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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
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

An extended/generalized phase-field finite element method for crack growth with global-local enrichment

In this paper, an extended/generalized finite element method (XFEM/GFEM) for simulating quasistatic crack growth based on a phase-field method is presented. The method relies on approximations to solutions associated with two different scales: a global scale, that is, structural and discretized with a coarse mesh, and a local scale encapsulating the fractured region, that is, discretized with a fine mesh. A stable XFEM/GFEM is employed to embed the displacement and damage fields at the global scale. The proposed method accommodates approximation spaces that evolve between load steps, while preserving a fixed background mesh for the structural problem. In addition, a prediction-correction algorithm is employed to facilitate the dynamic evolution of the confined crack regions within a load step. Several numerical examples of benchmark problems in two- and three-dimensional quasistatic fracture are provided to demonstrate the approach.

multiscale↗
DOE OSTI2024

Sequential formulation of all‐way coupled finite strain thermoporomechanics for largely deformable gas hydrate deposits

We develop a numerically stable sequential formulation of thermoporomechanics for largely deformable gas hydrate deposits, extended from the fixed stress split of infinitesimal transformation. Constitutive equations are based on the total Lagrangian approach for both flow and geomechanics, including dynamic full tensor permeability and thermal conductivity updated from the deformation gradient. For space discretization, we take the cell-centered finite volume and node-based finite element method for flow and geomechanics, respectively. Then, we propose a sequential implicit method for all-way coupled thermoporomechanics, where the nonisothermal multiphase flow problem of gas hydrates is solved implicitly first and then the geomechanics problem is solved implicitly at the next step. During solution of the flow problem, we fix the rate of first Pioal total stress for numerical stability as well as apply porosity correction and entropy correction to account for geomechanical effects. We test numerical examples where flow and geomechanics parameters are based on deep oceanic gas hydrate deposits. When applying depressurization, even though the results between the infinitesimal transformation and finite strain geomechanics are similar in the early stages due to small deformation, we find differences between them in the late times as deformation becomes large. Accordingly, permeability and thermal conductivity tensors become nonisotropic full tensors although they are initially isotropic. Furthermore, we identify numerical stability of the developed sequential method from the test cases that exhibit the highly complex coupled gas hydrate systems with large deformation. Thus, the proposed sequential formulation can be applied in largely deformable gas hydrate systems.

42 ENGINEERING↗
DOE OSTI2020

The second-generation Shifted Boundary Method and its numerical analysis

Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we present enhanced variational SBM formulations for the Poisson and Stokes problems with improved flexibility and robustness. These simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations. First, we show that these new SBM implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive. Second, we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at Dirichlet boundaries, therefore avoiding the calibration of an additional stabilization parameter. Finally, we prove enhanced L 2 -estimates without the cumbersome assumption – of earlier proofs – that the surrogate domain is convex. Instead we rely on a conventional assumption that the boundary of the true domain is smooth, which can also be replaced by requiring convexity of the true domain. The aforementioned improvements open the way to a more general and efficient implementation of the Shifted Boundary Method, particularly in complex three-dimensional geometries. We complement these theoretical developments with numerical experiments in two and three dimensions.

42 ENGINEERING↗
DOE OSTI2024

Bifurcation of equilibrium positions for ellipsoidal particles in inertial shear flows between two walls

We conducted a systematic numerical investigation of spherical, prolate and oblate particles in an inertial shear flow between two parallel walls, using smoothed particle hydrodynamics (SPH). It was previously shown that above a critical Reynolds number, spherical particles experience a supercritical pitchfork bifurcation of the equilibrium position in shear flow between two parallel walls, namely that the central equilibrium position becomes unstable, leading to the emergence of two new off-centre stable positions (Foxet al.,J. Fluid Mech., vol. 915, 2021). This phenomenon was unexpected given the symmetry of the system. In addition to confirming this finding, we found, surprisingly, that ellipsoidal particles can also return to the centre position from the off-centre positions when the particle Reynolds number is further increased, while spherical particles become unstable under this increased Reynolds number. By utilizing both SPH and the finite element method for flow visualization, we explained the underlining mechanism of this reverse of bifurcation by altered streamwise vorticity and symmetry breaking of pressure. Furthermore, we expanded our investigation to include asymmetric particles, a novel aspect that had not been previously modelled, and we observed similar trends in particle dynamics for both symmetric and asymmetric ellipsoidal particles. While further validation through laboratory experiments is necessary, our research paves the road for development of new focusing and separation methods for shaped particles.

