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At least 235 records · Page 13

All sources NASA NTRS DOE OSTI

DOE OSTI2015

KAPPA: A PACKAGE FOR SYNTHESIS OF OPTICALLY THIN SPECTRA FOR THE NON-MAXWELLIAN κ-DISTRIBUTIONS BASED ON THE CHIANTI DATABASE

Non-Maxwellian κ-distributions have been detected in the solar transition region and in flares. These distributions are characterized by a high-energy tail and a near-Maxwellian core and are known to have a significant impact on the resulting optically thin spectra arising from collisionally dominated astrophysical plasmas. We developed the KAPPA package for the synthesis of such line and continuum spectra. The package is based on the freely available CHIANTI database and software, and can be used in a similar manner. Ionization and recombination rates together with the ionization equilibria are provided for a range of κ values. Distribution-averaged collision strengths for excitation are obtained using an approximate method for all transitions in all ions available within CHIANTI. The validity of this approximate method is tested through a comparison with direct calculations. Typical precisions of better than 5% are found with all cases being within 10%. Tools for the calculation of synthetic line and continuum intensities are provided and described. Examples of the synthetic spectra and SDO/AIA responses to emission for the κ-distributions are given.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Eulerian thermo-mechanical simulations of heterogeneous solid propellants using an approximate projection method

We present a mathematical model that describes thermo-mechanical deformations and thermal gradients on the unsteady burning of a heterogeneous solid propellant. A scaling study shows that the deformations in solid at combustion timescales can be treated as quasi-static. The resulting thermo-mechanical formulation is formulated on a Cartesian grid and makes use of a weak form of Chorin-type projection method to deal with large difference in shear modulus of constituent materials. Further, a one-dimensional verification study is carried out by comparing numerical simulations with those of an analytical model. In addition, convergence studies for a two-dimensional propellant sandwich configuration are presented for the stress, velocity, and reference map components. Finally, simulations are carried out for a two-dimensional random propellant pack and the time-averaged burn rate and strains are reported.

42 ENGINEERING↗

NASA NTRS1982

Kinematic precision of gear trains

Kinematic precision is affected by errors which are the result of either intentional adjustments or accidental defects in manufacturing and assembly of gear trains. A method for the determination of kinematic precision of gear trains is described. The method is based on the exact kinematic relations for the contact point motions of the gear tooth surfaces under the influence of errors. An approximate method is also explained. Example applications of the general approximate methods are demonstrated for gear trains consisting of involute (spur and helical) gears, circular arc (Wildhaber-Novikov) gears, and spiral bevel gears. Gear noise measurements from a helicopter transmission are presented and discussed with relation to the kinematic precision theory.

Litvin, F. L.↗

NASA NTRS1983

Kinematic precision of gear trains

Litvin, F. L.↗

NASA NTRS1985

Evaluation of fault-tolerant system performance by approximate techniques

An approximate method for calculating the statistics of the performance of a fault-tolerant system is developed. An approximate method is necessary because the statistical model of the system behavior is large-scale and the time horizon of interest encompasses many cycles of the Redundancy Management logic. In the development, a compact representation of the necessary information called the v-transform is introduced and discussed. Based upon this representation, an approximation that leads to a very efficient computational procedure is suggested and numerically analyzed. A very brief discussion of other related work is also presented.

Walker, B. K.↗

NASA NTRS1972

Inviscid surface streamline program for use in predicting shuttle heating rates

A number of methods are currently under development for computing the exact three-dimensional flow field about real configurations. However, even when these methods are available, they will require large computational times on present generation computers. Thus, there is still a need to develop approximate methods to solve three-dimensional flow problems. An inviscid-surface-streamline program (for predicting shuttle heating rates) which uses approximate methods to obtain a solution is described.

