Free vibration of a centrally clamped spinning circular disk
Centrally clamped spinning circular disk free transverse vibration analysis within accuracy of numerical computations
Dodson, R. O., Jr.↗
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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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Dynamics of an explosive reaction center
Gas dynamic effects of reaction center in explosive gas mixture analyzed by model and numerical computation
Oppenheim, A. K.↗
Dynamics of an explosive reaction center
Gas dynamic effects of reaction center in explosive gas mixture, using model and numerical computation
Oppenheim, A. K.↗
The equilibrium and stability of the gaseous component of the galaxy, 2
A time-independent, linear, plane and axially-symmetric stability analysis was performed on a self-gravitating, plane-parallel, isothermal layer of nonmagnetic, nonrotating gas. The gas layer was immersed in a plane-stratified field isothermal layer of stars which supply a self-consistent gravitational field. Only the gaseous component was perturbed. Expressions were derived for the perturbed gas potential and perturbed gas density that satisfied both the Poisson and hydrostatic equilibrium equations. The equation governing the size of the perturbations in the mid-plane was found to be analogous to the one-dimensional time-independent Schrodinger equation for a particle bound by a potential well, and with similar boundary conditions. The radius of the neutral state was computed numerically and compared with the Jeans' and Ledoux radius. The inclusion of a rigid stellar component increased the Ledoux radius, though only slightly. Isodensity contours of the neutrual or marginally unstable state were constructed.
Kellman, S. A.↗
An on-line system for hand-printed input
The capability of graphic input/output systems is described. Topics considered are a character recognizer and dictionary building program, an initial flow chart element input program, and a system entitled The Assistant Mathematician, which uses ordinary mathematics to specify numeric computation. All three parts are necessary to allow a user to carry on a mathematical dialogue with the computer in the language and notation of his discipline or problem domain.
Williams, T. G.↗
Theoretical and observational analysis of spacecraft fields
In order to investigate the nondipolar contributions of spacecraft magnetic fields a simple magnetic field model is proposed. This model consists of randomly oriented dipoles in a given volume. Two sets of formulas are presented which give the rms-multipole field components, for isotropic orientations of the dipoles at given positions and for isotropic orientations of the dipoles distributed uniformly throughout a cube or sphere. The statistical results for an 8 cu m cube together with individual examples computed numerically show the following features: Beyond about 2 to 3 m distance from the center of the cube, the field is dominated by an equivalent dipole. The magnitude of the magnetic moment of the dipolar part is approximated by an expression for equal magnetic moments or generally by the Pythagorean sum of the dipole moments. The radial component is generally greater than either of the transverse components for the dipole portion as well as for the nondipolar field contributions.
Neubauer, F. M.↗
Electron pitch-angle diffusion driven by oblique whistler-mode turbulence.
A general description of cyclotron harmonic resonant pitch-angle scattering is presented. Quasi-linear diffusion coefficients are prescribed in terms of the wave normal distribution of plasma wave energy. Numerical computations are performed for the specific case of relativistic electrons interacting with a band of low frequency whistler-mode turbulence. A parametric treatment of the wave energy distribution permits normalized diffusion coefficients to be presented graphically solely as a function of the electron pitch-angle. The diffusion coefficients generally decrease with increasing cyclotron harmonic number. Higher harmonic diffusion is insignificant at very small electron pitch-angles, but becomes increasingly important as the pitch-angle increases. One thus expected the rate of pitch-angle scattering to decrease with increasing electron energy, since the resonant value of the latter varies proportionately with harmonic number. This indicates that, in mirror-type magnet field geometrics, such as the earth's radiation belts, the diffusion losses of high energy electrons are likely to be appreciably slower than those at low energy.
Lyons, L. R.↗
Theoretical analysis of rough-surface shadowing from point-source radiation.
The shadowing function, defined as the probability that a point on a rough surface will be illuminated by radiation from a source at fixed height above the surface, is considered. An exact expression for this probability is derived and evaluated approximately when the surface elevation is a normal random process. The effect of surface correlation is considered and shown to be appreciable. Several numerical computations of the shadowing function are presented.
Hardin, J. C.↗
A method for calculating laminar viscous, compressible flows with small pressure gradients
A method is presented for calculating laminar viscous, compressible flows in which pressure gradients are assumed to be neglibible in energy conservation and in developing property relations, but not in momentum conservation. The equations are developed from Navier-Stokes equations in a noninertial reference frame. The method is an extension of an approximate method developed for calculating combined forced and contained natural convection in a rotating tank. The restriction to small density and temperature variations in the previous method is removed. For illustration, a two-dimensional simulation of the rotating tank problem is formulated, and the numerical computation procedure to be used is indicated.
Martin, E. D.↗
Measured and calculated mean flow properties of a two-dimensional, hypersonic, turbulent wake
The hypersonic turbulent wake produced by a wedge was studied experimentally and its properties were compared with predictions obtained from a numerical computation procedure. In the computation procedure several models for the eddy viscosity formulation of the turbulent transport were examined. Conventional-defect models and a modified mixing-length model were found to yield good predictions of the experimental data. The classical mixing-length model gave unrealistic results. The experimental data displayed similarity when velocity and temperature defects were scaled by the maximum defects and the transverse coordinate was scaled by the velocity-defect half-width.