Mechanics↗
DOE OSTI2022

An efficient iterative method for dynamical Ginzburg-Landau equations

Here we propose a new finite element approach to solving the time-dependent Ginzburg-Landau equations for superconductivity under the temporal gauge and design an efficient preconditioner for the Newton iteration of the resulting discrete system. It solves the vector magnetic potential in $H$(curl) space by the lowest order of the second kind N´ed´elec element. This approach offers a simple way to deal with the boundary conditions, leading to a stable and reliable performance for superconductor geomtry with reentrant corners. The bench-marking in numerical simulations verifies the efficiency of the proposed preconditioner, which can be employed to significantly speed up in large-scale computations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Data for Clumping Index Estimation With 30°-tilted Cameras in Row Crops: Evaluation of Methods and Segment Size Effects

The clumping index (CI) quantifies the spatial distribution of foliage elements and is essential for accurately estimating the plant area index (PAI), canopy radiative transfer, and photosynthesis. Traditionally, the finite-length averaging method (LX), the gap size distribution method (CC), and a combined approach of CC and LX (CLX) have been applied to instruments like TRAC and digital hemispherical photography to estimate CI. However, a comprehensive evaluation of these methods in row crops remains limited, especially regarding the influence of segment size on CI. Meanwhile, digital cameras offer a cost-effective and user-friendly solution for canopy measurements in row crops, yet their application in this context remains underexplored. In this study, we employed a new approach using a 30°-tilted digital camera to estimate CI in corn and soybean fields, applying the LX, CC, and CLX methods. We systematically assessed the performance of these three methods by combining field measurements in real-world fields with simulations using the LESS 3D radiative transfer model. Our results showed that CLX applied to the whole image and 45° segment offered accurate estimation of CI (bias within ±0.1, RMSE < 0.2) and PAI (bias within ±0.4, RMSE < 1) in real-world fields and LESS simulations. The accuracy of the LX method was highly sensitive to segment size, with the best performance observed at the 15° segment (PAI bias within ±0.4). In contrast, the CC method remained stable across different segment sizes, and its performance was generally comparable to that of LX, except at the 15° segment. Across view zenith angles, CI derived from CC generally showed a continuous increase, while those from LX and CLX followed a rising trend at small zenith angles but began to decline at 68°, likely due to an increasing proportion of no-gap segments. Seasonally, LX tended to show decreasing CI during early growth stages but increased as the canopy matured, whereas CC and CLX showed gradually increasing CI before plateauing at peak PAI. The 30°-tilted camera effectively captured CI variations across different angles and growth stages, making it a practical and robust instrument for row crop canopy structure analysis. Applying these CI methods to digital cameras offers a low-cost and accessible CI estimation alternative, improving canopy structure monitoring accuracy in row crops.

Modeling↗
DOE OSTI2022

Modeling Isotope Separation in Electrochemical Lithium Deposition

Naturally occurring Li consists of two stable isotopes, 6 Li with an abundance of about 7.5%, and 7 Li making up the remainder with 92.5%. The development of a 6 Li enrichment technique, in terms of technical reliability and environmental safety to reach 6 Li future requirements, represents a key step in the roadmap for nuclear fusion energy supply worldwide. This paper uses finite element analysis-based models to simulate electrochemical Li isotope separation, which is an attractive method in terms of simplicity, safety, and scalability. In the model, we quantitatively analyze how different electrochemical factors including thermodynamics, charge-transfer kinetics, and diffusivities affect the separation process (separation factor), together with cell parameters, such as cell length and current density. The maximum separation factor of 1.128 could be obtained with the cell under the optimal thermodynamic, kinetic, and diffusive conditions, which is among the highest separation factors ever reported. Furthermore, these results will assist in designing the actual isotope separation setup with large separation factor and appropriate timing for sample collection.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2022

Pit Stability Predictions of Additively Manufactured SS316 Surfaces Using Finite Element Analysis

Stainless steels are susceptible to localized forms of corrosion attack, such as pitting. The size and lifetime of a nucleated pit can vary, depending on a critical potential or current density criterion, which determines if the pit repassivates or continues growing. This work uses finite element method (FEM) modeling to compare the critical pit radii predicted by thermodynamic and kinetic repassivation criteria. Experimental electrochemical boundary conditions are used to capture the active pit kinetics. Geometric and environmental parameters, such as the pit shape and size (analogous to additively manufactured lack-of-fusion pores), solution concentration, and water layer thickness were considered to assess their impact on the pit repassivation criterion. The critical pit radius (the transition point from stable growth to repassivation) predicted for a hemispherical pit was larger when using the repassivation potential (E rp ) criteria, as opposed to the current density criteria (pit stability product). Including both the pit stability product and E rp into its calculations, the analytical maximum pit model predicted a critical radius two times more conservative than the FEA approach, under the conditions studied herein. The complex pits representing lack-of-fusion pores were shown to have minimal impact on the critical radius in atmospheric conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Isotopic fractionation as in-situ sensor of subsurface reactive flow and precursor for rock failure

