknown moments to the lower order moments. Under very special conditions, an exact closure can be derived but in general closures are heuristically stated constitutive relations. Also, closure approaches depend on whether the mixing statistics are spatially and/or temporally continuous as in fluctuating turbulent fields, or discontinuous as in randomly mixed solid chunks of material. Thus, unconditional averaging is generally applied in the former case but conditional averaging is more appropriate when the mixing is discontinuous. In this work, the emphasis is on binary statistical mixtures of immiscible fluids as as such the quantities of interest are averages (flux, temperature) conditioned on the material type.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Closure models for the feedback of energetic particles on plasma turbulence

Energetic particles interact with the plasma surrounding them, resonating with certain types of plasma waves to stabilize them while destabilizing others, and changing the character of the background turbulence in ways that have not been fully quantified or understood. Interaction with the turbulent background plasma is key to the acceleration of many types of energetic particles including high-energy cosmic rays, solar energetic particles, and pick-up ions. The acceleration of particles is a process that would ideally be described by a kinetic model, a type of model that follows a probability distribution function (PDF) for all particles in 7-dimensional (x, y, z, v x , v y , v z , t) space. Because of the high dimensionality of a kinetic model, simulations that solve kinetic equations use the largest computational resources currently available, and are yet unable to simulate a realistic number of particles, reach the large scales necessary for astrophysical problems, and use high-precision numerical methods. Two available alternatives to kinetic plasma models have been explored for this problem, with limited success. One is a multi-fluid model produced by a cumulant discarding closure, which evolves coupled equations for the velocity, magnetic field, and internal energy for both the background plasma and the fluid of energetic particles. However, simulations that solve multi-fluid magnetohydrodynamic (MHD) equations are able to include the interaction with energetic particles only in crude ways, typically as an add-on pressure term. The second alternative is to use a hybrid method to couple a fluid description of the background plasma to a kinetic model or a Fokker–Planck model for the energetic particles. These methods are hampered by the physical modeling of the coupling. In this work, we develop a new model, which follows the PDF for all particles; this can be viewed as a step toward physical realism above a multi-fluid MHD model, while also being more computationally efficient than a kinetic model. The equations we develop model both the background plasma and the energetic particles self-consistently. Over the last decade, similar PDF methods have been developed to a high level of sophistication to model reactive flows and turbulent combustion for engineering applications. For treatment of the feedback of the energetic particles on a background plasma, a PDF closure approach should evaluate the mean characteristics, including the density, with better statistical quality than will particle-sampling procedures.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Techniques for improved statistical convergence in quantification of eddy diffusivity moments

While recent approaches, such as the macroscopic forcing method (MFM) or Green's function-based approaches, can be used to compute Reynolds-averaged Navier-Stokes closure operators using forced direct numerical simulations, MFM can also be used to directly compute moments of the effective nonlocal and anisotropic eddy diffusivities. The low-order spatial and temporal moments contain limited information about the eddy diffusivity but are often sufficient for quantification and modeling of nonlocal and anisotropic effects. However, when using MFM to compute eddy diffusivity moments, the statistical convergence can be slow for higher-order moments. In this work, we demonstrate that using the same direct numerical simulation (DNS) for all forced MFM simulations improves statistical convergence of the eddy diffusivity moments. We present its implementation in conjunction with a decomposition method that handles the MFM forcing semianalytically and allows for consistent boundary condition treatment, which we develop for both scalar and momentum transport. We demonstrate that for a two-dimensional Rayleigh-Taylor instability case study, using the same DNS for all forced MFM simulations results in convergence with 𝒪⁡(100) simulations rather than 𝒪⁡(1000) simulations. In conclusion, we then demonstrate the impacts of improved convergence on the quantification of the eddy diffusivity.

general physics↗
DOE OSTI2021

Situating the Vector Density Approach Among Contemporary Continuum Theories of Dislocation Dynamics

