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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2

Comparative Critical Mass Calculations for NNL and ENDF/B-VIII.0 Zirconium Hydride Thermal Neutron Scattering Laws

Zirconium hydride (ZrH x ) is a moderator material for TRIGA reactors and historical space reactor systems, such as SNAP-10A. Thermal neutron scattering laws (TSL) for two phases of this material, δ and ε, have been previously evaluated by Naval Nuclear Laboratory (NNL) and submitted to the National Nuclear Data Center (NNDC) for inclusion in the US national ENDF/B-VIII.1 nuclear data library. In contrast to the current ENDF/B-VIII.0 TSL evaluations, which consider only a single phase, the new evaluations are derived from separate ab initio calculations for both phases and include coherent elastic effects of the zirconium sublattice. To estimate the impact of these changes to the TSL evaluation of this material, comparative critical mass calculations were performed with MC21 for homogenous mixtures of high- enriched uranium (HEU) and ZrH x in bare and water reflected sphere configurations. These calculations yield an impact on the estimated critical mass as a function of 235 U loading density with maximum differences as large as 1% - 5% for over-moderated thermal spectrum systems. Consequently, the NNL TSL evaluations are anticipated to have a small impact on criticality calculations of thermal reactor systems regardless of the material phase. Nevertheless, characteristic differences exist in the predicted thermal spectra as function of energy for the two sets of TSL evaluations, which are attributed to difference in the underlying phonon density of states of hydrogen bound in ZrH x .

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Hyporheic Exchange Driven by Submerged Rigid Vegetation: A Modeling Study

Flow-vegetation interaction affects fluid flow hydraulics and associated material transport in river corridors. Concomitant changes in pressure within the flow field due to the presence of vegetation may act as a driver for the formation of hyporheic flow across the sediment-water interface. This potentially important process, however, has yet to be studied. In order to investigate vegetation-induced hyporheic exchange, a series of numerical models of interlinked surface-subsurface flow modified by plant stems was conducted. Periodically staggered plant stem arrays on a flat sediment bed were considered within a coupled multiphysics computational fluid dynamics approach. Plants were idealized as rigid cylinders and arranged in different streamwise and spanwise spacing distances. Each vegetation array was then subjected to a broad range of flow Reynolds Numbers (Re). The results showed that hyporheic flow occurs in all conditions with the presence of vegetation. The vegetation-induced hyporheic flux is found to be a function of Re via a power law. The flux increases with interstem space until the space reaches the distance that rigid stems no longer affect the flow structures in the vicinity of each other. Larger intervegetation distances lead to a larger hyporheic zone. A direct comparison with bedforminduced hyporheic flow showed that vegetation can induce higher hyporheic flux through relatively shallower exchange zones. The results of all the simulations were synthesized into predictive models for hyporheic flux, bulk residence time and exchange depth based on drag coefficient, vegetation density, and Reynolds Number.

54 ENVIRONMENTAL SCIENCES↗

Comparative critical mass calculations for NNL and ENDF/B-VIII.0 - Zirconium hydride thermal neutron scattering laws

Zirconium hydride (ZrH{sub x}) is a moderator material for TRIGA reactors and historical space reactor systems, such as SNAP-10A. Thermal neutron scattering laws (TSL) for two phases of this material, δ and ε, have been previously evaluated by Naval Nuclear Laboratory (NNL) and submitted to the National Nuclear Data Center (NNDC) for inclusion in the US national ENDF/B-VIII.1 nuclear data library. In contrast to the current ENDF/B-VIII.0 TSL evaluations, which consider only a single phase, the new evaluations are derived from separate ab initio calculations for both phases and include coherent elastic effects of the zirconium sublattice. To estimate the impact of these changes to the TSL evaluation of this material, comparative critical mass calculations were performed with MC21 for homogenous mixtures of high-enriched uranium (HEU) and ZrH{sub x} in bare and water reflected sphere configurations. These calculations yield an impact on the estimated critical mass as a function of {sup 235}U loading density with maximum differences as large as 1% - 5% for over-moderated thermal spectrum systems. Consequently, the NNL TSL evaluations are anticipated to have a small impact on criticality calculations of thermal reactor systems regardless of the material phase. Nevertheless, characteristic differences exist in the predicted thermal spectra as function of energy for the two sets of TSL evaluations, which are attributed to difference in the underlying phonon density of states of hydrogen bound in ZrH{sub x}. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Thermal Neutron Scattering Law Evaluation for Zirconium Carbide and Critical Mass Calculations