Greater utilization of subsurface reservoirs perturbs in-situ chemical-mechanical conditions with wide ranging consequences from decreased performance to project failure. Understanding the chemical precursors to rock deformation is critical to reducing the risks of these activities. To address this need, we investigated the coupled flow-dissolution- precipitation-adsorption reactions involving calcite and environmentally-relevant solid phases. Experimentally, we quantified (1) stable isotope fractionation processes for strontium during calcite nucleation and growth, and during reactive fluid flow; (2) consolidation behavior of calcite assemblages in the common brines. Numerically, we quantified water weakening of calcite using molecular dynamics simulations; and quantified the impact of calcite dissolution rate on macroscopic fracturing using finite element models. With microfluidic experiments and modeling, we show the effect of local flow fields on the dissolution kinetics of calcite. Taken together across a wide range of scales and methods, our studies allow us to separate the effects of reaction, flow, and transport, on calcite fracturing and the evolution of strontium isotopic signatures in the reactive fluids.

42 ENGINEERING↗
DOE OSTI2025

The approximate second order coupled-cluster method based on a size-consistent Brillouin–Wigner partitioning

We present a variant of the approximate second order coupled-cluster method (CC2) with a two-parameter size-consistent Brillouin–Wigner (BW-s) partitioning instead of a Møller–Plesset (MP) partitioning for the unperturbed Hamiltonian, which we refer to as BWs-CC2. The computational complexity of this model scales identically to CC2 with molecular size. Conventional CC2 and its regularized BWs-CC2 variants, as well as conventional MP2 and two of its regularized BW-s2 variants, were assessed on a 535 element database spanning thermochemistry, non-covalent interactions, barrier heights, and isomerization energies. To ensure a well-defined model chemistry, the assessment was performed using internally stable spin-polarized Hartree–Fock (HF) orbitals in the finite aug-cc-pVQZ basis without counterpoise corrections. As a result of using stable orbitals, contrary to conventional wisdom, we find that CC2 substantially outperforms MP2 on molecules with significantly spin contaminated reference orbitals without a significant increase in error on systems with a spin-pure reference, showing the value of its single substitutions. While no single choice of regularization parameters can be optimal for all datasets, we find that BWs-CC2 generally outperforms both CC2 and BW-s2 with a single judicious parameter choice. Additional tests on dipole moments and bond lengths of diatomics provide further support for the utility of this choice. Furthermore, the main outliers and poorest performing cases are associated with large amounts of spin-contamination in the HF reference, which is indicative of systems with either strong correlation or extensive artificial symmetry breaking. Overall, these findings argue that the perception of the quality of the CC2 ground state should be reevaluated and that it can be further improved upon by the soundly based BWs-CC2 variant with the recommended parameter choice.

Correlation energy↗
DOE OSTI2026

A projection method for particle resampling

Particle discretizations of partial differential equations are advantageous for high-dimensional kinetic models in phase-space due to their better scalability than continuum approaches with respect to dimension. Complex processes collectively referred to as particle noise hamper long time simulations with particle methods. One approach to address this problem is particle mesh adaptivity, or remapping, known as particle resampling and remeshing. Here, this work introduces a resampling method that projects particles to and from a (finite element) function space. The method is simple, using standard sparse linear algebra and finite element techniques, and it preserves all moments up to the order of a polynomial represented exactly by the continuum function space. It is distinguished from most other mesh-based methods in that new particle positions and number are decoupled from the mesh, allowing particle and continuum meshes to be adapted relatively independently. While this work is developed with structured particle and continuum phase-space grids on 1X + 1V Vlasov-Poisson models of Landau damping and two-stream instability, the method is well-suited to unstructured grids. Stable long time dynamics are demonstrated up to time T = 500. Reproducibility artifacts and data are publicly available.

