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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 1,567 records · Page 87
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

A Quasi-Parabolic technique for computation of three-dimensional viscous flows

A computational technique is presented for obtaining flowfield solutions to a parabolic form of the Navier-Stokes equations. The point of departure is the General Interpolant Method (GIM) which provides a discretization for partial differential equations on arbitrary three-dimensional geometries. The new scheme, termed Quasi-Parabolic, treats the parabolized equations but with 'time-like' terms appended. Addition of these extra terms, which are relaxed by iteration, avoid many of the singularities inherent in classical parabolic Navier-Stokes methods. Streamwise derivatives are approximated by three-point backward differences and the cross plane operators use an alternating forward-backward sweep. A two-step sequence is used to implement the difference scheme in the spatial dimensions and a time-like relaxation converges the quasi-parabolic procedure at each plane. Solutions are presented for flows in two and three dimensions. Inviscid flows are solved for internal and external applications and viscous flows in boundary layers and free shear layers are also computed with the GIM/Quasi-Parabolic scheme.

Spradley, L. W.↗
NASA NTRS2003

An Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids

An algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier-Stokes equations is presented. The method is constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system. The new approach is implemented within a three-dimensional unstructured-grid framework and results are presented for inviscid, laminar, and turbulent flows. Improvements to the baseline solution algorithm, such as line-implicit relaxation and a tight coupling of the turbulence model, are also presented. By storing nearest-neighbor terms in the residual computation, the dual scheme is computationally efficient, while requiring twice the memory of the flow solution. The scheme is expected to have a broad impact on computational problems related to design optimization as well as error estimation and grid adaptation efforts.

Nielsen, Eric J.↗
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 NTRS1990

Discrete approximations to optimal trajectories using direct transcription and nonlinear programming

A recently developed method for solving optimal trajectory problems uses a piecewise-polynomial representation of the state and control variables, enforces the equations of motion via a collocation procedure, and thus approximates the original calculus-of-variations problem with a nonlinear-programming problem, which is solved numerically. This paper identifies this method as a direct transcription method and proceeds to investigate the relationship between the original optimal-control problem and the nonlinear-programming problem. The discretized adjoint equation of the collocation method is found to have deficient accuracy, and an alternate scheme which discretizes the equations of motion using an explicit Runge-Kutta parallel-shooting approach is developed. Both methods are applied to finite-thrust spacecraft trajectory problems, including a low-thrust escape spiral, a three-burn rendezvous, and a low-thrust transfer to the moon.

Enright, Paul J.↗
DOE OSTI2019

Fractional Operators Applied to Geophysical Electromagnetics

A growing body of applied mathematics literature in recent years has focused on the application of fractional calculus to problems of anomalous transport. In these analyses, the anomalous transport (of charge, tracers, fluid, etc.) is presumed attributable to long–range correlations of material properties within an inherently complex, and in some cases self-similar, conducting medium. Rather than considering an exquisitely discretized (and computationally intractable) representation of the medium, the complex and spatially correlated heterogeneity is represented through reformulation of the governing equation for the relevant transport physics such that its coefficients are, instead, smooth but paired with fractional–order space derivatives. Here we apply these concepts to the scalar Helmholtz equation and its use in electromagnetic interrogation of Earth’s interior through the magnetotelluric method. We outline a practical algorithm for solving the Helmholtz equation using spectral methods coupled with finite element discretizations. Execution of this algorithm for the magnetotelluric problem reveals several interesting features observable in field data: long–range correlation of the predicted electromagnetic fields; a power–law relationship between the squared impedance amplitude and squared wavenumber whose slope is a function of the fractional exponent within the governing Helmholtz equation; and, a non–constant apparent resistivity spectrum whose variability arises solely from the fractional exponent. In geologic settings characterized by self–similarity (e.g. fracture systems; thick and richly–textured sedimentary sequences, etc.) we posit that these diagnostics are useful for geologic characterization of features far below the typical resolution limit of electromagnetic methods in geophysics.

