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NASA NTRS1991

An exploratory study of a three-dimensional shock wave turbulent boundary layer interaction in a corner

Three-dimensional shock wave turbulent boundary layer interactions in a corner have been studied at M about 3. The first phase, detailed mean wall static pressure distributions, has shown the interaction of a two-dimensional flow on one wall with the three-dimensional flow generated by a fin. Major three-dimensional effects on both flows were observed, extending from the interaction of the initial region of the three-dimensional flow and the corner. A large part of the resulting corner flow has little resemblance to either the two-dimensional or three-dimensional interacting flows.

Bogdonoff, S. M.↗

NASA NTRS1990

Three-dimensional mode resonances in boundary layers, jets and wakes

The paper emphasizes understanding and promoting mechanisms, such as resonance mechanisms, governing the first growth of three-dimensionality in experiments on instability and transition to turbulence. It is noted that in past experiments, only two-dimensional modes were directlly forced leaving three-dimensional disturbance content undefined, both in amplitude and wave numbers. An approach offering to seed three-dimensional oblique modes along with two-dimensional modes is discussed. The technique introduces controlled three-dimensional (oblique) time-periodic waves through a spanwise phase shift between neighbor elements; a two-dimensional disturbance is added simultaneously.

Corke, Thomas C.↗

NASA NTRS1991

The three-dimensional evolution of a plane mixing layer. Part 1: The Kelvin-Helmholtz roll-up

The Kelvin Helmholtz roll up of three dimensional, temporally evolving, plane mixing layers were simulated numerically. All simulations were begun from a few low wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity profile. The spanwise disturbance wavelength was taken to be less than or equal to the streamwise wavelength associated with the Kelvin Helmholtz roll up. A standard set of clean structures develop in most of the simulations. The spanwise vorticity rolls up into a corrugated spanwise roller, with vortex stretching creating strong spanwise vorticity in a cup shaped region at the vends of the roller. Predominantly streamwise rib vortices develop in the braid region between the rollers. For sufficiently strong initial three dimensional disturbances, these ribs collapse into compact axisymmetric vortices. The rib vortex lines connect to neighboring ribs and are kinked in the opposite direction of the roller vortex lines. Because of this, these two sets of vortex lines remain distinct. For certain initial conditions, persistent ribs do not develop. In such cases the development of significant three dimensionality is delayed. When the initial three dimensional disturbance energy is about equal to, or less than, the two dimensional fundamental disturbance energy, the evolution of the three dimensional disturbance is nearly linear (with respect to the mean and the two dimensional disturbances), at least until the first Kelvin Helmholtz roll up is completed.

Rogers, Michael M.↗

NASA NTRS1992

Progress in multi-dimensional upwind differencing

Multi-dimensional upwind-differencing schemes for the Euler equations are reviewed. On the basis of the first-order upwind scheme for a one-dimensional convection equation, the two approaches to upwind differencing are discussed: the fluctuation approach and the finite-volume approach. The usual extension of the finite-volume method to the multi-dimensional Euler equations is not entirely satisfactory, because the direction of wave propagation is always assumed to be normal to the cell faces. This leads to smearing of shock and shear waves when these are not grid-aligned. Multi-directional methods, in which upwind-biased fluxes are computed in a frame aligned with a dominant wave, overcome this problem, but at the expense of robustness. The same is true for the schemes incorporating a multi-dimensional wave model not based on multi-dimensional data but on an 'educated guess' of what they could be. The fluctuation approach offers the best possibilities for the development of genuinely multi-dimensional upwind schemes. Three building blocks are needed for such schemes: a wave model, a way to achieve conservation, and a compact convection scheme. Recent advances in each of these components are discussed; putting them all together is the present focus of a worldwide research effort. Some numerical results are presented, illustrating the potential of the new multi-dimensional schemes.