Hamilton, H. Harris↗

NASA NTRS1960

An Approximate Analytical Method for Studying Atmosphere Entry of Vehicles with Modulated Aerodynamic Forces

The dimensionless, transformed, nonlinear differential equation developed in NASA TR R-11 for describing the approximate motion and heating during entry into planetary atmospheres for constant aerodynamic coefficients and vehicle shape has been modified to include entries during which the aerodynamic coefficients and the vehicle shape are varied. The generality of the application of the original equation to vehicles of arbitrary weight, size, and shape and to arbitrary atmospheres is retained. A closed-form solution for the motion, heating, and the variation of drag loading parameter m/C(D)A has been obtained for the case of constant maximum resultant deceleration during nonlifting entries. This solution requires certain simplifying assumptions which do not compromise the accuracy of the results. The closed-form solution has been used to determine the variation of m/C(D)A required to reduce peak decelerations and to broaden the corridor for nonlifting entry into the earth's atmosphere at escape velocity. The attendant heating penalty is also studied.

Levy, Lionel L., Jr.↗

NASA NTRS2017

3DHZETRN: Inhomogeneous Geometry Issues

Historical methods for assessing radiation exposure inside complicated geometries for space applications were limited by computational constraints and lack of knowledge associated with nuclear processes occurring over a broad range of particles and energies. Various methods were developed and utilized to simplify geometric representations and enable coupling with simplified but efficient particle transport codes. Recent transport code development efforts, leading to 3DHZETRN, now enable such approximate methods to be carefully assessed to determine if past exposure analyses and validation efforts based on those approximate methods need to be revisited. In this work, historical methods of representing inhomogeneous spacecraft geometry for radiation protection analysis are first reviewed. Two inhomogeneous geometry cases, previously studied with 3DHZETRN and Monte Carlo codes, are considered with various levels of geometric approximation. Fluence, dose, and dose equivalent values are computed in all cases and compared. It is found that although these historical geometry approximations can induce large errors in neutron fluences up to 100 MeV, errors on dose and dose equivalent are modest (<10%) for the cases studied here.

Wilson, John W.↗

NASA NTRS1984

Methods for analysis of cracks in three-dimensional solids

Various analytical and numerical methods used to evaluate the stress intensity factors for cracks in three-dimensional (3-D) solids are reviewed. Classical exact solutions and many of the approximate methods used in 3-D analyses of cracks are reviewed. The exact solutions for embedded elliptic cracks in infinite solids are discussed. The approximate methods reviewed are the finite element methods, the boundary integral equation (BIE) method, the mixed methods (superposition of analytical and finite element method, stress difference method, discretization-error method, alternating method, finite element-alternating method), and the line-spring model. The finite element method with singularity elements is the most widely used method. The BIE method only needs modeling of the surfaces of the solid and so is gaining popularity. The line-spring model appears to be the quickest way to obtain good estimates of the stress intensity factors. The finite element-alternating method appears to yield the most accurate solution at the minimum cost.

Raju, I. S.↗

DOE OSTI2026

Solar and Storage Integration in the U.S. Southeast: Implications for Resource Adequacy [Slides]

In this study, we evaluate how an iterative portfolio approach compares to a more traditional capacity credit method, using the U.S. Southeast as a case study region. Using open-source planning and resource adequacy tools, we compare results using a capacity credit approximation method with those from iterating behind the two. We also explore how the iterative approach performs under a range of sensitivities, including higher load growth, regional coordination, and alternative weather years. We find that traditional capacity credit approximation methods can function well in today's system, but may face challenges for systems with higher levels of solar and storage. As such, integrating planning and resource adequacy models can address some of these gaps, helping planners deliver more reliable systems.

14 SOLAR ENERGY↗

NASA NTRS1990

Differential equation based method for accurate approximations in optimization

This paper describes a method to efficiently and accurately approximate the effect of design changes on structural response. The key to this new method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in msot cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacement are used to approximate bending stresses.

