Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Order”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 559 records · Page 31
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

First-order Fermi acceleration in solar flares as a mechanism for the second-step acceleration of prompt protons and relativistic electrons

Solar flare data from June 27, 1980 balloon-based observations were studied in terms of the hard X ray component. A temporal delay of 3 sec was observed for the X ray emissions above 235 keV. The delay occurred relative to the low-energy electrons and indicated a second acceleration stage. An estimation of the acceleration rate of the first-order Fermi process operating in a closed flare loop was found to be in agreement with the resulting data, including the acceleration of both protons and relativistic electrons. Additional support for the first-order Fermi process is noted in the fact that flares generally occur in magnetic loops, a condition which allows energetic particles to continually interact with the upward moving shock fronts. A correlation has also been observed between the delay times and the H-alpha areas, encouraging the interpretation that the delay times are the shock transit times.

Bai, T.↗
NASA NTRS1982

Second order closure for variable density free shear layer

A full second order closure turbulence model for the prediction of free shear flows with variable density is developed. The importance of density fluctuations due to inhomogeneities in fluid composition is emphasized. Some simplicity is achieved by using density weighted averaging to account implicitly for density fluctuation effects. Transport equations for various second order correlations - such as Reynolds stress, turbulent mass fluxes or density velocity correlations - are derived, modelled and solved, together with the mean equations for momentum and species conservation. Solutions of these equations are compared with the two different sets of experimental data for low speed free mixing layers (helium into nitrogen and freon 12 into air).

Vandromme, D.↗
NASA NTRS1983

First-order wetting transition at a liquid-vapor interface

Evidence from reflectance and contact angle measurements is presented that three-phase mixtures of i-C3H7OH-C7F14 exhibit a first-order wetting phase transition at the liquid-vapor interface at 38 C. Equilibration phenomena support this interpretation. Ellipsometry was used to measure the apparent thickness of the intruding layer in the three-phase mixture. At temperatures slightly above the wetting temperature T(w), the intruding layer's thickness is several hundred angstroms and its variation with temperature is extremely weak. Below T(w), three-phase contact can occur between the vapor and both the upper and lower liquid phases; one of the angles which characterizes this contact has a very simple temperature dependence. The thickness of the intruding layer, monitored as the solutions approached equilibrium, is found to depend quite weakly on the height spanned by the upper liquid phase in the vicinity of a first-order wetting transition.

Schmidt, J. W.↗
NASA NTRS1983

Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence

In a three dimensional simulation higher order derivative correlations, including skewness and flatness factors, are calculated for velocity and passive scalar fields and are compared with structures in the flow. The equations are forced to maintain steady state turbulence and collect statistics. It is found that the scalar derivative flatness increases much faster with Reynolds number than the velocity derivative flatness, and the velocity and mixed derivative skewness do not increase with Reynolds number. Separate exponents are found for the various fourth order velocity derivative correlations, with the vorticity flatness exponent the largest. Three dimensional graphics show strong alignment between the vorticity, rate of strain, and scalar-gradient fields. The vorticity is concentrated in tubes with the scalar gradient and the largest principal rate of strain aligned perpendicular to the tubes. Velocity spectra, in Kolmogorov variables, collapse to a single curve and a short minus 5/3 spectral regime is observed.

Kerr, R. A.↗
NASA NTRS1984

First order ball bearing kinematics

Two first order equations are given connecting geometry and internal motions in an angular contact ball bearing. Total speed, kinematic equivalence, basic speed ratio, and modal speed ratio are defined and discussed; charts are given for the speed ratios covering all bearings and all rotational modes. Instances where specific first order assumptions might fail are discussed, and the resulting effects on bearing performance reviewed.

Kingbury, E.↗
NASA NTRS1984

Computational aspects of the nonlinear normal mode initialization of the GLAS 4th order GCM

Using the normal modes of the GLAS 4th Order Model, a Machenhauer nonlinear normal mode initialization (NLNMI) was carried out for the external vertical mode using the GLAS 4th Order shallow water equations model for an equivalent depth corresponding to that associated with the external vertical mode. A simple procedure was devised which was directed at identifying computational modes by following the rate of increase of BAL sub M, the partial (with respect to the zonal wavenumber m) sum of squares of the time change of the normal mode coefficients (for fixed vertical mode index) varying over the latitude index L of symmetric or antisymmetric gravity waves. A working algorithm is presented which speeds up the convergence of the iterative Machenhauer NLNMI. A 24 h integration using the NLNMI state was carried out using both Matsuno and leap-frog time-integration schemes; these runs were then compared to a 24 h integration starting from a non-initialized state. The maximal impact of the nonlinear normal mode initialization was found to occur 6-10 hours after the initial time.

