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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 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Comparison of Different Upscaling Methods for Predicting Thermal Conductivity of Complex Heterogeneous Materials System: Application on Nuclear Waste Forms

To develop a strategy in thermal conductivity prediction of a complex heterogeneous materials system, loaded nuclear waste forms, the computational efficiency and accuracy of different upscaling methods have been evaluated. The effective thermal conductivity, obtained from microstructure information and local thermal conductivity of different components, is critical in predicting the life and performance of waste form during storage. Several methods, including the Taylor model, Sachs model, self-consistent model, and statistical upscaling method, were developed and implemented. Microstructure based finite element method (FEM) prediction results were used to as benchmark to determine the accuracy of the different upscaling methods. Micrographs from waste forms with varying waste loadings were used in the prediction of thermal conductivity in FEM and homogenization methods. Prediction results demonstrated that in term of efficiency, boundary models (e.g., Taylor model and Sachs model) are stronger than the self-consistent model, statistical upscaling method, and finite element method. However, when balancing computational efficiency and accuracy, statistical upscaling is a useful method in predicting effective thermal conductivity for nuclear waste forms.

36 MATERIALS SCIENCE↗
DOE OSTI2012

Iso-geometric analysis for neutron diffusion problems

Iso-geometric analysis can be viewed as a generalisation of the finite element method. It permits the exact representation of a wider range of geometries including conic sections. This is possible due to the use of concepts employed in computer-aided design. The underlying mathematical representations from computer-aided design are used to capture both the geometry and approximate the solution. In this paper the neutron diffusion equation is solved using iso-geometric analysis. The practical advantages are highlighted by looking at the problem of a circular fuel pin in a square moderator. For this problem the finite element method requires the geometry to be approximated. This leads to errors in the shape and size of the interface between the fuel and the moderator. In contrast to this iso-geometric analysis allows the interface to be represented exactly. It is found that, due to a cancellation of errors, the finite element method converges more quickly than iso-geometric analysis for this problem. A fuel pin in a vacuum was then considered as this problem is highly sensitive to the leakage across the interface. In this case iso-geometric analysis greatly outperforms the finite element method. Due to the improvement in the representation of the geometry iso-geometric analysis can outperform traditional finite element methods. It is proposed that the use of iso-geometric analysis on neutron transport problems will allow deterministic solutions to be obtained for exact geometries. Something that is only currently possible with Monte Carlo techniques. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Powder spreading, densification, and part deformation in binder jetting additive manufacturing

Binder jetting additive manufacturing (AM) can print complex structures in economical and scalable manner. Binder jetting AM comprises of deposition and weak binding of particles, known as green part, at room temperature and subsequent binder removal and sintering densification at high temperatures. However, during the densification (i.e., sintering), the part significantly deforms due to volume shrinkage. The deformation during sintering is difficult to predict, which prevents the widespread application of this technology. In this research, powder spreading simulation using discrete element method (DEM) was performed first to capture local variations in powder bed configuration. Second, finite element method (FEM) with a phenomenological continuum constitutive model was used to predict part shrinkage during the sintering process. DEM simulation showed variations in packing density, particle segregation, formation of uneven powder bed surface, and shift in particle size distribution (PSD). The sintering simulation modeled part deformation with a reasonable accuracy of 3% for solid-state sintering and intermediate liquid phase sintering. A demonstration case with non-uniform initial packing density showed that inhomogeneous green part density and PSD should be accounted for prediction of part deformation in binder jetting AM.

36 MATERIALS SCIENCE↗
DOE OSTI2019

Simulation of discrete cracks driven by nearly incompressible fluid via 2D combined finite-discrete element method

Here, we propose a novel hydraulic solver in order to simulate key mechanisms that control fluid-driven cracks in the framework of the combined finite-discrete element method (FDEM). The main innovative aspect of the present work is the independence of the fluid's critical time step size with the fracture opening. This advantage is extremely important because it means that very fine meshes can be used around areas of interest, such as boreholes, without penalizing the computational cost as fractures propagate (ie, open) and the fluid flows through them. This is a great advantage over other recently introduced approaches that exhibit a dependency of the time step in the form of Δt crit ∝ (l/a) 2 where l is the element size and a is the fracture aperture. This paper presents a series of benchmark cases for the proposed solver. The rationale adopted by the authors was to benchmark and validate the implementation of the hydraulic solver in an incremental fashion, starting from the simplest cases and building in complexity. The calculations shown in this work clearly demonstrate that the proposed approach is able to reproduce analytical results for fluid flow through a single crack. The results presented in this paper also demonstrate that the new approach is robust enough to deal with complex fracture patterns and complex geometries; the obtained fluid-driven fracture patterns in the vicinity of a borehole certainly stand to the scrutiny of human visual perception.