Wagner, R. D.↗
Further analytical study of hybrid rocket combustion
Analytical studies of the transient and steady-state combustion processes in a hybrid rocket system are discussed. The particular system chosen consists of a gaseous oxidizer flowing within a tube of solid fuel, resulting in a heterogeneous combustion. Finite rate chemical kinetics with appropriate reaction mechanisms were incorporated in the model. A temperature dependent Arrhenius type fuel surface regression rate equation was chosen for the current study. The governing mathematical equations employed for the reacting gas phase and for the solid phase are the general, two-dimensional, time-dependent conservation equations in a cylindrical coordinate system. Keeping the simplifying assumptions to a minimum, these basic equations were programmed for numerical computation, using two implicit finite-difference schemes, the Lax-Wendroff scheme for the gas phase, and, the Crank-Nicolson scheme for the solid phase.
Hung, W. S. Y.↗
An algorithm for calculation of the Jordan canonical form of a matrix
Jordan canonical forms are used extensively in the literature on control systems. However, very few methods are available to compute them numerically. Most numerical methods compute a set of basis vectors in terms of which the given matrix is diagonalized when such a change of basis is possible. Here, a simple and efficient method is suggested for computing the Jordan canonical form and the corresponding transformation matrix. The method is based on the definition of a generalized eigenvector, and a natural extension of Gauss elimination techniques.
Sridhar, B.↗
Theoretical analysis of rotating two phase detonation in a rocket motor
Tangential mode, non-linear wave motion in a liquid propellant rocket engine is studied, using a two phase detonation wave as the reaction model. Because the detonation wave is followed immediately by expansion waves, due to the side relief in the axial direction, it is a Chapman-Jouguet wave. The strength of this wave, which may be characterized by the pressure ratio across the wave, as well as the wave speed and the local wave Mach number, are related to design parameters such as the contraction ratio, chamber speed of sound, chamber diameter, propellant injection density and velocity, and the specific heat ratio of the burned gases. In addition, the distribution of flow properties along the injector face can be computed. Numerical calculations show favorable comparison with experimental findings. Finally, the effects of drop size are discussed and a simple criterion is found to set the lower limit of validity of this strong wave analysis.
Shen, I.↗
A rough earth scattering model for multipath prediction
The most important phenomena to be considered in a model of radio wave communication between earth satellites are scattering from the surface of the earth. A model is derived and implemented on a computer to predict the field received after reflection from a rough, spherical earth. The scattering integrals are computed numerically; the domain of integration is the appropriate region on the surface of the earth. Calculations have been performed at VHF frequencies and for terrain which could be described as marshy land. Rough surface scattering calculations must be performed over a spherical earth when satellites are involved. There is a definite dependence on the values of the roughness, and the correlation length.
Page, L. J.↗
On electromagnetic field problems in inhomogeneous media
Analysis of electromagnetic fields in inhomogeneous media is of practical interest in general scattering and propagation problems and in the study of lenses. For certain types of inhomogeneities, the fields may be represented in terms of two scalars. In a general orthogonal coordinate system, these potentials satisfy second order differential equations. Exact solutions of these equations are known only for a few particular cases and in general, an approximate or numerical technique must be employed. The present work reviews and generalizes some of the main methods of attack of the problem. The results are presented in a form appropriate for numerical computation.
Mohsen, A.↗
Rate effects on instabilities in slightly ionized plasmas
Results are presented of numerical computer calculations of dispersive wave growth rates in slightly ionized plasmas. The effects of employing a plasma model with detailed consideration of rate and radiative processes involving the electron quantum states were studied. Acoustic and electrothermal waves in unseeded argon are found to be frozen with the latter damped. Rate thermal modes can exhibit large growth. Mode mixing and switching in both seeded and unseeded argon are demonstrated.
Harstad, K. G.↗
The transmission of sonic boom signals into rooms through open windows.
This paper is the second of two companion papers. In the first paper, expressions for the acoustic field generated inside a room with an open window due to incoming transient or periodic signals have been presented. In this paper, the technique has been applied to the specific example of an N-wave type signal. Detailed mathematical analysis is followed by its approximate version and numerical computation. Results of controlled experiments, using simulated sonic booms, have been compared with theoretical predictions.
Vaidya, P. G.↗
Dynamic analysis of a system of hinge-connected rigid bodies with nonrigid appendages
Equations of motion are derived for use in simulating a spacecraft or other complex electromechanical system amenable to idealization as a set of hinge-connected rigid bodies of tree topology, with rigid axisymmetric rotors and nonrigid appendages attached to each rigid body in the set. In conjunction with a previously published report on finite-element appendage vibration equations, this report provides a complete minimum-dimension formulation suitable for generic programming for digital computer numerical integration.
Likins, P. W.↗