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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 217 records · Page 12

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NASA NTRS1975

A formulation consideration for orthogonal collocation procedures

Numerical instabilities often arise in the use of high-ordered collocation approximations for numerically solving parabolic partial differential equations. These problems may be reduced by formulations involving evaluation of collocation polynomials rather than combination of the polynomials into a power series. As an illustration, two formulations using shifted Legendre polynomials of order 26 and less are compared.

Lashmet, P. K.↗

NASA NTRS1976

Formulation of detailed consumables management models for the development (preoperational) period of advanced space transportation system: Executive summary

Formulation of models required for the mission planning and scheduling function and establishment of the relation of those models to prelaunch, onboard, ground support, and postmission functions for the development phase of space transportation systems (STS) was conducted. The preoperational space shuttle is used as the design baseline for the subject model formulations. Analytical models were developed which consist of a mission planning processor with appropriate consumables data base and a method of recognizing potential constraint violations in both the planning and flight operations functions. A flight data file for storage/retrieval of information over an extended period which interfaces with a flight operations processor for monitoring of the actual flights was examined.

Torian, J. G.↗

NASA NTRS1976

A space-time tensor formulation for continuum mechanics in general curvilinear, moving, and deforming coordinate systems

Tensor methods are used to express the continuum equations of motion in general curvilinear, moving, and deforming coordinate systems. The space-time tensor formulation is applicable to situations in which, for example, the boundaries move and deform. Placing a coordinate surface on such a boundary simplifies the boundary condition treatment. The space-time tensor formulation is also applicable to coordinate systems with coordinate surfaces defined as surfaces of constant pressure, density, temperature, or any other scalar continuum field function. The vanishing of the function gradient components along the coordinate surfaces may simplify the set of governing equations. In numerical integration of the equations of motion, the freedom of motion of the coordinate surfaces provides a potential for enhanced resolution of the continuum field function. An example problem of an incompressible, inviscid fluid with a top free surface is considered, where the surfaces of constant pressure (including the top free surface) are coordinate surfaces.

Avis, L. M.↗

NASA NTRS1977

A unique formulation of elastic airplane longitudinal equations of motion

Control-configured vehicle technology has increased the demand for detailed analysis of dynamic stability and control, handling and ride qualities, and control system dynamics at early stages of preliminary design. An approximate but reasonably accurate set of equations of motion are needed for these early analyses. Such a formulation is developed for the longitudinal dynamics of elastic airplanes. It makes use of only rigid-body aerodynamic stability derivatives in formulating the forces and moments due to elastic motion. Verification of accuracy using data for the B-1 airplane shows very good agreement. Frequencies and damping ratios of the coupled modes corresponding to complex roots of the characteristic equations agree closely with four symmetric elastic modes included.

Swaim, R. L.↗

NASA NTRS1977

The determination of aluminum, copper, iron, and lead in glycol formulations by atomic absorption spectroscopy

Initial screening tests and the results obtained in developing procedures to determine Al, Cu, Fe, and Pb in glycol formulations are described. Atomic absorption completion was selected for Cu, Fe and Pb, and after comparison with emission spectroscopy, was selected for Al also. Before completion, carbon, iron, and lead are extracted with diethyl dithio carbamate (DDC) into methyl isobutyl ketone (MIBK). Aluminum was also extracted into MIBK using 8-hydroxyquinoline as a chelating agent. As little as 0.02 mg/l carbon and 0.06 mg/l lead or iron may be determined in glycol formulations. As little as 0.3 mg/l aluminum may be determined.

Source record↗

NASA NTRS1978

Formulation of electrically conductive thermal-control coatings

The development and formulation of electrically conductive thermal control coating was undertaken for use on the International Sun Earth Explorer spacecraft. The primary effort was to develop a coating with a bulk resistivity of less than 100,000 ohm/sqm, an optical absorptance of approximately 0.55, and a normal emittance of 0.90. The required stability in space called for a bulk resistivity of less than 100,000 ohm/sq m, an absorptance of less than 0.67, and a normal emittance of 0.90 after exposure to approximately 4 x 10 to the 16th proton/sq cm of solar-wind particles and 5300 equivalent sun-hours. These exposures represent 2 years of ISEE flight conditions. Both the unsuccessful formulation efforts and the successful use of oxide pigments fired at 1448 K are described. Problems relative to the reactivity of specific coating vehicles exposed to high humidity are discussed.

Shai, M. C.↗

NASA NTRS1979

Computer formulations of aircraft models for simulation studies

Recent developments in formula manipulation compilers and the design of several symbol manipulation languages, enable computers to be used for symbolic mathematical computation. A computer system and language that can be used to perform symbolic manipulations in an interactive mode are used to formulate a mathematical model of an aeronautical system. The example demonstrates that once the procedure is established, the formulation and modification of models for simulation studies can be reduced to a series of routine computer operations.