58 GEOSCIENCES↗
DOE OSTI2018

Boundary node Petrov–Galerkin method in solid structures

Based on the interpolation of the Lagrange series and the Finite Block Method (FBM), the formulations of the Boundary Node Petrov–Galerkin Method (BNPGM) are presented in the weak form in this paper and their applications are demonstrated to the elasticity of functionally graded materials, subjected to static and dynamic loads. By introducing the mapping technique, a block of quadratic type is transformed from the Cartesian coordinate to the normalized coordinate with 8 seeds for two-dimensional problems. The first-order partial differential matrices of boundary nodes are obtained in terms of the nodal values of the boundary node, which can be utilized to determine the tractions on the boundary. Time-dependent partial differential equations are analyzed in the Laplace transformed domain and the Durbin’s inversion method is applied to determine the physical values in the time domain. Illustrative numerical examples are given and comparison has been made with the analytical solutions, the Boundary Element Method (BEM) and the Finite Element Method (FEM).

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Order parameter re-mapping algorithm for 3D phase field model of grain growth using FEM

Phase field modeling (PFM) is a well-known technique for simulating microstructural evolution. To model grain growth using PFM, typically each grain is assigned a unique non-conserved order parameter and each order parameter field is evolved in time. Traditional approaches using a one-to-one mapping of grains to order parameters present a challenge when modeling large numbers of grains due to the computational expense of using many order parameters. This problem is exacerbated when using an implicit finite element method (FEM), as the global matrix size is proportional to the number of order parameters. While previous work has developed methods to reduce the number of required variables and thus computational complexity and run time, none of the existing approaches can be applied for an implicit FEM implementation of PFM. Here, we present a modular, dynamic, scalable reassignment algorithm suitable for use in such a system. Polycrystal modeling with grain growth and stress require careful tracking of each grain’s position and orientation which is lost when using a reduced order parameter set. In conclusion, the method presented in this paper maintains a unique ID for each grain even after reassignment, to allow the PFM to be tightly coupled to calculations of the stress throughout the polycrystal. Implementation details and comparative results of our approach are presented.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Discrete and Continuum Plane-Hopper Flow Simulations with Experimental Validation Using X-Ray Imaging, Arch Profilometry and Wall Pressure Measurements

The flow of spherical glass beads, approximately cubic wood crumbles®, and wood microchips are investigated using a combination of discrete element modeling (DEM), finite element analysis (FEA), and physical experiments using a custom plane-flow hopper in which the flow is characterized using x-ray imaging, profilometry to measure arching geometry and pressure measurements at the wall. The purpose of this study is to investigate fundamental flow behavior, and for this purpose the simulations and physical tests are specially designed. During the physical tests and simulations, the hopper geometry begins as a V shape with the two opposing side walls touching at the bottom of the V. Basic tests are performed by first filling the hopper with material, and then rotating the opposing side walls inward about their common intersection axis to cause an approximately uniform stress condition throughout most of the hopper. The side walls then slide upward to effectively increase the size of the opening at the bottom of the hopper until the arch of material in the hopper breaks, and all of the material falls out of the hopper. More advanced tests are also performed in which the initial rotation of the walls is slightly reversed to decrease the pressure in the hopper, corresponding to “preshear” and “shear” conditions in standard shear tests. Shear tests of the materials are also performed using a Schulze automated ring shear tester with a standard size M shear cell, and the shear tests of the glass beads and wood crumbles® are also simulated using DEM to calibrate the DEM with the FEA. Reasonable agreement between predicted and measured flow behavior is obtained indicating that this type of physical tests and modeling shows promise for characterizing and predicting the flow behavior of compressible and anisotropic materials.