Kinetic methods↗
DOE OSTI2020

A Mixed Discontinuous Galerkin Method for Linear Elasticity with Strongly Imposed Symmetry

In this paper, we study a mixed discontinuous Galerkin (MDG) method to solve linear elasticity problem with arbitrary order discontinuous finite element spaces in d -dimension ( \(d=2,3\) ). This method uses polynomials of degree \(k+1\) for the stress and of degree k for the displacement ( \(k\ge 0\) ). The mixed DG scheme is proved to be well-posed under proper norms. Specifically, we prove that, for any \(k \ge 0\) , the \(H(\mathrm{div})\) -like error estimate for the stress and \(L^2\) error estimate for the displacement are optimal. We further establish the optimal \(L^2\) error estimate for the stress provided that the \({\mathcal {P}}_{k+2}-{\mathcal {P}}_{k+1}^{-1}\) Stokes pair is stable and \(k \ge d\) . Finally, we also provide numerical results of MDG showing that the orders of convergence are actually sharp.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

The role of breakup and coalescence in fine-scale bubble-induced turbulence. I. Dynamics

We study the effect of bubble breakup and coalescence on fine-scale dynamics of bubbly turbulent flows using direct numerical simulations. We perform two different simulations of dilute bubbly flows of void fraction 0.5%: one with bubbles breaking up and coalescing and the other without these physical processes. The volume of the fluid method is used for simulating bubbles undergoing breakup and coalescence while the bubbles are treated as rigid spheres in the immersed boundary method simulation. The energy spectrum in both types of simulation, consistent with previous studies, exhibits a -3 slope. We follow a single infinitesimal fluid element as it evolves to understand velocity gradient dynamics using conditional mean trajectories. We note finite-time divergence when the fluid element evolves under the action of inertial and pressure dynamics. The inertial, pressure, and viscous velocity gradient dynamics, when considered individually, produce the same results for bubble-induced turbulence (BIT) as with the classical homogeneous isotropic turbulence (HIT). Yet when the overall velocity gradient dynamics is considered, BIT results in non-cyclic trajectories moving toward stable node and unstable saddle while classical HIT shows cyclic behavior in their trajectories that move toward the origin. Interestingly, both the volume of fluid and immersed boundary simulations produce similar results. Therefore, there are two main takeaways from this research. First, new velocity gradient models are needed for BIT as their velocity gradients behavior is entirely different from the HIT. Second, we can neglect the bubble topology, breakup, and coalescence while studying or modeling the fine-scale dynamics of BIT.

42 ENGINEERING↗
DOE OSTI2022

In-situ, nanoscale fracture toughness measurements for improved mechanical interfaces

In this project, we demonstrated stable nanoscale fracture in single-crystal silicon using an in-situ wedge-loaded double cantilever beam (DCB) specimen. The fracture toughness KIC was calculated directly from instrumented measurement of force and displacement via finite element analysis with frictional corrections. Measurements on multiple test specimens were used to show K IC = 0.72 ± 0.07 MPa m 1/2 on {111} planes and observe the crack-growth resistance curve in <500 nm increments. The exquisite stability of crack growth, instrumented measurement of material response, and direct visual access to observe nanoscale fracture processes in an ideally brittle material differentiate this approach from prior DCB methods.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Three-dimensional modelling of a self-sustained atmospheric pressure glow discharge

The atmospheric pressure glow discharge (APGD) is a relatively simple and versatile plasma source used in diverse applications. Stable APGD operation at high currents, generally a challenge due to instabilities leading to glow-to-arc transition, has been demonstrated using actively-controlled cathodic cooling. This article presents the computational modelling and simulation of a self-sustained direct-current APGD in helium within a 10 mm pin-to-plate inter-electrode gap for currents ranging from 4 to 40 mA. The APGD model is comprised of the conservation equations for total mass, chemical species, momentum, thermal energy of heavy-species and of free electrons, and electric charge. The model equations are discretized using a nonlinear variational multi-scale finite element method that has demonstrated superior accuracy in other plasma flow problems, on a temporal and three-dimensional computational domain suitable to unveil the potential occurrence of instabilities. Modelling results show good agreement with experimental measurements of voltage drop and the same trend but higher values of temperature. The higher temperatures obtained by the simulations appear to be due to the absence of a near-cathode heat dissipation model. Here, the results also reveal that the distribution of electron density and of the ratio of atomic helium ions to total ions transitions from monotonically increasing away from the cathode to presenting a minimum near the centre of the gap with increasing current.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Feasibility Assessment of Using Electrical Impedance Tomography for Damage Localization in Graphite Microreactor Components