Abstract For the past century, dislocations have been understood to be the carriers of plastic deformation in crystalline solids. However, their collective behavior is still poorly understood. Progress in understanding the collective behavior of dislocations has primarily come in one of two modes: the simulation of systems of interacting discrete dislocations and the treatment of density measures of varying complexity that are considered as continuum fields. A summary of contemporary models of continuum dislocation dynamics is presented. These include, in order of complexity, the two-dimensional statistical theory of dislocations, the field dislocation mechanics treating the total Kröner–Nye tensor, vector density approaches that treat geometrically necessary dislocations on each slip system of a crystal, and high-order theories that examine the effect of dislocation curvature and distribution over orientation. Each of theories contain common themes, including statistical closure of the kinetic dislocation transport equations and treatment of dislocation reactions such as junction formation. An emphasis is placed on how these common themes rely on closure relations obtained by analysis of discrete dislocation dynamics experiments. The outlook of these various continuum theories of dislocation motion is then discussed.

Engineering↗
DOE OSTI2026

elm-diagnostics

elm-diagnostics is a Python package for computing diagnostic analyses and visualizations for the E3SM Land Model (ELM) component and is meant to support new feature development in ELM. The tool reads model history files and performs quantitative analyses including budget-closure checking, variable transformations, temporal aggregations, and statistical summaries to support model evaluation, validation, and scientific interpretation. The framework is designed for extensibility, with modular architecture enabling straightforward addition of new diagnostic methods, derived variables, analysis types, visualization approaches, and model-specific adaptations

Hoffman, Matt [Los Alamos National Laboratory]↗
DOE OSTI2023

A First Principles Approach to Spectral Phonon Transport in Heterostructures

Understanding thermal transport across interfaces which give rise to a thermal resistance (also known as Kapitza resistance) is a critical issue affecting the development of nanotechnologies. Much modern and emergent nanotechnology consist of adjacent materials, and phonon mediated heat transfer governs thermal behavior across internal interfaces in these devices. The physics of thermal transport in solids are governed both by phenomena occurring at the atomic scale and interactions with the material's microstructure. The forecasting of fundamental quantities such as temperature, heat flux and thermal conductivity typically employs the semi-classical Boltzmann transport equation to predict the macroscopic behavior of materials in terms of the microscopic dynamics of its heat carriers. Kapitza resistance was first discovered in liquid helium experiments and has led to a fundamental research thrust in micro and nano-scale heat transport, the behavior of thermal carriers across internal interfaces. Thermal interfacial resistance (TIR) is a widely studied phenomenon, first engaged by Swartz and Pohl through their development of the acoustic and diffuse mismatch methods, then continued through myriad efforts with varying methods and approaches in an attempt to resolve carrier behavior at thermal interfaces. Many of the fundamental approaches to TIR have been at the nanoscale, and research is conducted with molecular dynamics (MD) and density functional theory (DFT) methods. The limitations of these methods is system size; atomistic methods tend to be limited to system sizes of 100,000 atoms or less. Larger length-scale methods have also been pursued, based on the principles of acoustic or diffuse mismatch, but not all include simulation of TIR using a full phonon band spectrum, or temperature dependent methods. Our approach to enabling phonon transport in layered materials draws upon our previous work of demonstrating spectrally coupled phonon transport in homogeneous and heterogeneous materials. We use a semi-analytical approach in which the Bose-Einstein (B-E) statistics set the strength of the phonon radiance in a frequency group, but the B-E statistics are informed with information from the transport system. The B-E statistics in a single frequency group feels the influence of all the groups through the spatial temperature. We also include a new field term which is an indicator of the amount of non-equilibrium behavior of the phonon spectrum---this is added to the phonon source term in all groups to ensure closure and conservation of energy, as the phonon groups in the transport system and the analytical systems are coupled. This work builds upon our previous approach by adding a phonon coupling term at an internal interface, using the principles of the DMM through transmission and reflection coefficients. In this work, the coefficients are determined through computing a common temperature at the interface, influenced by the phonon band structure of both materials, in effect, providing mixing between the two material systems and using the common temperature to set the strength of the phonon radiance at the boundaries on either side of the interface. Our approach uses material properties computed along various crystallographic orientations, and while some isotropy is built into the interface condition, the material properties weight the phonon distributions in the proper crystalline direction. Greater resolution of phonon behavior in proximity to an interface, and more accurate predictions of TIR are obtained. While it is true the assumption of diffuse mismatch can yield inconsistent results compared to experiment especially at low temperatures, this work focuses on room temperature and beyond effects, for future applications in nuclear fuel, or thermoelectric devices; a modified mismatch approach may be feasible if applied properly. Additionally, our methods focus on bridging mesoscale to engineering scale