09 BIOMASS FUELS↗
DOE OSTI2016

A 3D finite element ALE method using an approximate Riemann solution

Arbitrary Lagrangian–Eulerian finite volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D finite element arbitrary Lagrangian–Eulerian SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problem results are presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Prediction of softening kinetics and recrystallization texture in non-isothermally annealed bulged tubes using CPFEM and CA models

A hierarchically coupled cellular automata (CA) model, crystal plasticity finite element method (CPFEM), and thermal finite element (FE) model is developed to predict the softening kinetics of the bulged steel tube during non-isothermal annealing. Through the developed model, the kinetics of softening mechanisms including static recovery (SRV) and static recrystallization (SRX), as well as the recrystallization texture are predicted. Later, the Johnson-Mehl-Avrami-Kohnogorov (JMAK) model based on the predicted SRX data is developed to interpret the recrystallization behavior of the material. To perform this study, diverse experimental tests including tube hydroforming (THF), annealing, uniaxial tensile test, hardness test, as well as microstructure observations through optical microscopy and Electron Backscatter Diffraction (EBSD) tests on steel tube are performed. The obtained experimental data are utilized to calibrate and verify the implemented CPFEM model for simulation of THF process, thermal FE model for prediction of the local temperature over annealing time, and CA algorithm for modeling of the softening kinetics and texture evolution throughout the annealing process. The study shows that the predicted deformation characteristics, softening kinetics, recrystallization texture and temperature profile during non-isothermal annealing are in good agreement with experimental data. During the annealing process, a total of four stages for the kinetics of softening mechanisms is observed: No softening; SRV only; SRV dominant; and SRX dominant. During the progress of SRX, the behavior of recrystallization is abruptly changed, confirming that two different mechanisms are controlling the kinetics of transformation.

36 MATERIALS SCIENCE↗
DOE OSTI2016

The NonConforming Virtual Element Method for the Stokes Equations

In this paper, we present the nonconforming virtual element method (VEM) for the numerical approximation of velocity and pressure in the steady Stokes problem. The pressure is approximated using discontinuous piecewise polynomials, while each component of the velocity is approximated using the nonconforming virtual element space. On each mesh element the local virtual space contains the space of polynomials of up to a given degree, plus suitable nonpolynomial functions. The virtual element functions are implicitly defined as the solution of local Poisson problems with polynomial Neumann boundary conditions. As typical in VEM approaches, the explicit evaluation of the non-polynomial functions is not required. This approach makes it possible to construct nonconforming (virtual) spaces for any polynomial degree regardless of the parity, for two- and three-dimensional problems, and for meshes with very general polygonal and polyhedral elements. We show that the nonconforming VEM is inf-sup stable and establish optimal a priori error estimates for the velocity and pressure approximations. Finally, numerical examples confirm the convergence analysis and the effectiveness of the method in providing high-order accurate approximations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A mass conservative, well balanced, tangency preserving and energy decaying method for the shallow water equations on a sphere

Here a fully discrete surface finite element method is proposed for solving the viscous shallow water equations in a bounded Lipschitz domain on the sphere based on a general triangular mesh. The method consists of a modified Crank–Nicolson method in time and a Galerkin surface finite element method in space for the fluid thickness H and the fluid velocity u. A finite element space tangential to the sphere at all finite element nodes is proposed to approximate the fluid velocity u. The proposed method has second-order accuracy in time and first-order accuracy in space, and preserves mass conservation, well balancedness, tangency of velocity to the sphere, and energy decay. Numerical experiments are presented to illustrate the accuracy of the proposed method and the preservation of the physical properties, including mass conservation, well balancedness, and energy decay. A numerical simulation of ocean mesoscale activity on a circular basin with a continental shelf is provided.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Physics-preserving enriched Galerkin method for a fully-coupled thermo-poroelasticity model

This paper proposes a new numerical method for a fully-coupled, quasi-static thermo-poroelasticity model in a unified enriched Galerkin (EG) method framework. In our method, the mechanics sub-problem is solved using a locking-free EG method, and the flow and heat sub-problems are solved using a locally-conservative EG method. The proposed method offers mass and energy conservation properties with much lower costs than other methods with the same properties, including discontinuous Galerkin methods and mixed finite element methods. The well-posedness and optimal a priori error estimates are carefully derived. Here, several numerical tests confirm the theoretical optimal convergence rates and the mass and energy conservation properties of the new method.