Zirconium carbide (ZrC) is a candidate material for use in advanced high temperature reactors, including space nuclear thermal propulsion applications. Thermal neutron scattering laws (TSLs) are generated for carbon bound in ZrC, C(ZrC), and zirconium bound in ZrC, Zr(ZrC), using ab initio lattice dynamics methods. These evaluations are to be submitted for inclusion in ENDF/B-VIII.1 and use the incoherent approximation for inelastic scattering as well as the new mixed elastic scattering treatment. The application of disordered alloy theory is introduced to appropriately capture the isotopic composition of Zr and C in the elastic scattering cross section. Localized higher energy vibrations in the C(ZrC) phonon density of states that are separated from lower energy modes result in quantized oscillations in the inelastic contributions to the TSL with a significant likelihood of large energy down-scattering and up-scattering interactions, where the latter increases in probability with temperature. The quanta of energy transfer during neutron thermalization is substantially greater than classically expected within the thermal neutron energy range. MC21 critical mass calculations of ZrC mixtures with high-enriched uranium demonstrate an impact of the TSLs when compared to free-gas treatment for 235 U concentrations less than 0.2 g/cm 3 . Additional MC21 critical mass calculations with homogenous mixtures of ZrC and reactor-grade graphite also demonstrate sensitivity to the ZrC TSL for thermal spectrum driven fission systems.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

A moving discontinuous Galerkin finite element method with interface condition enforcement for compressible flows

A variation of moving discontinuous Galerkin finite element method with interface condition enforcement (MDG-ICE) is developed for solving the compressible Euler equations. The MDG-ICE method, originating from the work of Corrigan et al. [1], [2], [3], [4], is based on the space-time DG formulation, where both flow field and grid geometry are considered as independent variables and the conservation laws are enforced both on discrete elements and element interfaces. The element conservation laws are solved in the standard discontinuous solution space to determine conservative quantities, while the interface conservation is enforced using a variational formulation in a continuous space to determine discrete grid geometry. The resulting over-determined system of nonlinear equations arising from the MDG-ICE formulation can then be solved in a least-squares sense, leading to an unconstrained nonlinear least-squares problem that is regularized and solved by Levenberg-Marquardt method. A number of numerical experiments for both 1D unsteady and 2D steady state compressible flow problems are conducted to assess the accuracy and robustness of the MDG-ICE method. Numerical results obtained indicate that the MDG-ICE method is able to implicitly detect and track all types of discontinuities via interface conservation enforcement and satisfy the conservation law on both elements and interfaces via grid movement and grid management, demonstrating that an exponential rate of convergence for Sod and Lax-Harden shock tube problems can be achieved and highly accurate solutions without overheating to both double-rarefaction wave and Noh problems can be obtained.