36 MATERIALS SCIENCE↗
DOE OSTI2025

Direct statistical simulation of the Lorenz96 system in model reduction approaches

Direct statistical simulation (DSS) of nonlinear dynamical systems bypasses the traditional route of accumulating statistics by lengthy direct numerical simulations by solving the equations that govern the statistics themselves. DSS suffers, however, from the curse of dimensionality as the statistics (such as correlations) generally have higher dimensions than the underlying dynamical variables. Here we investigate two approaches to reduce the dimensionality of DSS, illustrating each method with numerical experiments with the Lorenz96 dynamical system. The forms of DSS chosen here involve approximate closures at second and third order in the equal-time cumulants. We demonstrate significant reduction in computational effort that can be achieved without sacrificing the accuracy of DSS. The methods developed here can be applied to turbulent fluid and magnetohydrodynamical systems. Published by the American Physical Society 2025

Li, Kuan↗
DOE OSTI2023

Using National-Scale Data to Inform Coal Power Plant Redevelopment and Coal Community Revitalization Planning

In the United States, individual coal plants have high variation in their construction and operation. Coal plants commonly have multiple units, with different commissioning ages, operational position, and maintenance conditions – even multiple fuels. These units may be in changing states of utilization, with variation in productivity depending on economic contexts. Coal plants themselves may be temporarily offline, mothballed, retired, or decommissioned due to owner/operator portfolios or market conditions, and the current posture of the plant may be difficult to ascertain without local news sources (Tarekegne et al. 2021). Anticipated dates of plant closures are prospectively represented to regulators and to the Energy Information Administration (EIA), but may also experience uncertainty due to the engineering, environmental, economic and social complexity of closing a very large power plant. As noted in this report, closure of the first unit to the last within a single plant may span more than 20 years. Yet tracking and predicting the position of our nation’s coal fleets on a national scale is deeply important. In developing a case for federal datasets and an approach to building and curating these data, this report identified that data must have high fidelity at the plant-level to be meaningful in aggregate. Plant-scale detail is also a match for its application: national priorities in federal investment range from economic revitalization for coal plant communities to maintaining reliable electric grid operations. This document is organized into a statistical review of coal plant retirements, past and prospective, in the United States; trends in the relationship between closures and existing federal investment programs for community revitalization; and potential methods for accelerating site redevelopment through advanced geospatial analysis based on federal data.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2021

Data assimilation empowered neural network parametrizations for subgrid processes in geophysical flows

In the past couple of years, there has been a proliferation in the use of machine learning approaches to represent subgrid-scale processes in geophysical flows with an aim to improve the forecasting capability and to accelerate numerical simulations of these flows. Despite its success for different types of flow, the online deployment of a data-driven closure model can cause instabilities and biases in modeling the overall effect of subgrid-scale processes, which in turn leads to inaccurate prediction. To tackle this issue, we exploit the data assimilation technique to correct the physics-based model coupled with the neural network as a surrogate for unresolved flow dynamics in multiscale systems. In particular, we use a set of neural network architectures to learn the correlation between resolved flow variables and the parametrizations of unresolved flow dynamics and formulate a data assimilation approach to correct the hybrid model during their online deployment. We illustrate our framework in a set of applications of the multiscale Lorenz 96 system for which the parametrization model for unresolved scales is exactly known, and the two-dimensional Kraichnan turbulence system for which the parametrization model for unresolved scales is not known a priori. Our analysis, therefore, comprises a predictive dynamical core empowered by (i) a data-driven closure model for subgrid-scale processes, (ii) a data assimilation approach for forecast error correction, and (iii) both data-driven closure and data assimilation procedures. We show significant improvement in the long-term prediction of the underlying chaotic dynamics with our framework compared to using only neural network parametrizations for future prediction. Moreover, we demonstrate that these data-driven parametrization models can handle the non-Gaussian statistics of subgrid-scale processes, and effectively improve the accuracy of outer data assimilation workflow loops in a modular nonintrusive way.