Howard, J. C.↗

NASA NTRS1980

Analysis and calculation of macrosegregation in a casting ingot. MPS solidification model. Volume 1: Formulation and analysis

The physical and numerical formulation of a model for the horizontal solidification of a binary alloy is described. It can be applied in an ingot. The major purpose of the model is to calculate macrosegregation in a casting ingot which results from flow of interdendritic liquid during solidification. The flow, driven by solidification contractions and by gravity acting on density gradients in the interdendritic liquid, was modeled as flow through a porous medium. The symbols used are defined. The physical formulation of the problem leading to a set of equations which can be used to obtain: (1) the pressure field; (2) the velocity field: (3) mass flow and (4) solute flow in the solid plus liquid zone during solidification is presented. With these established, the model calculates macrosegregation after solidification is complete. The numerical techniques used to obtain solution on a computational grid are presented. Results, evaluation of the results, and recommendations for future development of the model are given. The macrosegregation and flow field predictions for tin-lead, aluminum-copper, and tin-bismuth alloys are included as well as comparisons of some of the predictions with published predictions or with empirical data.

Maples, A. L.↗

NASA NTRS1981

General formulation of optical paths for large zenith angles in the earth's curved atmosphere

Formulas that can be used to determine the optical path between two points along an atmospheric ray path are derived for the case when the local zenith angle of the ray path is larger than 70 deg. For angles less than 70 deg, these formulas reduce to the airmass function; viz., the secant of the zenith angle. The formulation presented in this paper is general enough to be applicable to a wide variety of atmospheric conditions, such as spherical and nonspherical atmospheres, and vertically and horizontally homogeneous as well as inhomogeneous atmospheres. A formulation for the case when atmospheric refraction is important also is presented here.

Wang, P.-H.↗

NASA NTRS1980

Formulation of additional observables for ENTREE

The S-band X and Y angles, SAMS, and TACAN range and bearing were incorporated into the ENTREE software for use by experimenters at LaRC for entry trajectory reconstruction purposes. Background discussions present the need for this added capability. Formulations for the various observables are presented. Both north-south and east-west antenna mounts were provided for in the S-band angle computations. Sub-vehicle terrain height variations are included in the SAMS model. Local magnetic variations were incorporated for the TACAN bearing computations. Observable formulations are discussed in detail along with the partial computations.

Findlay, J. T.↗

NASA NTRS1981

Principal stress formulation of continua motion

Principal stress coordinates are formulated for a material without tension, with the equations of motion projected onto a selected coordinate system. The translations are achieved by forming the local basis vector in correspondence with the local stress tensor. The principal stress coordinates are described as orthogonal and curvilinear, and the metric is defined. The kinematics and dynamics of the principal stress coordinates are analyzed, the latter in orthogonal coordinates, and an analytic formulation of the dynamics of a no-tension material is provided. Finally, elastic granular material such as sand, soil, etc., which are more complicated versions of no-tension material, are explored.

Zak, M.↗

NASA NTRS1982

The adaptation of a strap down formulation for processing inertial platform data

An estimator propagation formulation which ultilizes dynamic data (attitude and sensed acceleration information) from a gimballed inertial platform has been developed to aid in the Shuttle post-flight trajectory reconstruction process and aerodynamic coefficient determination studies. Unlike the classical inertial algorithms, this formulation yields a six degree-of-freedom fully coupled state and attitude estimate. Furthermore, this inertial version is shown to be independent of initial unknown platform misalignments. Results obtained using actual Inertial Measurement Unit (IMU) data and Aerodynamic Coefficient Identification Package (ACIP) strap down data from Shuttle flights are presented.

Heck, M. L.↗

NASA NTRS1982

The formulation of Lamb's Dust Veil Index

A catalog of the major explosive volcanic eruptions since 1500 AD and formulated the Dust Veil Index (DVI) is presented. The DVI quantifies the impact on the Earth's energy balance of changes in atmospheric composition due to explosive volcanic eruptions. The DVI for a particular eruption quantifies the climatic impact of the dust and aerosol injection from the eruption integrated over the years following the event. The formulation of the DVI is described. All references are to Lamb (1970). A distinction is made between the catalog of volcanic activity, and the tabulation of the northern hemisphere DVI apportioned over the years. The DVI data are updated to 1975 for any particular eruption, the catalog gives three DVI values: global, Southern Hemisphere, and Northern Hemisphere. The global DVI given in the catalog is considered. The other two DVIs relate to the impact on the hemispheres considered separately and their estimation involves an additional factor apportioning the dust veil between the hemispheres on the basis of the latitude of injection.