58 GEOSCIENCES↗
DOE OSTI2022

Geometrically necessary dislocation fingerprints of dislocation loop absorption at grain boundaries

Here we present a numerical methodology to compute the Nye-tensor fingerprints of dislocation loop absorption at grain boundaries (GBs) for comparison with TEM observations of irradiated polycrystals. Our approach links atomistic simulations of self-interstitial atom (SIA) prismatic loops gliding toward and interacting with GBs in body-centered cubic iron with experimentally extracted geometrically necessary dislocation (GND) maps to facilitate the interpretation of damage processes. The Nye-tensor analysis is strongly mesh-size dependent—corresponding to resolution-dependent TEM observations. The method computes GND fingerprints from discretized dislocation line segments extracted from molecular dynamics simulations of dislocation loops being absorbed at a GB. Specifically, we perform MD simulation of prismatic loops of two diameters and monitor the three stages of the absorption process: loop glide, the partial, and full absorption of the loops at a [1 0 0] symmetric tilt GB. These methods provide a framework for future investigations of the nature of defect absorption by grain boundaries under irradiation conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Airy function approach and Numerov method to study the anharmonic oscillator potentials V(x) = Ax{sup 2α} + Bx{sup 2}

The numerical solutions of the time independent Schrödinger equation of different one-dimensional potentials forms are sometime achieved by the asymptotic iteration method. Its importance appears, for example, on its efficiency to describe vibrational system in quantum mechanics. In this paper, the Airy function approach and the Numerov method have been used and presented to study the oscillator anharmonic potential V(x) = Ax{sup 2α} + Bx{sup 2}, (A>0, B<0), with (α = 2) for quadratic, (α =3) for sextic and (α =4) for octic anharmonic oscillators. The Airy function approach is based on the replacement of the real potential V(x) by a piecewise-linear potential v(x), while, the Numerov method is based on the discretization of the wave function on the x-axis. The first energies levels have been calculated and the wave functions for the sextic system have been evaluated. These specific values are unlimited by the magnitude of A, B and α. It’s found that the obtained results are in good agreement with the previous results obtained by the asymptotic iteration method for α =3.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Shadow Lagrangian dynamics for superfluidity

Motivated by a similar approach for Born-Oppenheimer molecular dynamics, this paper proposes an extended "shadow" Lagrangian density for quantum states of superfluids. The extended Lagrangian contains an additional field variable that is forced to follow the wave function of the quantum state through a rapidly oscillating extended harmonic oscillator. By considering the adiabatic limit for large frequencies of the harmonic oscillator, we can derive the two equations of motions, a Schrödinger-type equation for the quantum state and a wave equation for the extended field variable. The equations are coupled in a nonlinear way, but each equation individually is linear with respect to the variable that it defines. The computational advantage of this new system is that it can be easily discretized using linear time stepping methods, where we propose to use a Crank-Nicolson-type approach for the Schrödinger equation and an extended leapfrog scheme for the wave equation. Furthermore, the difference between the quantum state and the extended field variable defines a consistency error that should go to zero if the frequency tends to infinity. By coupling the time-step size in our discretization to the frequency of the harmonic oscillator we can extract an easily computable consistency error indicator that can be used to estimate the numerical error without additional costs. The findings are illustrated in numerical experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Effects of defects in composite wind turbine blades – Part 1: Characterization and mechanical testing

Abstract. The Montana State University Composite Material Technologies Research Group performed a study to ascertain the effects of defects that often result from the manufacture of composite wind turbine blades. The first step in this multiyear study was to systematically quantify and enter these defects into a database before embedding similar defects into manufactured coupons. Through the Sandia National Laboratories Blade Reliability Collaborative (BRC), it was determined that key defects to investigate were fiber waves and porosity. An inspection of failed commercial-scale wind turbine blades yielded metrics that utilized specific parameters to physically characterize a defect. Methods to easily and consistently discretize, measure, and assess these defects based on the identified parameters were established to allow for statistical analysis. Data relating flaw parameters to frequencies of occurrence were analyzed and found to fit within standard distributions. Additionally, mechanical testing of coupons with flaws based on these physical characterization data was performed to understand effects of these defects. Representative blade materials and manufacturing methods were utilized and both material properties and damage progression were measured. It was observed that flaw parameters directly affected the mechanical response. While the data gathered in this first step are widely useful, it was also intended for use as a foundation for the rest of the study, to perform probabilistic analysis and comparative analysis of progressive damage models.