42 ENGINEERING↗
DOE OSTI2023

Supervised machine learning-based multivariate regression of parallel closures for a high-collisionality deuterium-carbon plasma

Many plasmas of interest in laboratory experiments and space consist of multiple ion species. In tokamak edge plasmas, for instance, ionized impurities expelled from the vessel wall influence plasma transport. When describing multi-species plasmas using fluid equations, we need accurate closure relations to close the set of fluid equations. In this study, we introduce the development of fitting formulas for parallel closures using supervised machine learning, in conjunction with the recent closure theory, considering multi-ion collisions and arbitrary ion temperatures. We apply this approach to a high-collisionality deuterium-carbon plasma and demonstrate its effectiveness. As a result, the machine learning-based method for developing practical and accurate closures can be extended to a wider range of plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Gaussian process hydrodynamics

Abstract We present a Gaussian process (GP) approach, called Gaussian process hydrodynamics (GPH) for approximating the solution to the Euler and Navier-Stokes (NS) equations. Similar to smoothed particle hydrodynamics (SPH), GPH is a Lagrangian particle-based approach that involves the tracking of a finite number of particles transported by a flow. However, these particles do not represent mollified particles of matter but carry discrete/partial information about the continuous flow. Closure is achieved by placing a divergence-free GP prior ξ on the velocity field and conditioning it on the vorticity at the particle locations. Known physics (e.g., the Richardson cascade and velocity increment power laws) is incorporated into the GP prior by using physics-informed additive kernels. This is equivalent to expressing ξ as a sum of independent GPs ξ l , which we call modes, acting at different scales (each mode ξ l self-activates to represent the formation of eddies at the corresponding scales). This approach enables a quantitative analysis of the Richardson cascade through the analysis of the activation of these modes, and enables us to analyze coarse-grain turbulence statistically rather than deterministically. Because GPH is formulated by using the vorticity equations, it does not require solving a pressure equation. By enforcing incompressibility and fluid-structure boundary conditions through the selection of a kernel, GPH requires significantly fewer particles than SPH. Because GPH has a natural probabilistic interpretation, the numerical results come with uncertainty estimates, enabling their incorporation into an uncertainty quantification (UQ) pipeline and adding/removing particles (quanta of information) in an adapted manner. The proposed approach is suitable for analysis because it inherits the complexity of state-of-the-art solvers for dense kernel matrices and results in a natural definition of turbulence as information loss. Numerical experiments support the importance of selecting physics-informed kernels and illustrate the major impact of such kernels on the accuracy and stability. Because the proposed approach uses a Bayesian interpretation, it naturally enables data assimilation and predictions and estimations by mixing simulation data and experimental data.

Mathematics↗
DOE OSTI2026

Data-based filtered dissipation rate modelling for multi-modal turbulent combustion: evaluating a priori model generalizability