Kelly, P. M.↗

NASA NTRS1982

Alternative ways for formulation of hybrid stress elements

An element stiffness matrix can be derived by the conventional potential energy principle and, indirectly, also by generalized variational principles, such as the Hu-Washizu principle and the Hellinger-Reissner principle. The present investigation has the objective to show an approach which is concerned with the formulation of incompatible elements for solid continuum and for plate bending problems by the Hellinger-Reissner principle. It is found that the resulting scheme is equivalent to that considered by Tong (1982) for the construction of hybrid stress elements. In Tong's scheme the inversion of a large flexibility matrix can be avoided. It is concluded that the introduction of additional internal displacement modes in mixed finite element formulations by the Hellinger-Reissner principle and the Hu-Washizu principle can lead to element stiffness matrices which are equivalent to the assumed stress hybrid method.

Pian, T. H. H.↗

NASA NTRS1983

The aerodynamics of propellers and rotors using an acoustic formulation in the time domain

The aerodynamics of propellers and rotors is especially complicated because of the highly three-dimensional and compressible nature of the flow field. However, in linearized theory the problem is governed by the wave equation, and a numerically-efficient integral formulation can be derived. This reduces the problem from one in space to one over a surface. Many such formulations exist in the aeroacoustics literature, but these become singular integral equations if one naively tries to use them to predict surface pressures, i.e., for aerodynamics. The present paper illustrates how one must interpret these equations in order to obtain nonambiguous results. After the regularized form of the integral equation is derived, a method for solving it numerically is described. This preliminary computer code uses Legendre-Gaussian quadrature to solve the equation. Numerical results are compared to experimental results for ellipsoids, wings, and rotors, including effects due to lift. Compressibility and the farfield boundary conditions are satisfied automatically using this method.

Long, L. N.↗

NASA NTRS1983

Formulation and solution of rotary-wing aeroelastic stability and response problems

The state of the art in the formulation and solution of rotary-wing aeroelastic stability and response problems is reviewed in detail. The approximations used in the structural, inertia and aerodynamic operators are discussed. The important role of geometric nonlinearities, due to moderate deflections, and aerodynamic stall in the aeroelastic stability and response problem are identified. It is also shown that geometric nonlinearities are of primary importance in aeroelastic stability calculations, and have a more limited, though important, role in response calculations. Next, formulation of coupled rotor/fuselage problems is described, for both air and ground resonance type problems. Both topics, the isolated blade problem and the coupled rotor/fuselage problem, are treated for both hover and forward flight. Solution of aeroelastic stability and response problems proceeds in two stages. First, the spatial dependence is eliminated by using Galerkin's method, or by using the finite element method. Next the nonlinear, or linear, ordinary differential equation with periodic coefficients have to be solved for stability or response. Efficient numerical methods for accomplishing these objectives are presented in a comprehensive manner. The paper contains a number of illustrative numerical results which are intended to clarify various aspects of the modeling process and serve as representative results for both aeroelastic stability and response calculations for a variety of blade and rotor configurations.

Friedmann, P. P.↗

NASA NTRS1983

The compressible aerodynamics of rotating blades based on an acoustic formulation

An acoustic formula derived for the calculation of the noise of moving bodies is applied to aerodynamic problems. The acoustic formulation is a time domain result suitable for slender wings and bodies moving at subsonic speeds. A singular integral equation is derived in terms of the surface pressure which must then be solved numerically for aerodynamic purposes. However, as the 'observer' is moved onto the body surface, the divergent integrals in the acoustic formulation are semiconvergent. The procedure for regularization (or taking principal values of divergent integrals) is explained, and some numerical examples for ellipsoids, wings, and lifting rotors are presented. The numerical results show good agreement with available measured surface pressure data.

Long, L. N.↗

NASA NTRS1984

Comparison of the full potential and Euler formulations for computing transonic airfoil flows

A quantitative comparison between the Euler and full potential formulations with respect to speed and accuracy is presented. The robustness of the codes used is tested by a number of transonic airfoil cases. The computed results are from four transonic airfoil computer codes. The full potential codes use fully implicit iteration algorithms. The first Euler code uses a fully implicit ADI iteration scheme. The second Euler code uses an explicit Runge Kutta time stepping algorithm which is enhanced by a multigrid convergence acceleration scheme. Quantitative comparisons are made using various plots of lift coefficient versus the average mesh spacing along the airfoil. Besides yielding an asymptotic limit to the lift coefficient, these results also demonstrate the truncation error behavior of the various codes. Quantitative conclusions regarding the full potential and Euler formulations with respect to accuracy, speed, and robustness can be presented.

Flores, J.↗