Navon, I. M.↗
NASA NTRS1984

Empirically derived second order schemes for the advection equations with minimum dissipation and dispersion errors

Two second-order advection schemes of the Lax-Wendroff type are empirically derived which have accuracy and phase characteristics similar to that of a third-order scheme. The new schemes are compared with other currently used methods, and are shown to have superior behavior in simulating the advection of localized disturbances. The schemes are derived for constant flow and generalized to two-dimensional non-uniform flow.

Takacs, L. L.↗
NASA NTRS1984

Second- and third-order upwind difference schemes for hyperbolic conservation laws

Second- and third-order two time-level five-point explicit upwind-difference schemes are described for the numerical solution of hyperbolic systems of conservation laws and applied to the Euler equations of inviscid gas dynamics. Nonliner smoothing techniques are used to make the schemes total variation diminishing. In the method both hyperbolicity and conservation properties of the hyperbolic conservation laws are combined in a very natural way by introducing a normalized Jacobian matrix of the hyperbolic system. Entropy satisfying shock transition operators which are consistent with the upwind differencing are locally introduced when transonic shock transition is detected. Schemes thus constructed are suitable for shockcapturing calculations. The stability and the global order of accuracy of the proposed schemes are examined. Numerical experiments for the inviscid Burgers equation and the compressible Euler equations in one and two space dimensions involving various situations of aerodynamic interest are included and compared.

Yang, J. Y.↗
NASA NTRS1981

PAN AIR: A computer program for predicting subsonic or supersonic linear potential flows about arbitrary configurations using a higher order panel method. Volume 4: Maintenance document (version 1.1)

The Maintenance Document is a guide to the PAN AIR software system, a system which computes the subsonic or supersonic linear potential flow about a body of nearly arbitrary shape, using a higher order panel method. The document describes the over-all system and each program module of the system. Sufficient detail is given for program maintenance, updating and modification. It is assumed that the reader is familiar with programming and CDC (Control Data Corporation) computer systems. The PAN AIR system was written in FORTRAN 4 language except for a few COMPASS language subroutines which exist in the PAN AIR library. Structured programming techniques were used to provide code documentation and maintainability. The operating systems accommodated are NOS 1.2, NOS/BE and SCOPE 2.1.3 on the CDC 6600, 7600 and Cyber 175 computing systems. The system is comprised of a data management system, a program library, an execution control module and nine separate FORTRAN technical modules. Each module calculates part of the posed PAN AIR problem. The data base manager is used to communicate between modules and within modules. The technical modules must be run in a prescribed fashion for each PAN AIR problem. In order to ease the problem of supplying the many JCL cards required to execute the modules, a separate module called MEC (Module Execution Control) was created to automatically supply most of the JCL cards. In addition to the MEC generated JCL, there is an additional set of user supplied JCL cards to initiate the JCL sequence stored on the system.

Baruah, P. K.↗
NASA NTRS1983

Error analysis for a reduced-order discrete adaptive observer

The Kreisselmeier discrete adaptive observer is analyzed for the case in which the observer order is less than that of the plant. The state and parameter estimates from the observer are compared to the states and parameters for an arbitrary reduced-order model (ROM) of the plant, where the observer and ROM are of equal dimension. Conditions sufficient for ultimate boundedness of the observation errors are given, and expressions for the error bounds are derived.

Lilly, J. H.↗
NASA NTRS1984

Numerical formulation for a higher order plane finite dynamic element

The paper describes the development of an eight-node plane rectangular finite dynamic element and presents detailed descriptions of the associated numerical formulation involving the higher order dynamic correction terms pertaining to the related stiffness and inertia matrices. Numerical test results of free vibration analyses are presented in detail for the newly developed eight-node element and also the corresponding four-node element in order to make a clear comparison of the relative efficiencies of the corresponding finite element and dynamic element procedures. Such results indicate a superior pattern of solution convergence of the presently developed dynamic element.

Gupta, K. K.↗
NASA NTRS1985

Uniformly high-order accurate non-oscillatory schemes, 1

The construction and the analysis of nonoscillatory shock capturing methods for the approximation of hyperbolic conservation laws was begun. These schemes share many desirable properties with total variation diminishing schemes (TVD), but TVD schemes have at most first order accuracy, in the sense of truncation error, at extreme of the solution. A uniformly second order approximation was constucted, which is nonoscillatory in the sense that the number of extrema of the discrete solution is not increasing in time. This is achieved via a nonoscillatory piecewise linear reconstruction of the solution from its cell averages, time evolution through an approximate solution of the resulting initial value problem, and averaging of this approximate solution over each cell.