Manifold-based models offer a computationally efficient alternative to directly transporting the thermochemical state in computational simulations of turbulent reacting flows, projecting the high-dimensional thermochemical state-space onto a low-dimensional manifold. Recent efforts have yielded a manifold-based model applicable to multi-modal combustion, enabling reconstruction of the thermochemical state from solutions to two-dimensional manifold equations in mixture fraction and generalized progress variable that are parameterised by three scalar dissipation rates. In coarse-grained simulations such as Large Eddy Simulation (LES), closure of the multi-modal manifold equations and subfilter variances/covariance requires closure of three filtered scalar dissipation rates. Here, the present work adopts a data-based approach, providing closure for the three filtered scalar dissipation rates via deep neural networks (DNNs). High-fidelity datasets corresponding to an autoigniting n-dodecane jet flame and a bluff body swirl-stabilized confined lifted spray flame of two aviation fuels (Jet-A and C1) with different ignition propensities are leveraged to generate training data that spans a diverse range of thermodynamic conditions and combustion modes, including low- and high-temperature ignition regimes in addition to premixed and nonpremixed behaviour. A final DNN model is trained to enforce inherent physical constraints by learning nonlinear functional transformations of the three filtered scalar dissipation rates. The generalizability of this constrained DNN model is demonstrated a priori via conditional statistics evaluated on the lifted spray flame with C1–a configuration that had not been included in the training data. Excellent DNN agreement with conditional DNS statistics is observed, and integrated gradients are computed to identify the most sensitive input variables. The similarity of the marginal PDFs of the most informative input variables and outputs across configurations are quantified via the Wasserstein metric, demonstrating that data-based models may successfully generalize to unseen parametric conditions so long as the most informative input variables share similar distributions across training and testing datasets.

Data-based modelling↗
DOE OSTI2023

Multifidelity Approach to Sensitivity Estimation in Large-Eddy Simulation

A novel approach to compute affordable approximate sensitivities in a large-eddy simulation (LES) is proposed and assessed. The approach is based on solving a Reynolds-averaged Navier–Stokes (RANS) problem that has been linearized around the mean LES solution, with closure modeling required for the linearized changes in turbulent Reynolds stresses. In the present study, the closure modeling is based on a linearized algebraic turbulence model. The method is assessed for the flow over a NACA0012 airfoil at a fixed angle of attack, with the Reynolds number as the variable parameter. The results show that, provided an accurate linearized closure model, the method predicts the correct sensitivity of the skin friction coefficient and the mean velocity field at the cost of a linearized RANS, which provides an important proof-of-concept for this approach. Here, the linearized algebraic turbulence model with standard model coefficients produces a reasonably accurate sensitivity, but the results also suggest that accuracy could be gained from recalibrating the model coefficients for this new use of the model.

42 ENGINEERING↗
DOE OSTI2023

Statistical chronometry of Meteorites: II. Initial abundances and homogeneity of short-lived radionuclides

Astrophysical models of planet formation require accurate radiometric dating of meteoritic components by short-lived (Al-Mg, Mn-Cr, Hf-W) and long-lived (U-Pb) chronometers, to develop a timeline of such events in the solar nebula as formation of Ca-rich, Al-rich Inclusions (CAIs), chondrules, planetesimals, etc. CAIs formed mostly around a time (“t=0”) when the short-lived radionuclide 26 Al (t 1/2 = 0.72 Myr) was present and presumably homogeneously distributed at a known level we define as ( 26 Al/ 27 Al) SS = 5.23 × 10 -5 . The time of formation after t=0 of another object can be found by determining its initial ( 26 Al/ 27 Al) 0 ratio and comparing it to ( 26 Al/ 27 Al) SS . Dating of meteoritic objects using the Mn-Cr or Hf-W systems is hindered because the abundances ( 53 Mn/ 55 Mn) SS and ( 182 Hf/ 180 Hf) SS at t=0 are not known precisely. To constrain these quantities, we compile literature Al-Mg, Mn-Cr, Hf-W and Pb-Pb data for 13 achondrites and use novel statistical techniques to minimize the discrepancies between their times of formation across these systems. We find that for ( 53 Mn/ 55 Mn) SS = (7.80±0.36)×10 -6 , ( 182 Hf/ 180 Hf) SS = (10.41 ± 0.12) × 10-5, t SS = 4568.65 ± 0.10 Myr, and a 53 Mn half-life of 3.98 ± 0.22 Myr, these four free parameters make concordant 18 formation times recorded by the different systems in all six known volcanic achondrites (the quenched angrites D’Orbigny, Sahara 99555, Northwest Africa 1670; the psuedo-eucrites Asuka 881394 and Ibitira; and the basaltic achondrite Northwest Africa 7325). These parameters also make concordant the ages derived for chondrules from CB/CH achondrites, formed simultaneously in an impact. The other seven achondrites are not quite concordant, but are plutonic angrites or ‘carbonaceous achondrites’ for which simultaneous closure of the isotopic systems might not be expected. Our findings provide very strong support for homogeneity of 26 Al, 53 Mn, and 182 Hf in the solar nebula, and our approach offers a path for more precise chronometry