97 MATHEMATICS AND COMPUTING↗

Parallel-in-Time Solution of Scalar Nonlinear Conservation Laws

Here, we consider the parallel-in-time solution of scalar nonlinear conservation laws in one spatial dimension. The equations are discretized in space with a conservative finite-volume method using weighted essentially nonoscillatory (WENO) reconstructions, and in time with high-order explicit Runge–Kutta methods. The solution of the global, discretized space-time problem is sought via a nonlinear iteration that uses a novel linearization strategy in cases of nondifferentiable equations. Under certain choices of discretization and algorithmic parameters, the nonlinear iteration coincides with Newton’s method, although, more generally, it is a preconditioned residual correction scheme. At each nonlinear iteration, the linearized problem takes the form of a certain discretization of a linear conservation law over the space-time domain in question. An approximate parallel-in-time solution of the linearized problem is computed with a single multigrid reduction-in-time (MGRIT) iteration; however, any other effective parallel-in-time method could be used in its place. The MGRIT iteration employs a novel coarse-grid operator that is a modified conservative semi-Lagrangian discretization and generalizes those we have developed previously for nonconservative scalar linear hyperbolic problems. Numerical tests are performed for the inviscid Burgers and Buckley–Leverett equations. For many test problems, the solver converges in just a handful of iterations with a convergence rate independent of mesh resolution, including problems with (interacting) shocks and rarefactions.

97 MATHEMATICS AND COMPUTING↗

Relativistic partial waves for celestial amplitudes

The formalism of relativistic partial wave expansion is developed for four-point celestial amplitudes of massless external particles. In particular, relativistic partial waves are found as eigenfunctions to the product representation of celestial Poincaré Casimir operators with appropriate eigenvalues. The requirement of hermiticity of Casimir operators is used to fix the corresponding integral inner product, and orthogonality of the obtained relativistic partial waves is verified explicitly. The completeness relation, as well as the relativistic partial wave expansion follow. Example celestial amplitudes of scalars, gluons, gravitons and open superstring gluons are expanded on the basis of relativistic partial waves for demonstration. A connection with the formulation of relativistic partial waves in the bulk of Minkowski space is made in appendices.

79 ASTRONOMY AND ASTROPHYSICS↗

Deep Learning Explicit Differentiable Predictive Control Laws for Buildings

We present a differentiable predictive control (DPC) methodology for learning constrained control laws for unknown nonlinear systems. DPC poses an approximate solution to multiparametric programming problems emerging from explicit nonlinear model predictive control (MPC). Contrary to approximate MPC, DPC does not require supervision by an expert controller. Instead, a system dynamics model is learned from a small dataset of recorded observations of the perturbed system's dynamics and the control law is optimized offline by interaction with the learned system model. The DPC method is based on two sequential steps, i) system identification using a constrained neural state-space model, and ii) optimization of an explicit control law parametrized by another neural network in closed-loop simulation with the identified neural state-space model. The combination of a differentiable closed-loop system and penalty methods for constraint handling of system outputs and inputs allows us to optimize the control law's parameters directly by backpropagating economic MPC loss through the learned system model. By incorporating domain knowledge and leveraging established techniques from optimal control, our method leverages deep neural networks as nonlinear function approximators for system identification and control while avoiding concomitant costs of intractably large datasets, and computationally expensive over-parametrized models. The scalability, data efficiency, and constrained optimal control capability of the proposed DPC method are demonstrated in simulation using a multi-zone building emulator.

Drgona, Jan↗

Energy dependence of intermittency for charged hadrons in Au+Au collisions at RHIC

Density fluctuations near the QCD critical point can be probed via an intermittency analysis in relativistic heavy-ion collisions. We report the first measurement of intermittency in Au+Au collisions at $\sqrt{s{NN}}$ = 7.7-200 GeV measured by the STAR experiment at the Relativistic Heavy Ion Collider (RHIC). The scaled factorial moments of identified charged hadrons are analyzed at mid-rapidity and within the transverse momentum phase space. We observe a power-law behavior of scaled factorial moments in Au+Au collisions and a decrease in the extracted scaling exponent (ν) from peripheral to central collisions. The ν is consistent with a constant for different collisions energies in the mid-central (10-40%) collisions. Moreover, the ν in the 0-5% most central Au+Au collisions exhibits a non-monotonic energy dependence that reaches a minimum around $\sqrt{s{NN}}$ = 27 GeV. The physics implications on the QCD phase structure are discussed.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Neutron Characterization of 3D Printed Gas Turbine Alloy With Internal Cooling Structure