Harten, A.↗
NASA NTRS1985

Development and Testing of the Variable Vertical Resolution Fourth Order GCM

The vertical coordinate of the Fourth Order Model has been generalized so that the model can now run with an arbitrary number of vertical layers and so that the thicknesses of these layers can be arbitrarily specified (in the sigma coordinate). This Variable Vertical Resolution (VVR) version of the Fourth Order Model will soon replace the current production model. To assess the skill of the VVR model, it has been run with 9 equally spaced layers and compared with the current production model. In two Northern Hemispheric winter cases and one summer case, the two models were virtually identical in forecast skill for 6 to 7 days. After that the VVR model was slightly better in the winter cases and the production model was slightly better in the summer case. The only exception to this was that after 2 days the production model gave slightly more skillful 500 mb forecasts in the tropics for the summer case.

Helfand, H. M.↗
NASA NTRS1985

Parameterization of Surface Fluxes in the VVR Fourth Order GCM

The Variable Vertical Resolution (VVR) option of the GLAS Fourth Order General Circulation Model (GCM) allows one to enhance the vertical resolution of the region of the atmosphere adjacent to the Earth's surface. This, in turn, makes it possible to compute turbulent surface fluxes of heat, momentum and moisture directly from the prognosticated properties of the lowest model layer by use of the Monin-Obukhov surface layer similarity theory. The similarity theory applies formally only to the constant flux surface layer which is but a few tens of meters deep. It is not practically feasible to work with a lowest GCM layer thin enough to satisfy these formal constraints. It is shown that at least under conditions of neutral stratification, the similarity theory can be extended beyond its formal limits. The theory still gives reasonable looking results, when the distance from the ground becomes as large as 150 m. It is not infeasible to run the VVR model with a lowest layer thickness on the order of 300 m (the center of the layer would then be 150 m above the Earth's surface), and so if one can prescribe similarity functions phi sub m (zeta) and phi sub h (zeta) to adequately describe the entire extended surface layer, the problem of surface flux parameterization is solved.

Helfand, H. M.↗
NASA NTRS1985

A first-order time-domain Green's function approach to supersonic unsteady flow

A time-domain Green's Function Method for unsteady supersonic potential flow around complex aircraft configurations is presented. The focus is on the supersonic range wherein the linear potential flow assumption is valid. The Green's function method is employed in order to convert the potential-flow differential equation into an integral one. This integral equation is then discretized, in space through standard finite-element technique, and in time through finite-difference, to yield a linear algebraic system of equations relating the unknown potential to its prescribed co-normalwash (boundary condition) on the surface of the aircraft. The arbitrary complex aircraft configuration is discretized into hyperboloidal (twisted quadrilateral) panels. The potential and co-normalwash are assumed to vary linearly within each panel. Consistent with the spatial linear (first-order) finite-element approximations, the potential and co-normalwash are assumed to vary linearly in time. The long range goal of our research is to develop a comprehensive theory for unsteady supersonic potential aerodynamics which is capable of yielding accurate results even in the low supersonic (i.e., high transonic) range.

Freedman, M. I.↗
NASA NTRS1985

Exponential order statistic models of software reliability growth

Failure times of a software reliabilty growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented.

Miller, D. R.↗
NASA NTRS1985

Anomalous abundances of solar energetic particles and coronal gas: Coulomb effects and First Ionization Potential (FIP) ordering

The first ionization potential (FIP) ordering of elemental abundances in solar energetic particles and in the corona which can both be explained Coulomb effects is discussed. Solar energetic particles (SEP) and coronal gas have anomalous abundances relative to the photosphere. The anomalies are similar in both cases: which led to the conclusion that SEP acceleration is not selective, but merely preserves the source abundances. It is argued that SEP acceleration can be selective, because identical selectivity operates to determine the coronal abundances. The abundance anomalies are ordered by first ionization potential (FIP).

Mullan, D. J.↗
NASA NTRS1984

Higher-order parabolic approximations for sound propagation in stratified moving media

Asymptotic solutions of order k-n are developed for the equations governing the propagation of sound through a stratified moving medium. Here k is a dimensionless wave number and n is the arbitrary order of the approximation. These approximations are an extension of geometric acoustics theory and provide corrections to that theory in the form of multiplicative functions which satisfy parabolic partial differential equations. These corrections account for the diffraction effects caused by variation of the field normal to the ray path and the interaction of these transverse variations with the variation of the field along the ray. The theory is illustrated by application to simple examples.

Mcaninch, G. L.↗