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

An approximate inertial manifold (AIM) based closure for turbulent flows

A closure model for turbulent flows is developed based on a dynamical system theory. An appropriately discretized formulation of the governing equations is considered for this process. The key ingredient is an approximation of the system’s attractor, where all the trajectories in phase space are confined. This approximate inertial manifold based approach provides a path to track trajectories of the system in a lower-dimensional subspace. Unlike conventional coarse-graining approaches, the turbulent field is decomposed into resolved and unresolved dynamics using the properties of the governing equations. The novelty of the approach relies on the reconstruction of the unresolved field constrained by the governing equations. A posteriori tests for homogeneous isotropic turbulence and the Kuramoto–Sivashinsky equation show promising results for considerable dimension reduction with strong convergence properties. The proposed model outperforms the dynamic Smagorinsky model, and the computational overhead is competitive with similar approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

CIGS Technology Advancement via Fundamental Modeling of Defect/Impurity Interactions (Final Technical Report)

The primary goals of the proposed work were to provide modeling tools (and the associated insight which comes along with model development) for design and optimization of CuIn x Ga 1-x Se 2 (CIGS) and CdSeTe (CST) solar cell manufacturing processes and to establish the foundation for comprehensive end-to-end predictive modeling tools to enable optimization of thin film photovoltaic technology for performance, cost, yield, and reliability. The initial focus of efforts within this project was to develop coupled process/optical/device models for CIGS PV technology and to work with Siva Power to apply that TCAD (technology computer-aided design) system to improve the efficiency and reduce manufacturing costs for CIGS solar cells. Our approach to that end was to generate an extensive database of DFT calculations and to use those calculations via statistical thermodynamics methods and Monte Carlo simulation to develop and characterize models for the behavior of native defects as well as intentional and unintentional impurities, including the redistribution of the primary components of CIGS films. Increased effort went toward coupling those models for defect behavior and composition evolution to the performance of multicrystalline CIGS solar cells via prediction of doping level and recombination lifetime as function of manufacturing process. In the second budget period, the project pivoted to developing a similar system for the CdSeTe system, focused especially on understanding the role of Se/Te alloy concentration. Execution of the project resulted in the successful development of TCAD systems for both CIGS and CdSeTe thin film PV within the Synopsys Sentaurus framework by utilizing the Alagator interface. In the first budget period of the project, we developed quantitative models for the major components of CIGS PV and implemented them within a framework that couples process, optical, and device simulation. From the insights we have gained, we identified novel opportunities for enhancing CIGS solar cell performance and have laid the groundwork to further optimize the layer structure, composition profile, and thermal cycles for substantially improved efficiency and lower manufacturing costs. For the CIGS system, process changes to achieve greater than 1% absolute enhancement in efficiency were identified, but testing of those approaches was stymied by lack of a domestic CIGS manufacturing partner after the closure of Siva Power as well as Miasole. For CdSeTe, a fully capable TCAD system only became ready to apply near the end of the project period, so substantial opportunities remain to apply those models to enhance the leading thin film PV technology.