Vanleer, Bram↗

NASA NTRS1994

A note on two-dimensional asymptotic magnetotail equilibria

In order to understand, on the fluid level, the structure, the time evolution, and the stability of current sheets, such as the magnetotail plasma sheet in Earth's magnetosphere, one has to consider magnetic field configurations that are in magnetohydrodynamic (MHD) force equilibrium. Any reasonable MHD current sheet model has to be two-dimensional, at least in an asymptotic sense (B(sub z)/B (sub x)) = epsilon much less than 1. The necessary two-dimensionality is described by a rather arbitrary function f(x). We utilize the free function f(x) to construct two-dimensional magnetotail equilibria are 'equivalent' to current sheets in empirical three-dimensional models. We obtain a class of asymptotic magnetotail equilibria ordered with respect to the magnetic disturbance index Kp. For low Kp values the two-dimensional MHD equilibria reflect some of the realistic, observation-based, aspects of three-dimensional models. For high Kp values the three-dimensional models do not fit the asymptotic MHD equlibria, which is indicative of their inconsistency with the assumed pressure function. This, in turn, implies that high magnetic activity levels of the real magnetosphere might be ruled by thermodynamic conditions different from local thermodynamic equilibrium.

Voigt, Gerd-Hannes↗

NASA NTRS1995

Working toward a three-dimensional fatigue closure model for surface cracks

The first reliable elastic fracture mechanics solutions for a surface crack in a plate were obtained by Newman and Raju. The authors, both from the Mechanics of Materials Branch at NASA-Langley, used a highly detailed finite element solution requiring substantial computational resources. Computers have since become more powerful and available; however, many important related problems remain computationally expensive. The problem of three-dimensional fatigue crack growth taking into account plasticity-induced crack closure is one such problem. It is the goal of this research to provide an efficient method to account for three-dimensional crack closure in fatigue. Newman developed a two-dimensional plasticity-induced crack closure model for center cracked specimens. This model requires iterations to determine both the contact solution at each growth step and the extent of the plastic zone at the crack tip. A three-dimensional version of this model would require obtaining these nonlinear variables all along the crack front. This model must be efficient so that repeated calculations can be performed during crack growth simulations. The highly versatile line spring model (LSM) with contact, fatigue, and plasticity will form the basis of the closure model. There are several required additions to past work to address the three-dimensional crack closure problem. Initially, these additions will include (1) an improved LSM to more accurately obtain the crack opening displacement, stress intensity factors, and elastic T-stress near the ends of the surface crack; (2) a method to determine the extent of the plastic zone all along the crack front; (3) a method to determine the contact zone given a perfectly plastic layer of material on the crack surfaces; (4) a method to determine the magnitude of the compressive contact stress; and (5) a way to implement the degree of constraint along the curved crack front. During the summer ASEE program an enhanced LSM was developed. A method similar to that of 'strip synthesis' first introduced by Fujimoto was used. Briefly, the crack opening displacements of 'slices' of the surface crack in a direction parallel to the plate surface are considered in addition to the standard LSM approach that makes use of springs obtained from slices perpendicular to the plate surface. This enhancement is necessary so that an accurate three-dimensional representation of quantities such as contact zone size, plastic zone size, stress intensity factors, T-stress, and crack opening displacement can be determined. By combining results of previous investigations with the LSM, the problem of three-dimensional crack closure will be addressed. In addition to a closure model, the enhanced LSM can be used for many other problems including interacting surface cracks and fatigue crack growth of a through crack with a curved crack front.

Joseph, Paul F.↗

NASA NTRS2000

Object Based Numerical Zooming Between the NPSS Version 1 and a 1-Dimensional Meanline High Pressure Compressor Design Analysis Code

