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NASA NTRS1974

Compressible seal flow analysis using the finite element method with Galerkin solution technique

High pressure gas sealing involves not only balancing the viscous force with the pressure gradient force but also accounting for fluid inertia--especially for choked flow. The conventional finite element method which uses a Rayleigh-Ritz solution technique is not convenient for nonlinear problems. For these problems, a finite element method with a Galerkin solution technique (FEMGST) was formulated. One example, a three-dimensional axisymmetric flow formulation has nonlinearities due to compressibility, area expansion, and convective inertia. Solutions agree with classical results in the limiting cases. The development of the choked flow velocity profile is shown.

Zuk, J.↗

DOE OSTI2019

Formulation and characterization of a continuous crystal lattice orientation finite element method (LOFEM) and its application to dislocation fields

We report that since the 1950s, a large body of work has been published on connecting the curvature of a crystal lattice to geometrically necessary dislocations densities of a crystal lattice. Studying dislocation transmission through grains and across their boundaries requires the lattice curvature to be preserved. However, traditional crystal plasticity models and their numerical implementations do not formally preserve lattice curvature. In this paper, a continuous crystal lattice orientation finite element method (LOFEM) is proposed to rectify this impediment to the inclusion of dislocation-based constitutive models. The methodology is first presented, and then it is demonstrated for tension and compression deformations of a copper polycrystal. It is shown that under the same deformation histories, the lattice continuity constraint alters the evolving state in comparison to the traditional approach, including retarding the rate at which the crystallographic texture strengthens under monotonic deformation. Lastly, taking advantage of the finite element representation of the lattice orientation, the Nye tensor is computed on lattices misoriented by deformation and is subsequently used to compute evolving dislocation density distributions.

36 MATERIALS SCIENCE↗

DOE OSTI2020

PRISMS-PF: A general framework for phase-field modeling with a matrix-free finite element method

Abstract A new phase-field modeling framework with an emphasis on performance, flexibility, and ease of use is presented. Foremost among the strategies employed to fulfill these objectives are the use of a matrix-free finite element method and a modular, application-centric code structure. This approach is implemented in the new open-source PRISMS-PF framework. Its performance is enabled by the combination of a matrix-free variant of the finite element method with adaptive mesh refinement, explicit time integration, and multilevel parallelism. Benchmark testing with a particle growth problem shows PRISMS-PF with adaptive mesh refinement and higher-order elements to be up to 12 times faster than a finite difference code employing a second-order-accurate spatial discretization and first-order-accurate explicit time integration. Furthermore, for a two-dimensional solidification benchmark problem, the performance of PRISMS-PF meets or exceeds that of phase-field frameworks that focus on implicit/semi-implicit time stepping, even though the benchmark problem’s small computational size reduces the scalability advantage of explicit time-integration schemes. PRISMS-PF supports an arbitrary number of coupled governing equations. The code structure simplifies the modification of these governing equations by separating their definition from the implementation of the numerical methods used to solve them. As part of its modular design, the framework includes functionality for nucleation and polycrystalline systems available in any application to further broaden the phenomena that can be used to study. The versatility of this approach is demonstrated with examples from several common types of phase-field simulations, including coarsening subsequent to spinodal decomposition, solidification, precipitation, grain growth, and corrosion.

36 MATERIALS SCIENCE↗

DOE OSTI2015

Rolling Process Modeling Report. Finite-Element Model Validation and Parametric Study on various Rolling Process parameters

