Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “CALCULATION METHODS”

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 613 records · Page 34

A variational method for the calculation of dynamic polarizabilities and two-photon transition moments - The dressed molecule approach

The solution of the time-dependent Schroedinger equation of the molecule + radiation field system is analyzed. A quantized radiation field is used. The relationship between the oscillatory wave function and the dressed state wave function is established, the oscillatory wave function being the solution if the radiation field is turned on at t = 0 and the dressed state being the stationary solution satisfying the boundary condition only if the field is present at t = negative infinity. In general, the oscillatory wave function can be expressed using a complete set of dressed states. However, in the presence of a nonresonant radiation field, the system is well represented by a single dressed state. Molecular properties such as dynamic polarizabilities and two-photon transition moments can be deduced from the dressed state wave function instead of the oscillatory wave function as in previous methods. Because of its stationary character, the dressed state is more amenable to approximate calculations. A CI method is developed for this purpose. The CI matrix is simple in form and can be readily constructed using existing computer codes. The present method can also be adapted to calculate other optical properties.

Huo, W. M.↗

A Method for the Calculation of the Lateral Response of Airplanes to Random Turbulence

In this method, the gust velocities are represented as rolling gusts, yawing gusts, and side gusts. Random distributions of gust velocities across the span are taken into account in defining the rolling and yawing gusts. Complex stability derivatives are used to account for the random distribution of side gusts along the fuselage and vertical tail and the lag effects in gust penetration. A sample calculation procedure is presented for obtaining the response of the airplane in each degree of freedom.

LOADS, GUST - WINGS↗

Method of Characteristics Calculations and Computer Code for Materials with Arbitrary Equations of State and Using Orthogonal Polynomial Least Square Surface Fits

A numerical scheme using the method of characteristics to calculate the flow properties and pressures behind decaying shock waves for materials under hypervelocity impact is developed. Time-consuming double interpolation subroutines are replaced by a technique based on orthogonal polynomial least square surface fits. Typical calculated results are given and compared with the double interpolation results. The complete computer program is included.

Chang, T. S.↗

A method for the calculation of external lift, moment, and pressure drag of slender open-nose bodies of revolution at supersonic speeds

An approximate method is presented for the calculation of the external lift, moment, and pressure drag of slender open-nose bodies of revolution of supersonic speeds. The lift, moment, and pressure drag of a typical ram-jet body shape are calculated at Mach numbers 1.45, 1.60, 1.75, and 3.00; and the lift and moment results are compared with available experimental data. The agreement of the calculated lift and moment data with the experimental data is excellent. The pressure-drag comparison was not presented because of the uncertainty of the amount of skin-friction drag present in the experimental results.

Brown, Clinton E↗

Application of a multi-level grid method to transonic flow calculations

A multi-level grid method was studied as a possible means of accelerating convergence in relaxation calculations for transonic flows. The method employs a hierarchy of grids, ranging from very coarse to fine. The coarser grids are used to diminish the magnitude of the smooth part of the residuals. The method was applied to the solution of the transonic small disturbance equation for the velocity potential in conservation form. Nonlifting transonic flow past a parabolic arc airfoil is studied with meshes of both constant and variable step size.

South, J. C., Jr.↗

Calculation of Counterrotating Propellers

A method for calculation of a counterrotating propeller which is similar to Walchner's method for calculation of the single propeller in the free air stream is developed and compared with measurements. Several dimensions which are important for the design are given end simple formulas for the gain in efficiency derived. Finally a survey of the behavior of the propeller for various operating conditions is presented.

Ginzel, F.↗

Application of a multi-level grid method to transonic flow calculations

A multi-level grid method has been studied as a possible means of accelerating convergence in relaxation calculations for transonic flows. The method employs a hierarchy of grids, ranging from very coarse (e.g., 8 x 2 mesh cells) to fine (e.g., 128 x 32); the coarser grids are used to diminish the magnitude of the smooth part of the residuals, hopefully with far less total work than would be required with, say, optimal SLOR iterations on the finest grid. The method was applied to the solution of the transonic small-disturbance equation for the velocity potential in the conservation form. Nonlifting transonic flow past a parabolic-arc airfoil is the example studied, with meshes of both constant and variable step size.

South, J. C., Jr.↗

A Method for the Calculation of Lattice Energies of Complex Crystals with Application to the Oxides of Molybdenum

A theoretical study has been made of molybdenum dioxide and molybdenum trioxide in order to extend the knowledge of factors Involved in the oxidation of molybdenum. New methods were developed for calculating the lattice energies based on electrostatic valence theory, and the coulombic, polarization, Van der Waals, and repulsion energie's were calculated. The crystal structure was examined and structure details were correlated with lattice energy.