Within NASA's High Performance Computing and Communication (HPCC) program, NASA Glenn Research Center is developing an environment for the analysis/design of propulsion systems for aircraft and space vehicles called the Numerical Propulsion System Simulation (NPSS). The NPSS focuses on the integration of multiple disciplines such as aerodynamics, structures, and heat transfer, along with the concept of numerical zooming between 0- Dimensional to 1-, 2-, and 3-dimensional component engine codes. The vision for NPSS is to create a "numerical test cell" enabling full engine simulations overnight on cost-effective computing platforms. Current "state-of-the-art" engine simulations are 0-dimensional in that there is there is no axial, radial or circumferential resolution within a given component (e.g. a compressor or turbine has no internal station designations). In these 0-dimensional cycle simulations the individual component performance characteristics typically come from a table look-up (map) with adjustments for off-design effects such as variable geometry, Reynolds effects, and clearances. Zooming one or more of the engine components to a higher order, physics-based analysis means a higher order code is executed and the results from this analysis are used to adjust the 0-dimensional component performance characteristics within the system simulation. By drawing on the results from more predictive, physics based higher order analysis codes, "cycle" simulations are refined to closely model and predict the complex physical processes inherent to engines. As part of the overall development of the NPSS, NASA and industry began the process of defining and implementing an object class structure that enables Numerical Zooming between the NPSS Version I (0-dimension) and higher order 1-, 2- and 3-dimensional analysis codes. The NPSS Version I preserves the historical cycle engineering practices but also extends these classical practices into the area of numerical zooming for use within a companies' design system. What follows here is a description of successfully zooming I-dimensional (row-by-row) high pressure compressor results back to a NPSS engine 0-dimension simulation and a discussion of the results illustrated using an advanced data visualization tool. This type of high fidelity system-level analysis, made possible by the zooming capability of the NPSS, will greatly improve the fidelity of the engine system simulation and enable the engine system to be "pre-validated" prior to commitment to engine hardware.

Follen, G.↗

NASA NTRS2010

Two-Dimensional Synthetic-Aperture Radiometer

A two-dimensional synthetic-aperture radiometer, now undergoing development, serves as a test bed for demonstrating the potential of aperture synthesis for remote sensing of the Earth, particularly for measuring spatial distributions of soil moisture and ocean-surface salinity. The goal is to use the technology for remote sensing aboard a spacecraft in orbit, but the basic principles of design and operation are applicable to remote sensing from aboard an aircraft, and the prototype of the system under development is designed for operation aboard an aircraft. In aperture synthesis, one utilizes several small antennas in combination with a signal processing in order to obtain resolution that otherwise would require the use of an antenna with a larger aperture (and, hence, potentially more difficult to deploy in space). The principle upon which this system is based is similar to that of Earth-rotation aperture synthesis employed in radio astronomy. In this technology the coherent products (correlations) of signals from pairs of antennas are obtained at different antenna-pair spacings (baselines). The correlation for each baseline yields a sample point in a Fourier transform of the brightness-temperature map of the scene. An image of the scene itself is then reconstructed by inverting the sampled transform. The predecessor of the present two-dimensional synthetic-aperture radiometer is a one-dimensional one, named the Electrically Scanned Thinned Array Radiometer (ESTAR). Operating in the L band, the ESTAR employs aperture synthesis in the cross-track dimension only, while using a conventional antenna for resolution in the along-track dimension. The two-dimensional instrument also operates in the L band to be precise, at a frequency of 1.413 GHz in the frequency band restricted for passive use (no transmission) only. The L band was chosen because (1) the L band represents the long-wavelength end of the remote- sensing spectrum, where the problem of achieving adequate spatial resolution is most critical and (2) imaging airborne instruments that operate in this wavelength range and have adequate spatial resolution are difficult to build and will be needed in future experiments to validate approaches for remote sensing of soil moisture and ocean salinity. The two-dimensional instrument includes a rectangular array of patch antennas arranged in the form of a cross. The ESTAR uses analog correlation for one dimension, whereas the two-dimensional instrument uses digital correlation. In two dimensions, many more correlation pairs are needed and low-power digital correlators suitable for application in spaceborne remote sensing will help enable this technology. The two-dimensional instrument is dual-polarized and, with modification, capable of operating in a polarimetric mode. A flight test of the instrument took place in June 2003 and it participated in soil moisture experiments during the summers of 2003 and 2004.

