Numerical solution for 1.5-dimensional, time-dependent magnetohydrodynamic problems
Numerical solution to problems of theta pinches and solar flares in strong magnetic fields
MAGNETIC FIELD↗
SEARCH · Engineering Papers
Results for “time-dependent problem”
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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Time-dependent perturbation - Variation method. III.
Extension of minimum variational principle applied to time-dependent perturbational problems instead of original stationarity principle
TIME DEPENDENCY↗
A recursive formulation for computing the coefficients of the time-dependent f and g series solution to the two-body problem.
Recursive generation of expansion coefficients of time-dependent f and g series in two-body problem, using algebraic recurrence formulas
SERIES EXPANSION↗
On the bound of first excursion probability
Method has been developed to improve the lower bound of the first excursion probability that can apply to the problem with either constant or time-dependent barriers. The method requires knowledge of the joint density function of the random process at two arbitrary instants.
Yang, J. N.↗
Effects of circular geometry in simulation of convection in rotating spacecraft tanks
For computational simulation of the convection and mixing of stratified fluid in a rotating tank (such as used in Apollo flights) with time-dependent rotation, the Navier-Stokes convection problem was formulated for a circular tank configuration. The final equations results from a general approximate theory for combined forced and contained natural convection in a time-dependent rotating system. The equations are cast in terms of vorticity and stream function in a form convenient for computation, with a transformed coordinate system, and appropriate boundary conditions are derived. Accurate representations for the cryogenic supercritical oxygen thermodynamic properties are used in the computations, and an efficient numerical finite difference scheme and computational method are employed.
Martin, E. D.↗
Method for Approximating the Vacuum Motions of Spinning Symmetrical Bodies with Nonconstant Spin Rates
A method for approximating the vacuum motions of spinning rigid symmetrical bodies with varying spin rates and inertias has been completed. The analysis includes the effects of time varying thrust misalignments, mass unbalance, and jet damping. Results are given in the form of equations for space referenced Euler angles, flight-path angles, body referenced attitude rates, and earth-referenced vehicle-trajectory coordinates. The method consists of dividing the problem into intervals during which the time-dependent variables are assumed constant at their mean interval value. In order to check this procedure, solutions for various interval sizes are compared with solutions obtained with numerical methods. Although the method is somewhat lengthy for accurate hand computation in most cases, it is readily programed for machine solutions. Probably more important, the general solutions give insight into the separate effects of the variables and, in many cases, can be quickly used to determine the approximate ranges of the variables required for the desired solution to a given problem. In this respect, equations for determining maximum wobble have been derived for certain input conditions. The method has been shown to compare closely with the numerical solutions of two sample problems. The sample problems also illustrated the relatively large effect of pitch and yaw jet damping on body motions.
VACUUM↗
Applications of NASTRAN to nuclear problems
The extent to which suitable solutions may be obtained for one physics problem and two engineering type problems is traced. NASTRAN appears to be a practical tool to solve one-group steady-state neutron diffusion equations. Transient diffusion analysis may be performed after new levels that allow time-dependent temperature calculations are developed. NASTRAN piecewise linear anlaysis may be applied to solve those plasticity problems for which a smooth stress-strain curve can be used to describe the nonlinear material behavior. The accuracy decreases when sharp transitions in the stress-strain relations are involved. Improved NASTRAN usefulness will be obtained when nonlinear material capabilities are extended to axisymmetric elements and to include provisions for time-dependent material properties and creep analysis. Rigid formats 3 and 5 proved to be very convenient for the buckling and normal-mode analysis of a nuclear fuel element.
Spreeuw, E.↗
Transient heating in the upper atmosphere
The time-dependent response of the upper atmosphere to transient heat sources is considered. The basic problem is that of heating a compressible, heat-conducting fluid, which is described in the one-dimensional case by an analytic solution. Comparisons with satellite drag data of such first-order solutions are shown to be useful in determining energy requirements and in determining some constraints on the spatial distribution of the heating. Recent OGO-6 mass spectrometer and interferometric temperature measurements show that atmospheric disturbances during geomagnetic storms are much more prominent in the auroral zones. These results suggest that joule dissipation of auroral currents are important contributors to orbital perturbations of satellites.
Thomas, G. E.↗
An analysis of the ''laminar instability'' problem in gas-cooled nuclear reactor passages.
Instability of gas-cooled nuclear reactor passages in steady laminar flow studied by time-dependent analysis
LAMINAR FLOW↗
Use of source distributions for evaluating theoretical aerodynamics of thin finite wings at supersonic speeds
A series of publications on the source-distribution methods for evaluating the aerodynamics of thin wings at supersonic speeds is summarized, extended, and unified. Included in the first part are the deviations of: (a) the linearized partial-differential equation for unsteady flow at a substantially constant Mach number. b) The source-distribution solution for the perturbation-velocity potential that satisfies the boundary conditions of tangential flow at the surface and in the plane of the wing; and (c) the integral equation for determining the strength and the location of sources to describe the interaction effects (as represented by upwash) of the bottom and top wing surfaces through the region between the finite wing boundary and the foremost Mach wave. The second part deals with steady-state thin-wing problems. The third part of the report approximates the integral equation for unsteady upwash and includes a solution of approximate equation. Expressions are then derived to evaluate the load distributions for time-dependent finite-wing motions.