Nelson, Jared W. (ORCID:0000000207736091)↗
DOE OSTI2017

High Order Accurate Finite Difference Modeling of Seismo-Acoustic Wave Propagation in a Moving Atmosphere and a Heterogeneous Earth Model Coupled Across a Realistic Topography

Here, we develop a numerical method for simultaneously simulating acoustic waves in a realistic moving atmosphere and seismic waves in a heterogeneous earth model, where the motions are coupled across a realistic topography. We model acoustic wave propagation by solving the linearized Euler equations of compressible fluid mechanics. The seismic waves are modeled by the elastic wave equation in a heterogeneous anisotropic material. The motion is coupled by imposing continuity of normal velocity and normal stresses across the topographic interface. Realistic topography is resolved on a curvilinear grid that follows the interface. The governing equations are discretized using high order accurate finite difference methods that satisfy the principle of summation by parts. We apply the energy method to derive the discrete interface conditions and to show that the coupled discretization is stable. The implementation is verified by numerical experiments, and we demonstrate a simulation of coupled wave propagation in a windy atmosphere and a realistic earth model with non-planar topography.

58 GEOSCIENCES↗
DOE OSTI2020

Comparing field data using Alpert multi-wavelets

In this paper we introduce a method to compare sets of full-field data using Alpert tree-wavelet transforms. The Alpert tree-wavelet methods transform the data into a spectral space allowing the comparison of all points in the fields by comparing spectral amplitudes. The methods are insensitive to translation, scale and discretization and can be applied to arbitrary geometries. This makes them especially well suited for comparison of field data sets coming from two different sources such as when comparing simulation field data to experimental field data. We have developed both global and local error metrics to quantify the error between two fields. Additionally, we verify the methods on two-dimensional and three-dimensional discretizations of analytical functions. Furthermore, we then deploy the methods to compare full-field strain data from a simulation of elastomeric syntactic foam.

42 ENGINEERING↗
NASA NTRS1995

On the Importance of the Dynamics of Discretizations

It has been realized recently that the discrete maps resulting from numerical discretizations of differential equations can possess asymptotic dynamical behavior quite different from that of the original systems. This is the case not only for systems of Ordinary Differential Equations (ODEs) but in a more complicated manner for Partial Differential Equations (PDEs) used to model complex physics. The impact of the modified dynamics may be mild and even not observed for some numerical methods. For other classes of discretizations the impact may be pronounced, but not always obvious depending on the nonlinear model equations, the time steps, the grid spacings and the initial conditions. Non-convergence or convergence to periodic solutions might be easily recognizable but convergence to incorrect but plausible solutions may not be so obvious - even for discretized parameters within the linearized stability constraint. Based on our past four years of research, we will illustrate some of the pathology of the dynamics of discretizations, its possible impact and the usage of these schemes for model nonlinear ODEs, convection-diffusion equations and grid adaptations.

Sweby, Peter K.↗
DOE OSTI2017

Overset meshing coupled with hybridizable discontinuous Galerkin finite elements

We introduce the use of hybridizable discontinuous Galerkin (HDG) finite element methods on overlapping (overset) meshes. Overset mesh methods are advantageous for solving problems on complex geometrical domains. We also combine geometric flexibility of overset methods with the advantages of HDG methods: arbitrarily high-order accuracy, reduced size of the global discrete problem, and the ability to solve elliptic, parabolic, and/or hyperbolic problems with a unified form of discretization. This approach to developing the ‘overset HDG’ method is to couple the global solution from one mesh to the local solution on the overset mesh. We present numerical examples for steady convection–diffusion and static elasticity problems. The examples demonstrate optimal order convergence in all primal fields for an arbitrary amount of overlap of the underlying meshes.

42 ENGINEERING↗
NASA NTRS1993

Method of implementing digital phase-locked loops

In a new formulation for digital phase-locked loops, loop-filter constants are determined from loop roots that can each be selectively placed in the s-plane on the basis of a new set of parameters, each with simple and direct physical meaning in terms of loop noise bandwidth, root-specific decay rate, or root-specific damping. Loops of first to fourth order are treated in the continuous-update approximation (BLT yields 0) and in a discrete-update formulation with arbitrary BLT. Deficiencies of the continuous-update approximation in large-BLT applications are avoided in the new discrete-update formulation. A new method for direct, transient-free acquisition with third- and fourth-order loops can improve the versatility and reliability of acquisition with such loops.