LeVine, David M.↗

DOE OSTI2024

Hutchinson Trace Estimation for high-dimensional and high-order Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) have proven effective in solving partial differential equations (PDEs), especially when some data are available by seamlessly blending data and physics. However, extending PINNs to high-dimensional and even high-order PDEs encounters significant challenges due to the computational cost associated with automatic differentiation in the residual loss function calculation. Herein, we address the limitations of PINNs in handling high-dimensional and high-order PDEs by introducing the Hutchinson Trace Estimation (HTE) method. Starting with the second-order high-dimensional PDEs, which are ubiquitous in scientific computing, HTE is applied to transform the calculation of the entire Hessian matrix into a Hessian vector product (HVP). This approach not only alleviates the computational bottleneck via Taylor-mode automatic differentiation but also significantly reduces memory consumption from the Hessian matrix to an HVP’s scalar output. We further showcase HTE’s convergence to the original PINN loss and its unbiased behavior under specific conditions. Comparisons with the Stochastic Dimension Gradient Descent (SDGD) highlight the distinct advantages of HTE, particularly in scenarios with significant variability and variance among dimensions. We further extend the application of HTE to higher-order and higher-dimensional PDEs, specifically addressing the biharmonic equation. By employing tensor-vector products (TVP), HTE efficiently computes the colossal tensor associated with the fourth-order high-dimensional biharmonic equation, saving memory and enabling rapid computation. The effectiveness of HTE is illustrated through experimental setups, demonstrating comparable convergence rates with SDGD under memory and speed constraints. Additionally, HTE proves valuable in accelerating the Gradient-Enhanced PINN (gPINN) version as well as the Biharmonic equation. Overall, HTE opens up a new capability in scientific machine learning for tackling high-order and high-dimensional PDEs.

Curse of dimensionality↗

DOE OSTI2022

A survey of unsupervised learning methods for high-dimensional uncertainty quantification in black-box-type problems

Constructing surrogate models for uncertainty quantification (UQ) on complex partial differential equations (PDEs) having inherently high-dimensional O(10 n ), n ≥ 2, stochastic inputs (e.g., forcing terms, boundary conditions, initial conditions) poses tremendous challenges. The “curse of dimensionality” can be addressed with suitable unsupervised learning techniques used as a pre-processing tool to encode inputs onto lower-dimensional subspaces while retaining its structural information and meaningful properties. In this work, we review and investigate thirteen dimension reduction methods including linear and nonlinear, spectral, blind source separation, convex and non-convex methods and utilize the resulting embeddings to construct a mapping to quantities of interest via polynomial chaos expansions (PCE). Here, we refer to the general proposed approach as manifold PCE (m-PCE), where manifold corresponds to the latent space resulting from any of the studied dimension reduction methods. To investigate the capabilities and limitations of these methods we conduct numerical tests for three physics-based systems (treated as black-boxes) having high-dimensional stochastic inputs of varying complexity modeled as both Gaussian and non-Gaussian random fields to investigate the effect of the intrinsic dimensionality of input data. We demonstrate both the advantages and limitations of the unsupervised learning methods and we conclude that a suitable m-PCE model provides a cost-effective approach compared to alternative algorithms proposed in the literature, including recently proposed expensive deep neural network-based surrogates and can be readily applied for high-dimensional UQ in stochastic PDEs.