The objective of this research work is to investigate the residual strains induced by the presence of a exit hole and internal hollow geometry present in a 3D printed IN718 similar to that seen in a gas turbine blade. The specimens were manufactured with an internal hollow structure that ended with an exit hole, and fabricated by direct metal laser sintering additive manufacturing technique. Using this technique, metal powder was melted by a laser source and rapidly cooled to form the part layer by layer. Rapid heating and cooling generate large thermal gradients and residual stresses in the 3D printed material. To be aligned with industry standards, specimens were heat-treated to relieve most of the residual stresses as well as to investigate whether IN718 still preserved a nonhomogeneous stress state after the thermal treatment. Roughness and microstructure analysis was performed to understand the heat-treated sample properties. To investigate the volumetric residual strain, the neutron diffraction technique was used with a definite neutron wavelength. Bragg’s law was used to determine lattice spacing. Interplanar lattice spacing and stress-free state lattice spacings were measured to calculate the strains. Residual strains were measured in the x and y direction to understand the impact of the presence of a exit hole and internal hollow geometry. The results of volumetric residual strain in the x and y directions showed no significant variations in the distribution of the strain due to the presence of a hollow structure as well as the exit hole. Overall, no significant stress concentration was observed in the heat treated sample. Sample geometry, instrumentation for neutron diffraction, and material properties are discussed in detail in this paper.

Raju, Nandhini↗

CUAS Regulatory Authority in the United States [Slides]

Slides describing: (1) How the United States (U.S.) Passes Federal Laws, (2) Initial Actions in Regulatory Space for CUAS, (3) Department of Justice (DOJ): Flow-down Authority, (4) Department of Homeland Security (DHS): Flow-down Authority, (5) CUAS Authority Granting Timeline, (6) CUAS Regulations, (7) Defining UAS Threats, (8) CUAS actions permitted pursuant to 50 USC 2661 for the Department of Energy, (9) Penalties

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Quasi-Helmholtz decomposition, Gauss' laws and charge conservation for finite element particle-in-cell

Development of particle-in-cell (PIC) methods using finite element based methods (FEMs) have been a topic of renewed interest; this has largely been driven by (a) the ability of finite element methods to better model geometry, (b) better understanding of function spaces that are necessary to represent all Maxwell quantities, and (c) more recently, the fundamental rubrics that should be obeyed in space and time so as to satisfy Gauss' laws and the equation of continuity. In that vein, methods have been developed recently that satisfy these equations and are agnostic to time stepping methods. While this development is indeed a significant advance, it should be noted that implicit FEM transient solvers support an underlying null space that corresponds to a gradient of a scalar potential ∇Φ(r) (or t∇Φ(r) in the case of wave equation solvers). While explicit schemes do not suffer from this drawback, they are only conditionally stable with time step sizes that are mesh dependent and very small. Furthermore, the null space produces spurious charge that can corrupt the desired physics of a PIC simulation. The way to overcome this bottleneck, and indeed, satisfy all four Maxwell's equation is to use a quasi-Helmholtz formulation on a tessellation. In the re-formulation presented, we strictly satisfy the equation of continuity and Gauss' laws for both the electric and magnetic flux densities. Results illustrating the efficacy of this scheme will be demonstrated by analyzing non-neutral beams with space-charge and the adiabatic expansion of a neutral plasma with realistic parameters (Debye length and real mass ratios).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Spatial Intermittency of Particle Distribution in Relativistic Plasma Turbulence

Abstract Relativistic magnetically dominated turbulence is an efficient engine for particle acceleration in a collisionless plasma. Ultrarelativistic particles accelerated by interactions with turbulent fluctuations form nonthermal power-law distribution functions in the momentum (or energy) space, f ( γ ) d γ ∝ γ − α d γ , where γ is the Lorenz factor. We argue that in addition to exhibiting non-Gaussian distributions over energies, particles energized by relativistic turbulence also become highly intermittent in space. Based on particle-in-cell numerical simulations and phenomenological modeling, we propose that the bulk plasma density has lognormal statistics, while the density of the accelerated particles, n , has a power-law distribution function, P ( n ) dn ∝ n − β dn . We argue that the scaling exponents are related as β ≈ α + 1, which is broadly consistent with numerical simulations. Non-space-filling, intermittent distributions of plasma density and energy fluctuations may have implications for plasma heating and for radiation produced by relativistic turbulence.