Chaney, William S.↗

Numerical Strip-Yield Calculation of CTOD

Many existing methods to calculate CTOD can be costly and complicated, or apply only to particular configurations. A new numerical method for calculating CTOD was investigated. NASGRO's Boundary Element module NASBEM was adapted to calculate displacements at any point on the crack. Demonstrated for a number of crack configurations: a) finite and infinite domains; b) center and edge cracks; and c) complex cases with several cracks and holes. Great accuracy at minimal computational cost.

Beek, Joachim↗

Data reduction and evaluation procedures

The computational procedures that are involved in exhaust emissions data reduction and the use of these computational procedures for determining the quality of the data that is obtained from exhaust measurements were considered. Four problem areas were calculated: (1) the various methods for performing the carbon balance, (2) the method for calculating water correction factors, (3) the method for calculating the exhaust molecular weight, and (4) assessing the quality of the data.

Mirsky, W.↗

Two practical methods for the calculation of the horizontal tail area necessary for a statically stable airplane

This report is concerned with the problem of calculation of the horizontal tail area necessary to give a statically stable airplane. Two entirely different methods are developed, and reduced to simple formulas easily applied to any design combination. Detailed instructions are given for use of the formulas, and all calculations are illustrated by examples. The relative importance of the factors influencing stability is also shown. (author)

Diehl, Walter S↗

Structural system reliability calculation using a probabilistic fault tree analysis method

The development of a new probabilistic fault tree analysis (PFTA) method for calculating structural system reliability is summarized. The proposed PFTA procedure includes: developing a fault tree to represent the complex structural system, constructing an approximation function for each bottom event, determining a dominant sampling sequence for all bottom events, and calculating the system reliability using an adaptive importance sampling method. PFTA is suitable for complicated structural problems that require computer-intensive computer calculations. A computer program has been developed to implement the PFTA.

Torng, T. Y.↗

Methods of Stress Calculation in Rotating Disks

The paper describes nethods of computing the stresses in disks of a given profile as well as methods of choosing the disk profiles for a given stress distribution for turhines, turbo blowers, and so forth. A new method of in tegrating the differential equations of Stodola leads to a simplification of the computation for disks of hyperbolic profile.

Tumarkin, S.↗

A comparison of the spanwise loading calculated by various methods with experimental loadings obtained on a 45 degree sweptback wing of aspect ratio 8.02 at a Reynolds number of 4.0 x 10(6)

This report compares the experimental force and moment data obtained by pressure measurements on a wing of aspect ratio 8.02, 45 degree sweptback of the quarter-chord line, taper ratio of 0.45, and NACA 63sub1a012 airfoil sections with the calculated loadings obtained by the standard methods proposed by Weissinger, Falkner, and Multopp, as well as by several variations of these methods.

Schneider, Willaim C↗

APPLICATION OF VARIATIONAL METHODS TO RADIATION HEAT-TRANSFER CALCULATIONS

A variational method is presented for solving a class of integral equations which arise in radiation heat-transfer problems. First, to demonstrate the formulation of radiation problems in terms of integral equations, consideration is given to a system consisting of two nonblack, finite, parallel plates. After a general description of the variational method, its use is illustrated by application to the parallel-plate system. Comparisons are made which show very good agreement with exact solutions.

E. M. Sparrow↗

An implicit method for the calculation of inlet flow fields

Inlet flow fields are calculated by an implicit, time marching procedure to solve the thin layer Navier-Stokes equations formulated in body fitted coordinates. Because the method can be used for a flow field with both subsonic and supersonic regions, it is applicable to subcritical as well as supercritical inlet operation. Results are presented and discussed for an inlet of current design practice. Results include inviscid calculations performed for supercritical inlet operation with uniform and nonuniform inflow boundary conditions as well as for subcritical inlet operation with uniform inflow boundary conditions. Results for viscous calculations performed for supercritical inlet operation with uniform inflow boundary conditions are also discussed.

Biringen, S.↗

Comparison of DFT with Traditional Methods for the Calculation of Vibrational Frequencies and Bond Energies

The vibrational frequencies of MO2 are computed at many levels of theory, including HF, B3LYP, BP86, CASSCF, MP2, and CCSD(T). The computed results are compared with the available experimental results. Most of the methods fail for at least one state of the systems considered. The accuracy of the results and the origin of the observed failures are discussed. The B3LYP bond energies are compared with traditional methods for a variety of systems, ranging from FeCOn+ to SiCln and its positive ions. The cases where B3LYP differs from the traditional methods are discussed.

Bauschlicher, Charles W.↗