42 ENGINEERING↗

DOE OSTI2025

Bias-Variance Trade-Off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs

Physics-Informed Neural Networks (PINNs) have triggered a paradigm shift in scientific computing, leveraging mesh-free properties and robust approximation capabilities. While proving effective for low-dimensional partial differential equations (PDEs), the computational cost of PINNs remains a hurdle in high-dimensional scenarios. This is particularly pronounced when computing high-order and high-dimensional derivatives in the physics-informed loss. Randomized Smoothing PINN (RS-PINN) introduces Gaussian noise for stochastic smoothing of the original neural net model, enabling the use of Monte Carlo methods for derivative approximation, which eliminates the need for costly automatic differentiation. Despite its computational efficiency, especially in the approximation of high-dimensional derivatives, RS-PINN introduces biases in both loss and gradients, negatively impacting convergence, especially when coupled with stochastic gradient descent (SGD) algorithms. We present a comprehensive analysis of biases in RS-PINN, attributing them to the nonlinearity of the Mean Squared Error (MSE) loss as well as the intrinsic nonlinearity of the PDE itself. We propose tailored bias correction techniques, delineating their application based on the order of PDE nonlinearity. The derivation of an unbiased RS-PINN allows for a detailed examination of its advantages and disadvantages compared to the biased version. Specifically, the biased version has a lower variance and runs faster than the unbiased version, but it is less accurate due to the bias. To optimize the bias-variance trade-off, we combine the two approaches in a hybrid method that balances the rapid convergence of the biased version with the high accuracy of the unbiased version. In addition to methodological contributions, we present an enhanced implementation of RS-PINN. Extensive experiments on diverse high-dimensional PDEs, including Fokker-Planck, Hamilton-Jacobi-Bellman (HJB), viscous Burgers’, Allen-Cahn, and Sine-Gordon equations, illustrate the bias-variance trade-off and highlight the effectiveness of the hybrid RS-PINN. Empirical guidelines are provided for selecting biased, unbiased, or hybrid versions, depending on the dimensionality and nonlinearity of the specific PDE problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

High-dimensional data analytics in civil engineering: A review on matrix and tensor decomposition

Recent developments in sensing and monitoring techniques have led to the generation of high-dimensional data in the field of civil engineering. High-dimensional data analytics methods have thus been developed to interpret such complex data. Among the different high-dimensional data analytics techniques, matrix and tensor decomposition methods have acquired a notable interest in the civil engineering community over the past decade. Due to their unique ability to deal with highly redundant and correlated data, these methods are establishing themselves as promising and efficient tools to analyze high-dimensional data in the civil engineering arena. In this paper, high-dimensional data is referred to as a data set in which the number of features is comparable or larger than the number of observations. This review paper aims to summarize the applications of matrix and tensor decomposition methods in civil engineering over the last decade. The survey begins with a general overview of matrix and tensor decomposition followed by highlighting their significance in the field. Afterward, various applications of these high-dimensional data analytics methods in civil engineering are presented, while the advantages offered by these methods are discussed. Lastly, challenges and potential research avenues for employing matrix and tensor decomposition and future emerging trends for their novel use are highlighted.

42 ENGINEERING↗

DOE OSTI2020

Uncovering interpretable relationships in high-dimensional scientific data through function preserving projections

Abstract In many fields of science and engineering, we frequently encounter experiments or simulations datasets that describe the behavior of complex systems and uncovering human interpretable patterns between their inputs and outputs via exploratory data analysis is essential for building intuition and facilitating discovery. Often, we resort to 2D embeddings for examining these high-dimensional relationships (e.g. dimensionality reduction). However, most existing embedding methods treat the dimensions as coordinates for samples in a high-dimensional space, which fail to capture the potential functional relationships, and the few methods that do take function into consideration either only focus on linear patterns or produce non-linear embeddings that are hard to interpret. To address these challenges, we proposed function preserving projections (FPP), which construct 2D linear embeddings optimized to reveal interpretable yet potentially non-linear patterns between the domain and the range of a high-dimensional function. The intuition here is that humans are good at understanding potentially non-linear patterns in 2D but unable to interpret non-linear mapping from high-dimensional space to 2D. Therefore, we should restrict the projection to linear but not the pattern we are seeking. Using FPP on real-world datasets, one can obtain fundamentally new insights about high-dimensional relationships in extremely large datasets that could not be processed with existing dimension reduction methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Plasmons in two-dimensional topological insulators

Here, we analyze collective excitations in models of two-dimensional topological insulators using the random phase approximation. In a two-dimensional extension of the Su-Schrieffer-Heeger model, edge plasmonic excitations with induced charge-density distributions localized at the boundaries of the system are found in the topologically nontrivial phase, dispersing similarly as one-dimensional bulk plasmons in the conventional Su-Schrieffer-Heeger chain. For two-dimensional bulk collective modes, we reveal regimes of enhanced interband wave function correlations, leading to characteristic hardening and softening of inter- and intraband bulk plasmonic branches, respectively. In the two-dimensional Haldane Chern insulator model, chiral, unidirectional edge plasmons in nano-ribbon architectures are observed, which can be characterized by an effective Coulomb interaction cross section. Bulk collective excitations in the two-dimensional Haldane model are shown to be originated by single-particle band structure details in different topological phases.