Microreactors have great potential to decrease capital costs and construction timelines, reducing the barriers to implementing advanced nuclear reactor technologies. However, the lower power output of these microreactors introduces economic challenges if the operation and maintenance costs cannot be reduced sufficiently. Many microreactor concepts use graphite materials for in-core moderator and structural purposes, which will require periodic inspection or, ideally, in situ structural health monitoring. This work describes an initial evaluation of the feasibility of leveraging graphite’s semiconducting properties to perform electrical impedance tomography (EIT) for defect localization. First, a study was performed to identify the best methods for bonding electrical contacts to minimize the effects of contact resistance that interfere with impedance measurements of the graphite. After determining the best bonding approach, electrodes were attached to multiple graphite components with varying geometries (e.g., simple block and more representative microreactor hexagonal block). In parallel, finite element analysis approaches were developed and implemented to analyze the impact of defects and contact resistances and to inform an iterative inverse model for reconstructing the conductivity distribution. The results of this study show that defect localization in graphite components is possible using EIT if a sufficient number of electrodes (to improve spatial resolution) can be bonded using a technique with very low contact resistance and those contact resistances remain stable during reactor operation. If the reactor core and vessel design do not allow electrodes to be bonded during reactor operation, then it may be possible to detach/reattach electrodes between reactor operation and outages if a suitable mechanical connection that offers repeatable contact resistance can be identified. Alternatively, future work could focus on identifying contacts that can survive the harsh reactor operating environment so that contacts do not need to be removed.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2022

Fast Solution of Fully Implicit Runge--Kutta and Discontinuous Galerkin in Time for Numerical PDEs, Part I: the Linear Setting

Fully implicit Runge--Kutta (IRK) methods have many desirable properties as time integration schemes in terms of accuracy and stability, but high-order IRK methods are not commonly used in practice with numerical PDEs due to the difficulty of solving the stage equations. This paper introduces a theoretical and algorithmic preconditioning framework for solving the systems of equations that arise from IRK methods applied to linear numerical PDEs (without algebraic constraints). Additionally, this framework also naturally applies to discontinuous Galerkin discretizations in time. Under quite general assumptions on the spatial discretization that yield stable time integration, the preconditioned operator is proven to have condition number bounded by a small, order-one constant, independent of the spatial mesh and time-step size, and with only weak dependence on number of stages/polynomial order; for example, the preconditioned operator for 10th-order Gauss IRK has condition number less than two, independent of the spatial discretization and time step. The new method can be used with arbitrary existing preconditioners for backward Euler-type time-stepping schemes and is amenable to the use of three-term recursion Krylov methods when the underlying spatial discretization is symmetric. The new method is demonstrated to be effective on various high-order finite-difference and finite element discretizations of linear parabolic and hyperbolic problems, demonstrating fast, scalable solution of up to 10th-order accuracy. The new method consistently outperforms existing block preconditioning approaches, and in several cases, the new method can achieve 4th-order accuracy using Gauss integration with roughly half the number of preconditioner applications and wallclock time as required using standard diagonally IRK methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A subdivision-stabilized B-spline mixed material point method

Subjected to external loadings, polymeric materials, e.g., biological tissues, hydrogels, and elastomers, may undergo extreme, nearly incompressible, (self-)contact deformations. For numerical modeling employing mesh-based techniques such as the finite element method (FEM), these deformations pose significant challenges due to large distortions in the deformed geometry, accuracy issues stemming from volumetric locking effects, and increased computational cost from complex contact searches. As an alternative to mesh-based methods, the material point method (MPM), a continuum-based particle technique, is gaining attention for its ability to handle extreme distortions and capture no-slip contact without added cost. For nearly incompressible material behaviors, while mixed formulations can address locking effects by treating displacements and pressure as independent fields, they can suffer from numerical instabilities close to the incompressibility limit due to the violation of the inf-sup condition, leading to inaccurate nodal pressure solutions. Here we propose an efficient and stable mixed B-spline material point method with highest achievable regularity for quasi-compressible polymeric materials. Using the two-scale relation of B-splines, we introduce a subdivision-stabilization for the two-field mixed MPM and obtain numerically stable, oscillation-free nodal solutions with equal-order interpolations with optimal regularity. Building on the Eulerian-Lagrangian nature of MPM, a previously-converged solution framework is adopted to mitigate issues related to cell-crossing and numerical fracture artifact present in standard MPM. We assess the stability and accuracy of the developed mixed MPM at large deformations for soft materials through the benchmark Cook’s membrane problem. Additionally, we test the robustness of the proposed MPM by modeling several examples, including the compression and indentation of a circular block into a quasi-compressible substrate and the twisting deformation of a rectangular block. The findings demonstrate the MPM’s capabilities for modeling practical soft material applications.

36 MATERIALS SCIENCE↗