Pacific Northwest National Laboratory (PNNL) has been investigating manufacturing processes for the uranium-10% molybdenum alloy plate-type fuel for high-performance research reactors in the United States. This work supports the U.S. Department of Energy National Nuclear Security Administration’s Office of Material Management and Minimization Reactor Conversion Program. This report documents modeling results of PNNL’s efforts to perform finite-element simulations to predict roll-separating forces for various rolling mill geometries for PNNL, Babcock & Wilcox Co., Y-12 National Security Complex, Los Alamos National Laboratory, and Idaho National Laboratory. The model developed and presented in a previous report has been subjected to further validation study using new sets of experimental data generated from a rolling mill at PNNL. Simulation results of both hot rolling and cold rolling of uranium-10% molybdenum coupons have been compared with experimental results. The model was used to predict roll-separating forces at different temperatures and reductions for five rolling mills within the National Nuclear Security Administration Fuel Fabrication Capability project. This report also presents initial results of a finite-element model microstructure-based approach to study the surface roughness at the interface between zirconium and uranium-10% molybdenum.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2022

High-temperature compressive creep tests of U 3 Si 2 with spark plasma sintering: Experiments and finite element modeling

This paper reports a systematic high-temperature creep behavior of dense U 3 Si 2 pellets using a spark plasma sintering (SPS) apparatus at elevated temperatures and pressures under vacuum conditions. The stress exponent was subsequently derived to be 3.21 at 1173 K and 2.17 at 1223 K, respectively, indicating a grain boundary sliding creep mechanism. The creep activation energy was determined to be 203.6 ± 19.0 kJ/mol, which agrees well with the literature. Finite element modeling was performed using the creep parameters fitted from the strain-time plot. Additionally, the results suggest an excellent match with the experimental data, confirming the validity of the experiments. Microstructure characterizations indicate that the main phase of the specimens after creep tests remains to be U 3 Si 2 , with a 4 μm thick layer of nano-sized particles induced from the diffusion between U 3 Si 2 and alumina disc used to avoid electric current passing through the sample. The successful conduct of creep experiments demonstrates the great potential of SPS to perform high-temperature mechanical testing of nuclear fuels under vacuum conditions. The subsequent finite element modeling exhibits excellent capabilities for accurately predicting material performance in the creep tests and provides a practical tool in evaluating nuclear fuels’ performance for a much-extended time scale.

36 MATERIALS SCIENCE↗

DOE OSTI2018

Development of Finite Element Field Solver in Gyrokinetic Toroidal Code

A new finite element (FE) field solver has been implemented in the gyrokinetic toroidal code (GTC) in attempt to extend the simulation domain to magnetic axis and beyond the last closed flux surface, which will enhance the capability the GTC code since the original finite difference (FD) solver will lose its capability in such circumstances. A method of manufactured solution is employed in the unit fidelity test for the new FE field solver, which is then further verified through integrated tests with three typical physical cases for the comparison between the new FE field solver and the original finite difference field solver. The results by the newly implemented FE field solver are in great accord with the original solver.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1992

The semi-discrete Galerkin finite element modelling of compressible viscous flow past an airfoil

A method is developed to solve the two-dimensional, steady, compressible, turbulent boundary-layer equations and is coupled to an existing Euler solver for attached transonic airfoil analysis problems. The boundary-layer formulation utilizes the semi-discrete Galerkin (SDG) method to model the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby permitting the use of a uniform finite element grid which provides high resolution near the wall and automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes, through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past NACA 0012 and RAE 2822 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack. All results show good agreement with experiment, and the coupled code proved to be a computationally-efficient and accurate airfoil analysis tool.

Meade, Andrew J., Jr.↗

NASA NTRS1985

On the existence and stability conditions for mixed-hybrid finite element solutions based on Reissner's variational principle

The extensions of Reissner's two-field (stress and displacement) principle to the cases wherein the displacement field is discontinuous and/or the stress field results in unreciprocated tractions, at a finite number of surfaces ('interelement boundaries') in a domain (as, for instance, when the domain is discretized into finite elements), is considered. The conditions for the existence, uniqueness, and stability of mixed-hybrid finite element solutions based on such discontinuous fields, are summarized. The reduction of these global conditions to local ('element') level, and the attendant conditions on the ranks of element matrices, are discussed. Two examples of stable, invariant, least-order elements - a four-node square planar element and an eight-node cubic element - are discussed in detail.