2-dimensional systems↗

DOE OSTI2020

Development and Validation of SAM Multi-dimensional Flow Model for Thermal Mixing and Stratification Modeling

Thermal mixing and stratification in large pools or enclosures are very important phenomena that are critical to nuclear reactor safety. Because of the wide ranges of time and length scales associated with such phenomena, accurate modeling and simulation of thermal mixing and stratification remain as the key unresolved, challenging problems for reactor transient analyses. In traditional system analysis codes, simplified zero-dimensional (0-D) models are widely used for their high numerical efficiency, but they generally suffer from very limited prediction accuracies or range of applicability. Like traditional system analysis codes, the current version of the SAM code has implemented such simplified 0-D and one-dimensional mixing models. On the other hand, high-resolution Computational Fluid Dynamics (CFD) tools are often used to model complex thermal mixing and stratification phenomena. They are, however, generally numerically expensive, and they require large amounts of computational resources. It is therefore desirable to implement advanced and efficient thermal mixing and stratification modeling capabilities embedded in a system analysis code. This approach will improve the accuracy of reactor safety analyses when thermal mixing and stratification are involved, and also avoid using the large computational resources needed for high-resolution CFD analysis. Currently, with the support of the U.S. DOE Office of Nuclear Energy’s Nuclear Energy Advanced Modeling and Simulation program, an effort has been launched to develop and implement a multi-dimensional flow model in the system analysis code SAM, and demonstrate its applications to model thermal mixing and stratification phenomena in large enclosures. The main outcomes of this research and development activity are summarized in this report, which presents an attempt to include a built-in advanced multi-dimensional flow model in a system analysis code with the focus on overcoming the simulation challenges of thermal mixing and stratification phenomena. In this report, we start with the introduction of existing SAM code capabilities to simulate thermal mixing and stratification phenomena, which is followed by a short summary of the multi-dimensional model implemented in the SAM code, including both the physical model and the Finite Element Method code implementation. In this study, two options were implemented in the SAM code to model turbulent flows: a relatively simple built-in turbulence model and an interface to accept externally computed turbulent viscosities (e.g., from a high- resolution CFD simulation). Code validation studies on this newly added capability were then carried out to compare SAM simulation results with experimental data from the SUPERCAVNA facility, which was designed to study the complex flow recirculation and thermal stratification phenomena relevant to sodium fast reactor designs. In this study, one transient and two steady-state test cases were used for code validation. Different approaches have been used to model the complex turbulence flow fields in the SUPERCAVNA facility. A highly simplified zero-equation turbulence model was first used, but it was determined that it is too simple to capture the complex turbulence flow fields in these test cases. Subsequently, the code validation continued with the use of turbulent viscosity data from high-resolution STAR-CCM+ CFD simulations to improve the accuracy of the results. Using this approach, the SAM simulation results showed very good agreement with both the SUPERCAVNA experimental data and STAR-CCM+ simulation results. In this report, we demonstrate the development, implementation, and successful validation of a multi-dimensional flow model in the SAM code, which aims to improve the simulation accuracy for complex thermal mixing and stratification phenomena. Lessons have also been learned, including that in cases where the flow fields are not well predicted by the zero-equation model, the iinput of turbulent viscosities from an external source can enhance the overall predictive capabilities needed to accurately capture complex thermal-hydraulic phenomena. Therefore, future research will be needed to further improve the code’s capabilities, such as by developing a more efficient and robust approach to capture the turbulence effects in the SAM code.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS2014