Pritchard, Jocelyn I.↗

NASA NTRS1965

On a general estimation principle and a theory of comparison-factors

General estimation principle and comparison- factors theory - approximation methods

APPROXIMATION METHOD↗

NASA NTRS1965

An analytical and experimental investigation of the motion of a rotating space station

Solutions for angular motion equations of rotating space station by approximation method using small angle theory and exact computer method

APPROXIMATION METHOD↗

NASA NTRS1990

Acoustic fatigue life prediction for nonlinear structures with multiple resonant modes

An efficient method is presented for estimating the high-cycle fatigue lives of complex nonlinear structures. The procedure is based on an application of the method of equivalent linearization to construct a time-domain representation of the stress or strain response of a nonlinear structure. Fatigue estimates are obtained by processing the time-domain signal, and it is a simple matter to incorporate any damage accumulation model desired in the procedure. The method may also be applied to a wide range of complex nonlinear systems. Comparisons are presented of estimated fatigue lives for a nonlinear beam with random excitation obtained using the approximate method and using a conventional numerical simulation. The two techniques are found to give nearly identical results regardless of the level of nonlinearity. The number of calculations required in the approximate method is nearly the same as in a linear system and is not significantly affected by the type and level of nonlinearity in the structure.

Sun, J. Q.↗

DOE OSTI2021

A virtual element generalization on polygonal meshes of the Scott-Vogelius finite element method for the 2-D Stokes problem

The Virtual Element Method (VEM) is a Galerkin approximation method that extends the Finite Element Method (FEM) to polytopal meshes. In this paper, we present a conforming formulation that generalizes the Scott-Vogelius finite element method for the numerical approximation of the Stokes problem to polygonal meshes in the framework of the virtual element method. In particular, we consider a straightforward application of the virtual element approximation space for scalar elliptic problems to the vector case and approximate the pressure variable through discontinuous polynomials. We assess the effectiveness of the numerical approximation by investigating the convergence on a manufactured solution problem and a set of representative polygonal meshes. Finally, we numerically show that this formulation is convergent with optimal convergence rates except for the lowest-order case on triangular meshes, where the method coincides with the $\mathbb{P}_1$ – $\mathbb{P}_0$ Scott-Vogelius scheme, and on square meshes, which are situations that are well-known to be unstable.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1991

High order filtering methods for approximating hyperbolic systems of conservation laws

The essentially nonoscillatory (ENO) schemes, while potentially useful in the computation of discontinuous solutions of hyperbolic conservation-law systems, are computationally costly relative to simple central-difference methods. A filtering technique is presented which employs central differencing of arbitrarily high-order accuracy except where a local test detects the presence of spurious oscillations and calls upon the full ENO apparatus to remove them. A factor-of-three speedup is thus obtained over the full-ENO method for a wide range of problems, with high-order accuracy in regions of smooth flow.

Lafon, F.↗

NASA NTRS1961

Method for Approximating the Vacuum Motions of Spinning Symmetrical Bodies with Nonconstant Spin Rates

The analysis includes non-constant spin rates and inertias and considers the effects of time-varying thrust misalignments, mass unbalance, and jet damping. The method was developed for bodies having small trans verse angular velocities. Results are presented in the form of equations for space-referenced Euler angles, flight-path angles, body-referenced attitude rates, and earth-referenced vehicle-trajectory coordinates. Also, equations for maximum wobble have been derived for certain input conditions. Comparisons with numerical solutions are included for two sample problems.

Martz, C. William↗

NASA NTRS1992

New literal approximations for the longitudinal dynamic characteristics of flexible flight vehicles

The goal of the literal approximation method is to obtain simple literal (analytical) approximations for key dynamic characteristics of flexible flight vehicles. A basic question regarding the method is its usefulness as an additional design tool for existing design and simulation procedures. Two aspects of this question are: (1) ease of derivation and use of the literal approximations, and (2) the suitability of one set of literal approximations to describe the dynamics of a large set of significantly different vehicles. These issues are addressed by incorporating symbolic manipulation software into the literal approximation method for the analysis of a fifth order model of the longitudinal dynamics of a flexible flight vehicle. The automated literal approximation generated in this fashion reduces the manual derivation time by an approximate factor of four. A single set of literal approximations is shown to provide adequate approximations for the dynamics of significantly different flight vehicles configurations, such as an aircraft, a missile, and a hypersonic vehicle.

Livneh, Rafael↗