79 ASTRONOMY AND ASTROPHYSICS↗

Unsupervised machine learning discovery of structural units and transformation pathways from imaging data

We show that unsupervised machine learning can be used to learn chemical transformation pathways from observational Scanning Transmission Electron Microscopy (STEM) data. To enable this analysis, we assumed the existence of atoms, a discreteness of atomic classes, and the presence of an explicit relationship between the observed STEM contrast and the presence of atomic units. With only these postulates, we developed a machine learning method leveraging a rotationally invariant variational autoencoder (VAE) that can identify the existing molecular fragments observed within a material. The approach encodes the information contained in STEM image sequences using a small number of latent variables, allowing the exploration of chemical transformation pathways by tracing the evolution of atoms in the latent space of the system. The results suggest that atomically resolved STEM data can be used to derive fundamental physical and chemical mechanisms involved, by providing encodings of the observed structures that act as bottom-up equivalents of structural order parameters. The approach also demonstrates the potential of variational (i.e., Bayesian) methods in the physical sciences and will stimulate the development of more sophisticated ways to encode physical constraints in the encoder–decoder architectures and generative physical laws and causal relationships in the latent space of VAEs.

97 MATHEMATICS AND COMPUTING↗

North Dakota Integrated Carbon Storage Complex Feasibility Study. Final report

In spring 2017, the Energy & Environmental Research Center (EERC) initiated an effort to determine the feasibility of developing a commercial-scale CO 2 geologic storage complex able to store 50+ million tonnes (Mt) of CO 2 in central North Dakota safely, permanently, and economically. The objective was to fulfill the goals of the U.S. Department of Energy (DOE) Carbon Storage Assurance Facility Enterprise (CarbonSAFE) Initiative and address technical and nontechnical challenges specific to commercial-scale deployment of a CO2 storage project. The findings clearly show that the concept of capturing CO 2 from a lignite-fired electrical generation facility in central North Dakota and safely and permanently storing the CO 2 in the deep subsurface is indeed technically, economically, and socially feasible. This project evaluated two study areas and their respective geologic storage complexes located adjacent to separate coal-fired facilities in North Dakota: the Basin Electric Power Cooperative (BEPC)-owned Great Plains Synfuels Plant (GPSP) and the Minnkota Power Cooperative (Minnkota)-owned Milton R. Young Station (MRYS). These locations, one with CO 2 capture in place and an existing CO 2 pipeline, are bolstered by progressive North Dakota pore space ownership and long-term liability laws. These elements and a motivated team created an ideal synergistic scenario for ensuring success of the CarbonSAFE Initiative and promoting North Dakota’s statewide vision for carbon management. The project included drilling two new geologic characterization wells, integrating an existing 3-D seismic survey, creating a geologic model subsequently used for injection simulation, a risk assessment, public outreach, and generating a site development plan based on results. In addition, the performance of select National Risk Assessment Partnership tools was evaluated. The geologic characterization wells were drilled ~5600 feet deep to the Broom Creek Formation; ~350 feet of core was retrieved from each well. The core included the Broom Creek (targeted injection zone) and a portion of the overlying Opeche Shale (seal). The Flemmer-1 well, west of Beulah, North Dakota, yielded 169 feet of sandstone. The BNI-1 well located south of Center, North Dakota, yielded 124 feet of sandstone. In each case, laboratory analysis of the sandstone showed permeability in the 300–1000-mD range, with porosity of 20%–30%. The Flemmer-1 well was sited within the boundaries of an existing 3-D seismic survey. Colocating the well with the seismic survey maximized the relationship between new and legacy data and developed a first-of-its-kind interpretation of the geologic fabric of the Broom Creek. Geologic characterization data were integrated into a 5544-mi 2 geocellular model that encompassed both new wells and stratigraphy from the surface to the Amsden Formation (underlying