Integrated Aeromechanics with Three-Dimensional Solid-Multibody Structures

A full three-dimensional finite element-multibody structural dynamic solver is coupled to a three-dimensional Reynolds-averaged Navier-Stokes solver for the prediction of integrated aeromechanical stresses and strains on a rotor blade in forward flight. The objective is to lay the foundations of all major pieces of an integrated three-dimensional rotor dynamic analysis - from model construction to aeromechanical solution to stress/strain calculation. The primary focus is on the aeromechanical solution. Two types of three-dimensional CFD/CSD interfaces are constructed for this purpose with an emphasis on resolving errors from geometry mis-match so that initial-stage approximate structural geometries can also be effectively analyzed. A three-dimensional structural model is constructed as an approximation to a UH-60A-like fully articulated rotor. The aerodynamic model is identical to the UH-60A rotor. For preliminary validation measurements from a UH-60A high speed flight is used where CFD coupling is essential to capture the advancing side tip transonic effects. The key conclusion is that an integrated aeromechanical analysis is indeed possible with three-dimensional structural dynamics but requires a careful description of its geometry and discretization of its parts.

Three-Dimensional↗

DOE OSTI2022

Interactive Exploration of High-Dimensional Phase Diagrams

High-dimensional thermodynamic phase stability databases are becoming increasingly common due to the convergence of three recent trends: (i) the widespread interest in so-called “high-entropy” alloys, (ii) the availability of high-throughput computational assessments of phase stability in broad composition spaces and (iii) the ongoing development of ever-increasingly broad, multicomponent, multiphase CALPHAD databases. Although automated computational tools can readily process such high-dimensional data, scientists are often unable to visualize the relevant phase relations, an ability that is crucial to gaining an intuitive understanding of the stability constraints governing materials design. The present work addresses this need by providing algorithms that enable the interactive exploration of phase equilibria in high-dimensional spaces. These algorithms concentrate the complex nonlinear nonsmooth optimization needed into a preprocessing step that generates a large number of high-dimensional yet elementary graphical primitives. Furthermore, these primitives can then be cross-sectioned to yield 3-dimensional views in a computationally efficient manner that enables an interactive exploration of high-dimensional spaces. All of these operations are highly parallelizable, thus facilitating scaling of this method to large data sets.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Dimensionality effects on multicomponent ionic transport and surface complexation in porous media

Coulombic interactions between charged species in pore water and at surface/solution interfaces are of pivotal importance for multicomponent reactive transport in porous media. In this study, we investigate the impact of domain dimensionality on electrostatically coupled dispersion and surface-solution reactions during transport of acidic plumes and major ions in porous media. Column and quasi two-dimensional flow-through experiments were performed, with identical silica porous media and under the same advection-dominated conditions. Equal mass fluxes of different electrolyte solutions (i.e., HCl - pH ~ 2.8, NaBr - 100 mM, HCl - pH ~ 2.8 plus NaBr - 100 mM) were continuously injected in the 1-D and 2-D experiments and breakthrough curves of pH and major ions were measured at the outlet of the domains. The presence of pronounced ionic strength gradients in the transverse direction in the 2-D setup caused distinct retardation and transport behaviors of protons and major ions which were not observed in the one-dimensional column experiments. Furthermore, in the cases of salt electrolytes injection, considerably enhanced release of H + (>61%) from the quartz surface was observed in the multidimensional system compared to the one-dimensional setup. Reactive transport modeling was performed to reproduce the experimental outcomes and to analyse the coupling between transport processes, based on the Nernst-Planck formulation of diffusive/dispersive fluxes and on surface complexation reactions at the solid-solution interface. Electrostatic interactions between Na + , B – , and H + , and deprotonation of the quartz surface upon the formation of sodium outer-sphere complexes, are the primary controllers of the spatial and temporal features displayed by the pH and major ions measurements. The reactive transport simulations allowed us to interpret the experimental observations, to visualize the distribution and spatio-temporal evolution of dissolved and solid species, to identify a spatially heterogeneous zonation of Coulombic interactions with distinct behavior at the fringe and core of the injected plumes in the multidimensional setup, and to quantify the different components of the Nerst-Planck fluxes of the charged solutes. This study demonstrates that the domain dimensionality directly affects electrostatic interactions between charged aqueous species in the pore water and surface complexation reactions at the solid-solution interface. The non-trivial effects of dimensionality on multicomponent ionic transport result in a significantly different behavior in 1-D and 2-D systems.

58 GEOSCIENCES↗