Stephens, Scott A.↗
DOE OSTI2015

A point-centered arbitrary Lagrangian Eulerian hydrodynamic approach for tetrahedral meshes

We present a three dimensional (3D) arbitrary Lagrangian Eulerian (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes. The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point. This type of an approach is termed a point-centered hydrodynamic (PCH) method. The conservation equations are discretized using an edge-based finite element (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved at the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Runge–Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems are presented.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Error analysis of finite element solutions for postbuckled cylinders

A general method of error analysis and correction is investigated for the discrete finite-element results for cylindrical shell structures. The method for error analysis is an adaptation of the method of successive approximation. When applied to the equilibrium equations of shell theory, successive approximations derive an approximate continuous solution from the discrete finite-element results. The advantage of this continuous solution is that it contains continuous partial derivatives of an order higher than the basis functions of the finite-element solution. Preliminary numerical results are presented in this paper for the error analysis of finite-element results for a postbuckled stiffened cylindrical panel modeled by a general purpose shell code. Numerical results from the method have previously been reported for postbuckled stiffened plates. A procedure for correcting the continuous approximate solution by Newton's method is outlined.

Sistla, Rajaram↗
DOE OSTI2015

Discrete Modeling of Early-Life Thermal Fracture in Ceramic Nuclear Fuel

Fracturing of ceramic fuel pellets heavily influences performance of light water reactor (LWR) fuel. Early in the life of fuel, starting with the initial power ramp, large thermal gradients cause high tensile hoop and axial stresses in the outer region of the fuel pellets, resulting in the formation of radial and axial cracks. Circumferential cracks form due to thermal gradients that occur when the power is ramped down. These thermal cracks cause the fuel to expand radially, closing the pellet/cladding gap and enhancing the thermal conductance across that gap, while decreasing the effective conductivity of the fuel in directions normal to the cracking. At lower length scales, formation of microcracks is an important contributor to the decrease in bulk thermal conductivity that occurs over the life of the fuel as the burnup increases. Because of the important effects that fracture has on fuel performance, a realistic, physically based fracture modeling capability is essential to predict fuel behavior in a wide variety of normal and abnormal conditions. Modeling fracture within the context of the finite element method, which is based on continuous interpolations of solution variables, has always been challenging because fracture is an inherently discontinuous phenomenon. Work is underway at Idaho National Laboratory to apply two modeling techniques model fracture as a discrete displacement discontinuity to nuclear fuel: The extended finite element method (XFEM), and discrete element method (DEM). XFEM is based on the standard finite element method, but with enhancements to represent discontinuous behavior. DEM represents a solid as a network of particles connected by bonds, which can arbitrarily fail if a fracture criterion is reached. This paper presents initial results applying the aforementioned techniques to model fuel fracturing. This work has initially focused on early life behavior of ceramic LWR fuel. A coupled thermal-mechanical XFEM method that includes discontinuities in both temperature and displacement fields at crack locations has been developed and is being applied to thermal fracture of LWR fuel. A DEM model of coupled heat conduction and solid mechanics has been developed and used to simulate random initiation and propagation of thermally driven cracks during initial power cycles. This DEM model predicts the formation of realistic radial cracking patterns during power rise and circumferential cracks as power is ramped down. These initial results are very encouraging, and these techniques are expected to provide improved understanding of fuel behavior in a wide variety of conditions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
NASA NTRS1978

Application of the finite element method to rotary-wing aeroelasticity

Recent research in rotary-wing aeroelasticity has indicated that all fundamental problems in this area are inherently nonlinear. The non-linearities in this problem are due to the inclusion of finite slopes, due to moderate deflections, in the structural, inertia and aerodynamic operators associated with this aeroelastic problem. In this paper the equations of motion, which are both time and space dependent, for the aeroelastic problem are first formulated in P.D.E. form. Next the equations are linearized about a suitable equilibrium position. The spatial dependence in these equations is discretized using a local Galerkin method of weighted residuals resulting in a finite element formulation of the aeroelastic problem. As an illustration the method is applied to the coupled flap-lag problem of a helicopter rotor blade in hover. Comparison of the solutions with previously published solutions establishes the convergence properties of the method. It is concluded that this formulation is a practical tool for solving rotary-wing aeroelastic stability or response problems.

Friedmann, P.↗