14 SOLAR ENERGY↗
DOE OSTI2020

Characterization and CST Batch Contact Equilibrium Testing of Modified Tank 9H Process Supernate Samples in Support of TCCR

The Tank Closure Cesium Removal (TCCR) system uses ion exchange columns filled with crystalline silicotitanate (CST) media to process radioactive waste solutions for the removal of ¹³⁷Cs. TCCR currently focuses on dissolving Savannah River Site (SRS) radioactive tank waste (primarily sodium saltcake solids) within Tank 10H followed by at-tank ion exchange column treatment. Two supernate batches from Tank 10H have been processed through the TCCR unit and processing of a third batch is expected soon. After processing of this supernate batch, plans are to replace the CST columns and process dissolved salt solution from Tank 9H through Tank 10H and then through the new CST columns installed in the TCCR unit. The new columns are expected to contain either a media similar to an archived CST batch (IE-911) or the R9120-B CST media used in the current TCCR columns (the two materials are fundamentally the same; just different specifications, product names, and preconditioning steps). Samples of Tank 9H dissolved saltcake were received at the Savannah River National Laboratory (SRNL) and characterized. The Tank 9H supernate contained a high sodium concentration (~9.6 M Na⁺) and will require dilution to near 6 M [Na⁺] prior to processing through the TCCR unit. The cesium concentration in Tank 9H is currently significantly higher than was observed with Tank 10H. Three dilutions of the Tank 9H supernate were conducted to mimic possible dilutions that could be conducted in the tank farm prior to TCCR processing using inhibited water, sodium hydroxide, and sodium nitrate solutions. Dilution #1 was prepared by diluting the Tank 9H supernate by a factor of 1.6 with inhibited water, Dilution #2 was prepared by diluting the Tank 9H supernate by a factor of 3.7 with a mixed sodium hydroxide/sodium nitrate diluent, and Dilution #3 was prepared by also diluting by a factor of 3.7 but with sodium hydroxide only. All three dilutions have similar Na⁺ concentrations (~6 M), but Dilutions #2 and #3 contain significantly less cesium. Major and key minor components of the diluted Tank 9H supernate samples are provided in Table ES-1. Batch contact equilibrium tests were conducted with the Tank 9H dilutions and the two different CST media batches being considered for use in the new TCCR columns. Results are summarized in Table ES-2 and compared to ZAM model predictions. The highest cesium distribution coefficient and percent removal were observed with Dilution #3. IE-911 CST (an archived CST media batch) was more effective at removing cesium than the more recently prepared R9120-B CST media, though both media samples removed >88% of the cesium and the differences may not be statistically different considering the overall uncertainty. Based on the results, maximum cesium loadings were calculated for each CST media type and Tank 9H dilution. In general, maximum cesium loadings from dilutions of this supernate batch are quite high (approaching 0.1 mmol total Cs⁺/g CST for Dilution #1). The highest calculated maximum ¹³⁷Cs loading for the Tank 9H dilutions using the ZAM model with input of the tank compositions and batch contact results was 207 Ci/kg CST (Dilution #1 with IE-911 CST). In all cases, higher maximum cesium loading values were predicted for IE-911 CST versus R9120-B, although the differences varied considerably between the dilutions. The maximum loading value for IE-911 CST with Tank 9H Dilution #1 was only 7% higher than the maximum loading for R9120-B. The maximum loading value for IE-911 CST with Dilution #3 was 24% higher than the maximum loading for R9120-B. Dilution #2 was intermediate between these values. Note that these maximum loading values are the theoretical calculated values, and actual operating conditions will cause differences. A CST binder dilution (correction) factor near 0.7 (relative to pure powder CST) was required for each batch contact test with IE-911 engineered CST using the three Tank 9H dilutions. Correction factors calculated for R9120-B CST ranged from 0.56 to 0.66 for the three dilutions. Following the batch contact tests, the CST samples were isolated from the Tank 9H solution, washed, dried, and digested in acid following established procedures. The analysis results are provided in Table ES-3. Total cesium loading values determined by CST digestion were similar to the calculated loading values based on solution analysis (Table ES-2) for all samples. In addition, the CST was observed to load calcium (R9120-B sample only), iron, strontium, lead, uranium, and plutonium after contact with the waste supernate, as has been observed previously.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