the Broom Creek). The model was later expanded vertically to include the deeper Black Island–Deadwood interval to examine its potential viability as a storage target. The geocellular model provided the foundation for dynamic simulation of CO 2 into the Broom Creek. Results of the simulation suggest that the Broom Creek could accept the DOE target rate of 2 Mt/yr of CO 2 into as few as two wells. To bracket the expected capture from MRYS, simulations were also investigated for a 4-Mt/yr rate near MRYS. Although more wells are needed (two additional), the Broom Creek still has the storage resource to accept the CO 2 at the increased rate. A risk assessment exercise was conducted to identify and assess technical and nontechnical risks that could prevent potential candidate storage complexes within the study area from serving as commercial storage sites. The assessment identified and evaluated six technical risk categories: 1) CO 2 injectivity, 2) storage capacity, 3) lateral migration of CO 2 , 4) lateral pressure propagation, 5) vertical migration of CO 2 or formation brine, and 6) induced seismicity. Following two rounds of analysis and scoring, no risks were determined to preclude continued efforts to develop carbon capture, utilization, and storage (CCUS) in central North Dakota. The risk assessment results will be used to guide future site characterization, modeling and simulation, and monitoring activities. A specific nontechnical strategic risk based on challenges that may be realized in amalgamation of pore space resulted in vertically expanding the geologic model to incorporate the potential for stacked storage in multiple saline reservoirs. By including the Black Island–Deadwood interval (the basal sedimentary reservoir in this region), the amalgamated areal extent could be reduced by as much as 45%. Working with a smaller geographic area reduces risks and costs associated with monitoring and pore space leasing. An economic evaluation incorporating capture; transport (<5 mi); Class VI wells; permitting; and monitoring, verification, and accounting suggests implementing commercial-scale CCUS is economically attractive if the federal tax benefits of 45Q are included. This is validated by Minnkota’s continued pursuit of CO 2 capture and geologic storage at MRYS through its Project Tundra initiative, indicating that there is a business case for CCUS in central North Dakota. Currently, North Dakota is the only state with underground injection control (UIC) Class VI primacy. Built into the North Dakota Century Code is a series of regulatory requirements that guide the process to obtain a Class VI CO 2 storage facility permit. As part of this project, a site development plan was compiled to assure compliance with North Dakota’s requirements to permit a commercial-scale CO 2 storage operation and includes a prospective time line encompassing a general breakdown of activities. In total, an estimated 30 months would be needed to execute the necessary steps to attain a North Dakota CO 2 storage facility permit. Outreach was an integral part of the project and encompassed any project-related activity that had contact or exposure beyond the project team. The goals of outreach were to foster an environment from which stakeholders could make informed decisions about the project and gauge community receptiveness to a CCUS project. A consistent set of messages and outreach products were developed in conjunction with an outreach advisory board that integrated project partners and team members. To gauge public acceptability of geologically storing CO 2 , 5611 households in the project area were invited to participate in an online survey. The survey results indicate that the public attitude regarding CCUS is neutral to positive, with strong sentiment that CO 2 capture and storage may be an approach to maintain the economic vitality of the region. To achieve project objectives, critical support in the form of financial backing, engineering evaluations, site access, outreach collaboration, operations data, risk assessment/evaluation, and software access was provided by BEPC, the North Dakota Industrial Commission Lignite Research Council, ALLETE Clean Energy, BNI Energy, North American Coal Corporation, Minnkota, Prairie Public Broadcasting, Computer Modelling Group Ltd., and Schlumberger.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Scaling Behavior of Thermally Driven Fractures in Deep Low‐Permeability Formations: A Plane Strain Model With 1‐D Heat Conduction