Evvard, John C↗
Boundary condition computational procedures for inviscid, supersonic steady flow field calculations
Results are given of a comparative study of numerical procedures for computing solid wall boundary points in supersonic inviscid flow calculatons. Twenty five different calculation procedures were tested on two sample problems: a simple expansion wave and a simple compression (two-dimensional steady flow). A simple calculation procedure was developed. The merits and shortcomings of the various procedures are discussed, along with complications for three-dimensional and time-dependent flows.
Abbett, M. J.↗
Time-dependent Structural Analysis of Metal-epoxy Composites
In an effort to reduce structural weight while maintaining structural integrity on the space shuttle and other proposed space vehicles, various composite materials are being evaluated to determine their applicability and reliability in load carrying situations. While most of the composites being considered for structural components are of the metal-metal type, there are some applications for which metal-epoxy composites are proposed. An approximate method is presented to analyze plane stress orthotropic linear viscoelastic problems under isothermal conditions. A computer program which is based on the method was used to solve a simple uniaxial creep problem for a Maxwell type material. This solution is presented and compared with the analytical solution.
Dehoff, P. H.↗
Convection in the tanks of a rotating spacecraft
A general study of convection and mixing of a stratified fluid in a rotating container is described, with application to the special problem of fluid heating and convection in a spacecraft tank. The analysis was based on a set of approximate equations for the Navier-Stokes description of fluid convection with small density variations in a rotating system, including effects of body forces due to temperature stratification (caused by a heater) and arbitrary time-dependent rotation of the tank about a noncentral axis. An efficient numerical finite difference scheme and computational method are described for the convection of vorticity and energy in a two-dimensional tank. Special procedures were developed for analysis of the thermodynamic states resulting from the approximate flow equations derived for small density variations. Results of the numerical simulation are presented for studying the effectiveness of rotation maneuvers in mixing stratified oxygen in the tanks of an Apollo spacecraft. Significant effects of the rotation maneuvers are discussed, including the reduction of the potential for pressure collapse.
Source record↗
Genetic implications of the shapes of Martian and lunar craters.
Discussion of the problem of lunar crater genesis in the light of some considerations prompted by lunar and Martian crater similarities. By analogy with the moon, Martian craters seem both to vary in initial shape according to the energy of the impact that formed them and to have been modified subsequently by endogenic and surface processes. A proposed model for the geologic development of large Martian and lunar craters outlines a time-dependent sequence of events. Craters which have undergone rapid isostatic adjustment on the moon have distinctive morphologies and occur preferentially along mare basin-upland margins.
Pike, R. J.↗
Dynamic characteristics of a two-stage variable-mass flexible missile with internal flow
A general formulation of the dynamical problems associated with powered flight of a two stage flexible, variable-mass missile with internal flow, discrete masses, and aerodynamic forces is presented. The formulation comprises six ordinary differential equations for the rigid body motion, 3n ordinary differential equations for the n discrete masses and three partial differential equations with the appropriate boundary conditions for the elastic motion. This set of equations is modified to represent a single stage flexible, variable-mass missile with internal flow and aerodynamic forces. The rigid-body motion consists then of three translations and three rotations, whereas the elastic motion is defined by one longitudinal and two flexural displacements, the latter about two orthogonal transverse axes. The differential equations are nonlinear and, in addition, they possess time-dependent coefficients due to the mass variation.
Meirovitch, L.↗
Recursive computation of the coefficients of the time-dependent f and g series solution of Keplerian motion and a study of the convergence properties of the solution
Recursive computation of coefficients for time dependent f and g series solution to two-body problem of Keplerian motion
TWO-BODY PROBLEM↗
The one-dimensional time-dependent interaction of a satellite with the ionospheric plasma
Numerical solution for one dimensional, time dependent problem of collisionless plasma impinging on flat conducting plate
Sheldon, J. W.↗
An analysis of the relaxation of laminar boundary layer on a flat plate after passage of an interface with application to expansion-tube flows
The relaxation of the accelerating-gas boundary layer to the test-gas boundary layer over a flat plate in an expansion tube is analyzed. Several combinations of test gas and acceleration gas are considered. The problem is treated in two conically similar limits: (1) when the time lag between the arrival of the shock and the interface at the leading edge of the plate is very large, and (2) when this lag is negligible. The time-dependent laminar-boundary-layer equations of a binary mixture of perfect gases are taken as the flow-governing equations. This coupled set of differential equations, written in terms of the Lam-Crocco variables, has been solved by a line-relaxation finite-difference techniques. The results presented include the Stanton number and the local skin-friction coefficient as functions of shock Mach number and the nondimensional distance-time variable. The results indicate that more than 95 percent of the test-gas boundary layer exists over a length, measured from the leading edge of the plate, equal to about three-tenths of the distance traversed by the interface in the free stream.
Gupta, R. N.↗