15 GEOTHERMAL ENERGY↗
DOE OSTI2014

Spatially adaptive stochastic methods for fluid–structure interactions subject to thermal fluctuations in domains with complex geometries

We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid–structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation–dissipation balance condition to develop compatible stochastic driving fields for our discretization. We perform analysis that shows our condition is sufficient to ensure results consistent with statistical mechanics. We show the Gibbs–Boltzmann distribution is invariant under the stochastic dynamics of the semi-discretization. To generate efficiently the required stochastic driving fields, we develop a Gibbs sampler based on iterative methods and multigrid to generate fields with O(N) computational complexity. Our stochastic methods provide an alternative to uniform discretizations on periodic domains that rely on Fast Fourier Transforms. To demonstrate in practice our stochastic computational methods, we investigate within channel geometries having internal obstacles and no-slip walls how the mobility/diffusivity of particles depends on location. Our methods extend the applicability of fluctuating hydrodynamic approaches by allowing for spatially adaptive resolution of the mechanics and for domains that have complex geometries relevant in many applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Coupling methods between finite element-based Boussinesq-type wave and particle-based free-surface flow models [Coupling methods between finite element-based Boussinesq-typewave and particle-based free-surface flow models]

We develop one-way coupling methods between a Boussinesq-type wave model based on the discontinuous Galerkin finite element method and a free-surface flow model based on a mesh-free particle method to strike a balance between accuracy and computational cost. In our proposed model, computation of the wave model in the global domain is conducted first, and the nonconstant velocity profiles in the vertical direction are reproduced by using its results. Computation of the free-surface flow is performed in a local domain included within the global domain with interface boundaries that move along the reproduced velocity field in a Lagrangian fashion. To represent the moving interfaces, we used a polygon wall boundary model for mesh-free particle methods. Verification and validation tests of our proposed model are performed, and results obtained by the model are compared with theoretical values and experimental results to show its accuracy and applicability.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Feasibility Study on Implementing a Staggered-Grid Finite Volume Method for System Analysis Code Development Under the MOOSE Framework

Here, this work summarizes a feasibility study on testing numerical algorithms that are suitable and efficient for advanced system analysis code development under the mutli-physics framework, MOOSE. The key to the test bed is the implementation of high-order one-dimensional staggered-grid finite volume method (SG-FVM), and its direct interaction with the linear/nonlinear solver, PETSc. The test bed utilized a more flexible code structure to enable the finite volume method implementation and direct interacting with the solver package, instead of using the natively supported finite element method by the framework. Using a suite of selected test problems with different problem sizes and levels of complexity, the implemented SG-FVM demonstrated superior performance improvement against a direct finite element method implementation through MOOSE. On two computer systems, the speedup was observed to be significant, with at least one order of magnitude of solving time reduction. For a complex reactor model, transient simulation was performed using the newly developed finite volume method code, the results of which agree very well with the reference results from the finite element method code. Overall, this study demonstrates a successful feasibility study on the proposed numerical algorithms and software structure to support advanced system analysis tool development.

MOOSE↗
DOE OSTI2022

A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method

Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure under severe dynamic loading conditions. Second-order phase-field fracture models have gained wide adoption given their ability to capture the formation of complex fracture patterns, e.g. via crack merging and branching, and their suitability for implementation within the context of the conventional finite element method. Higher-order phase-field models have also been proposed to increase the regularity of the exact solution and thus increase the spatial convergence rate of its numerical approximation. However, they require special numerical techniques to enforce the necessary continuity of the phase field solution. In this paper, we derive a fourth-order phase-field model of fracture in two independent ways; namely, from Hamilton’s principle and from a higher-order micromechanics-based approach. The latter approach is novel, and provides a physical interpretation of the higher-order terms in the model. In addition, we propose a continuous/discontinuous Galerkin (C/DG) method for use in computing the approximate phase-field solution. This method employs Lagrange polynomial shape functions to guarantee -continuity of the solution at inter-element boundaries, and enforces the required regularity with the aid of additional variational and interior penalty terms in the weak form. Finally, the phase-field equation is coupled with the momentum balance equation to model dynamic fracture problems in hyper-elastic materials. Two benchmark problems are presented to compare the numerical behavior of the C/DG method with mixed finite element methods.

42 ENGINEERING↗
DOE OSTI2017

A Weak Galerkin Method for the Reissner–Mindlin Plate in Primary Form

We developed a new finite element method for the Reissner–Mindlin equations in its primary form by using the weak Galerkin approach. Like other weak Galerkin finite element methods, this one is highly flexible and robust by allowing the use of discontinuous approximating functions on arbitrary shape of polygons and, at the same time, is parameter independent on its stability and convergence. Furthermore, error estimates of optimal order in mesh size h are established for the corresponding weak Galerkin approximations. Numerical experiments are conducted for verifying the convergence theory, as well as suggesting some superconvergence and a uniform convergence of the method with respect to the plate thickness.

97 MATHEMATICS AND COMPUTING↗