Karlovitz, L. A.↗

NASA NTRS1991

Finite element nonlinear flutter and fatigue life of 2-D panels with temperature effects

A frequency domain method for two-dimensional nonlinear panel flutter with thermal effects obtained from a consistent finite element formulation is presented. The von Karman nonlinear strain-displacement relation is used to account for large deflections, and the quasi-steady first-order piston theory is employed for aerodynamic loading. The finite element frequency domain results are compared with analytical time domain solutions. In a limit-cycle motion, the panel frequency and stress can be determined, thus fatigue life can be predicted. The influence of temperature and dynamic pressure on panel fatigue life is presented. An endurance dynamic pressure can be established at a given temperature from the present method.

Mei, Chuh↗

NASA NTRS1993

Three-dimensional finite element progressive failure analysis of composite laminates under axial extension

A three-dimensional (3D) progressive failure algorithm is developed, where the layerwise laminate theory (LWLT) of Reddy is used for kinematic description. The finite element model based on the layerwise theory predicts both inplane and interlaminar stresses with the same accuracy as that of a conventional 3D finite element model and provides a convenient format for modeling the 3D stress fields in composite laminates. A parametric study is conducted to investigate the effect of out-of-plane material properties, 3D stiffness reduction methods, and boundary conditions on the failure loads and strains of a composite laminate under axial extension. The results indicate that different parameters have a different degree of influence on the failure loads and strains. The predictive ability of various phenomenological failure criteria is evaluated in the light of experimental results available in the literature, and the predictions of the LWLT are compared with those of the first-order shear deformation theory. It is concluded that a 3D stress analysis is necessary to predict accurately the failure behavior of composite laminates.

Reddy, Yeruva S.↗

NASA NTRS1984

Penalty function finite element analysis of steady viscous incompressible flow in rotating coordinates

Finite element methods for incompressible viscous flow in turbomachines have not been presented in the literature previously. This paper develops a penalty function primitive variable method including Coriolis and centrifugal force terms for steady flow in a rotating coordinate system. Simplex elements are used with the result of solution times comparable to equivalent finite different solutions. Example cases considered are Couette flow, Poiseuile flow, flow over a step and flow in a rotating channel. Both laminar and turbulent flows are discussed. The accuracy of computed solutions compares well with theoretical solutions and experimenal measurements.

Rosen, M. C.↗

NASA NTRS1998

Numerical Differentiation for Adaptively Refined Finite Element Meshes

Postprocessing of point-wise data is a fundamental process in many fields of research. Numerical differentiation is a key operation in computational electromagnetics. In the case of data obtained from a finite element method with automatic mesh refinement much work needs still to be done. This paper addresses some issues in differentiating data obtained from a finite element electromagnetic code with adaptive mesh refinement, and it proposes a methodology for deriving the electric field given the magnetic field on a mesh of linear triangular elements. The procedure itself is nevertheless more general and might be extended for numerically differentiating any point-wise solution based on triangular meshes.

Borgioli, Andrea↗

NASA NTRS1995

A finite element propagation model for extracting normal incidence impedance in nonprogressive acoustic wave fields

A propagation model method for extracting the normal incidence impedance of an acoustic material installed as a finite length segment in a wall of a duct carrying a nonprogressive wave field is presented. The method recasts the determination of the unknown impedance as the minimization of the normalized wall pressure error function. A finite element propagation model is combined with a coarse/fine grid impedance plane search technique to extract the impedance of the material. Results are presented for three different materials for which the impedance is known. For each material, the input data required for the prediction scheme was computed from modal theory and then contaminated by random error. The finite element method reproduces the known impedance of each material almost exactly for random errors typical of those found in many measurement environments. Thus, the method developed here provides a means for determining the impedance of materials in a nonprogressirve wave environment such as that usually encountered in a commercial aircraft engine and most laboratory settings.