Abstract Injection of cold fluids through/into deep formations may cause significant cooling, thermal stress, and possible thermal fracturing. In this study, the thermal fracturing of low‐permeability formations under one‐dimensional heat conduction was investigated using a plane strain model. Dimensionless governing equations, with dimensionless fracture length , aperture , spacing , time , and effective confining stress , were derived. Solution of single thermal fracture was derived analytically, while solution of multiple fractures with constant (or dynamic) spacing were obtained using the displacement discontinuity method (and stability analysis). For single fracture, increases nonlinearly with and then transitions to scaling law , indicating that late‐time fracture length increases linearly with the square root of cooling time. For constantly spaced fractures, deviates from the single‐fracture solution at a later for a larger , showing slower propagation under inter‐fracture stress interaction . For dynamically spaced fractures, fracture arrest induced by stress interaction was determined by the stability analysis; the fully transient solution provides evolution of dimensionless fracture length, spacing, aperture, and pattern; a similar scaling law, with , obtained shows the effect of both stress interaction and fracture arrest. The solution and scaling law provide fast predictions for all reservoir and cooling conditions using (single) model parameter . Application to a geothermal site with demonstrates that thermal fractures reach 0.67, 6.25, and 78.00 m in length, 0.49, 2.30, and 13.00 m in spacing, and 0.43, 2.09, and 12.19 mm in aperture at 1, 100, and 10,000 days.

Chen, Bin↗

Fluid Dynamics Effects on Microstructure Prediction in Single-Laser Tracks for Additive Manufacturing of IN625

Single-track laser fusion were simulated using a heat-transfer-solidification-only (HTS) model and its extension with fluid dynamics (HTS_FD) model using a parallel open-source code, which included laminar fluid dynamics, flat-free surface of the molten alloy, heat transfer, phase-change, evaporation, and surface tension phenomena. The results illustrate that the fluid dynamics affects the solidification and ensuing microstructure. For the HTS_FD simulations, thermal gradient, G was found to exhibit a maximum at the extremity of the solidified pool ( i.e. , at the free surface), while for HTS simulations, G exhibited a maximum around the entire edge of the solidified pool. HTS_FD simulations predicted a wider range of cooling rates than the HTS simulations, exhibited an increased spread in the solidification speed, V variation within the melt-pool with respect to the HTS model results. Primary dendrite arm spacing (PDAS) were evaluated based on power law correlations and marginal stability theory models using the ( G , V ) from HTS and HTS_FD simulations to quantify the effect of the fluid dynamics on the microstructure. At low-laser powers and low-scan speeds, the PDAS obtained with the fluid dynamics model (HTS_FD) was larger by more than 30 pct with respect to the PDAS calculated with the simple HTS model. A new PDAS correlation, i.e. , \( \lambda_{1} \left[ {\mu {\text{m}}} \right] = 832\;G\left[ {\text{K/m}} \right]^{ - 0.5} V\left[ {\text{m/s}} \right]^{ - 0.25} \) , which uses the ( G , V ) results from the HTS_FD model was developed and validated against experimental results.

36 MATERIALS SCIENCE↗

Learning emergent partial differential equations in a learned emergent space

We propose an approach to learn effective evolution equations for large systems of interacting agents. This is demonstrated on two examples, a well-studied system of coupled normal form oscillators and a biologically motivated example of coupled Hodgkin-Huxley-like neurons. For such types of systems there is no obvious space coordinate in which to learn effective evolution laws in the form of partial differential equations. In our approach, we accomplish this by learning embedding coordinates from the time series data of the system using manifold learning as a first step. In these emergent coordinates, we then show how one can learn effective partial differential equations, using neural networks, that do not only reproduce the dynamics of the oscillator ensemble, but also capture the collective bifurcations when system parameters vary. The proposed approach thus integrates the automatic, data-driven extraction of emergent space coordinates parametrizing the agent dynamics, with machine-learning assisted identification of an emergent PDE description of the dynamics in this parametrization.

97 MATHEMATICS AND COMPUTING↗