Watson, Willie R.↗

DOE OSTI2026

Finite-element boundary-integral simulation of thin wires and inhomogeneous penetrable bodies in subsurface multilayered anisotropic media

With the prevailing presence of drilling wells near the subsurface in mature oil and gas fields, the application of electromagnetic methods can be particularly challenging where the electromagnetic field is affected by the steel casing. In the past decades, borehole-to-surface and crosswell electromagnetic methods have been utilized for monitoring of reservoir and underground CO 2 storage. This paper presents a unified finite-element boundary-integral (FEBI) method capable of simultaneously modeling the complex electromagnetic interactions between thin metallic wires (representing steel casings) with 3D trajectory and arbitrary 3D inhomogeneous penetrable bodies (such as CO 2 plumes or hydrocarbon reservoirs) within anisotropic multilayered subsurface environments. Unlike existing approaches that treat these components separately or require dense discretization, or are limited to vertical wells, our unified formulation preserves flexible electromagnetic coupling while delivering improved computational efficiency. Assuming the background formation is multilayered anisotropic media, the surface integral equation method is applied to model the thin wires and boundaries of the inhomogeneous bodies. Meanwhile, the finite element method is applied to model the volume of inhomogeneous bodies. Here, the performance of the proposed FEBI method is assessed through comparison with reference numerical results and its practical significance is demonstrated through CO 2 plume monitoring scenarios.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1990

Finite-element models of continental extension

Numerical models of the initial deformation of extending continental lithosphere, computed to investigate the control of preexisting thermal and mechanical heterogeneities on the style of deformation, are presented. The finite element method is used to calculate deformation with a viscoelastic-plastic model for the lithosphere. Comparisons of the results of analytic models and finite-element models using this method show that good results may be obtained by the numerical technique, even with elements containing both brittle and viscoelastic sampling points. It is shown that the gross style of initial extensional deformation is controlled by the depth and width of the initial heterogeneity which localizes deformation.

Lynch, H. David↗

DOE OSTI2016

Demonstration of finite element simulations in MOOSE using crystallographic models of irradiation hardening and plastic deformation

This report describes the implementation of a crystal plasticity framework (VPSC) for irradiation hardening and plastic deformation in the finite element code, MOOSE. Constitutive models for irradiation hardening and the crystal plasticity framework are described in a previous report [1]. Here we describe these models briefly and then describe an algorithm for interfacing VPSC with finite elements. Example applications of tensile deformation of a dog bone specimen and a 3D pre-irradiated bar specimen performed using MOOSE are demonstrated.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1983

CLFE2D: A generalized plane strain finite element program laminated composites subject to mechanical and hygrothermal loading

CLFE2D is a two dimensional generalized plane strain finite element code, using a linear, four node, general quadrilateral, isoparametric element. The program is developed to calculate the displacements, strains, stresses, and strain energy densities in a finite width composite laminate. CLFE2D offers any combination of the following load types: nodal displacements, nodal forces, uniform normal strain, or hygrothermal. The program allows the user to input one set of three dimensional orthotropic material properties. The user can then specify the angle of material principal orientation for each element in the mesh. Output includes displacements, stresses, strains and strain densities at points selected by the user. An option is also available to plot the underformed and deformed finite element meshes.

Buczek, M. B.↗

NASA NTRS1978

Application of finite element techniques in predicting the acoustic properties of turbofan inlets

An analytical technique was developed for predicting the acoustic performance of turbofan inlets carrying a subsonic axisymmetric steady flow. The finite element method combined with the method of weighted residuals is used in predicting the acoustic properties of variable area, annular ducts with or without acoustic treatments along their walls. An approximate solution for the steady inviscid flow field is obtained using an integral method for calculating the incompressible potential flow field in the inlet with a correction to account for compressibility effects. The accuracy of the finite element technique was assessed by comparison with available analytical solutions for the problems of plane and spinning wave propagation through a hard walled annular cylinder with a constant mean flow.

Majjigi, R. K.↗