Solar sources and the cosmic ray transport equation
Cosmic ray transport equation for solar sources, using Fisk numerical method by applying transformation of independent variable U/r,T/
Gleeson, L. J.↗
SEARCH · Engineering Papers
Results for “Numerical 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.
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Permeability of one-dimensional potential barriers
Numerical method for computing exact permeability /tunneling probability/ of one dimensional potential barrier
Le Roy, D. J.↗
Finite difference solution to the three-dimensional, incompressible thermal energy boundary-layer equation
An implicit numerical method has been adopted for the solution to the three-dimensional, energy boundary-layer equation. The energy equation is written in terms of a dimensionless temperature function, the relative stagnation-enthalpy difference, and transformed by the introduction of a Blasius-type transformation of coordinates as well as dimensionless stream functions. The method is applied to the problem consisting of an infinite cylinder joined with its axis perpendicular to a thin, flat, heated plate. A Prandtl number equal to one is simply considered.
Fillo, J. A.↗
Pressurized expulsion of nonisothermal single-phase cryogen
The performance of single-phase storage and expulsion systems as affected by temperature variations within the stored cryogen which are generated during heat transfer is discussed. Peculiar operating responses are indicated by spontaneous changes in fluid pressure which accompany g level changes, increased heater surface temperature, and durations of pressure cycles which differ considerably from that which is computed for an isothermal cryogen. The nonisothermal characteristics are predicted with a numerical model which includes the simultaneous solution of the time dependent conservation equations of mass, energy, and momentum in two space dimensions of Cartesian coordinates for boundary conditions which approximate those of the flight cryogenic system. The methodology of the numerical method and some comparisons between the predictions and the Apollo 12 flight data are included.
Forester, C. K.↗
Current conduction in junction gate field effect transistors
The internal physical mechanism that governs the current conduction in junction-gate field effect transistors is studied. A numerical method of analyzing the devices with different length-to-width ratios and doping profiles is developed. This method takes into account the two dimensional character of the electric field and the field dependent mobility. Application of the method to various device models shows that the channel width and the carrier concentration in the conductive channel decrease with increasing drain-to-source voltage for conventional devices. It also shows larger differential drain conductances for shorter devices when the drift velocity is not saturated. The interaction of the source and the drain gives the carrier accumulation in the channel which leads to the space-charge-limited current flow. The important parameters for the space-charge-limited current flow are found to be the L/L sub DE ratio and the crossover voltage.
Kim, C.↗
Numerical calculation of boundary-induced interference in slotted or perforated wind tunnels including viscous effects in slots
A numerical method is presented for calculating the incompressible boundary-induced interference in wind tunnels of rectangular cross section with slotted or perforated walls. The method includes a wall representation which is capable of satisfying a generalized homogeneous boundary condition including the effects of viscosity within the slots. The effects of viscosity in the slots are found to be very significant. The method allows for a variation in the boundary conditions along the tunnel walls. The model can be any configuration and can be located anywhere in the test section. The interference can be computed at any point in the test section.
Keller, J. D.↗
Hypersonic bodies of maximum drag for a given lift-to-drag ratio.
The problem considered in this paper is concerned with the aerodynamic design of the forebody shape of reentry vehicles in the blunt, homothetic, elliptic transversal contour, power-law longitudinal contour, raked-off configurational set. In particular, the forebody shape which maximizes the ratio of the forebody pressure drag to the free-stream dynamic pressure for a given lift-to-drag ratio and given geometric properties is determined. This problem is considered because recent survey articles indicate that its solution will provide useful qualitative design information about manned vehicles entering the earth's atmosphere from any of the foreseeable planetary missions. Single-integral equations relating the lift and drag in Newtonian hypersonic flow to the forebody geometry are derived and used to formulate the optimization problem which is solved by a direct numerical method.
Mcmillan, W., III↗
Prediction of flow profiles in arteries from local measurements.
This paper develops an approximate numerical method for calculating flow profiles in arteries. The theory takes into account the nonlinear terms of the Navier-Stokes equations as well as the large deformations of the arterial wall. The method, assuming axially symmetric flow, determines velocity distribution and wall shear at a given location from the locally measured values of the pressure, pressure gradient, and pressure-radius relation. The computed results agree well with the corresponding experimental data.
Ling, S. C.↗
Computation of supersonic flow fields about bodies in coning motion using a shock-capturing finite-difference technique.
A numerical method for computing the nonlinear inviscid flow field surrounding a body performing coning motion is described. The method permits accurate computation of the aerodynamic moment due to one of the four motions characterizing an arbitrary nonplanar motion. Results of computations for a slender circular cone in coning motion are presented, and show good agreement with experiment for angles of attack up to twice the cone half angle. The computational results display significant departure of the side moment from the linear theory value with increasing angle of attack, but agree well with experimental measurements. This indicates that the initial nonlinear behavior of the aerodynamic moment is determined primarily by the inviscid flow.
Schiff, L. B.↗
Three dimensional nozzle-exhaust flow field analysis by a reference plane technique.
A numerical method based on reference plane characteristics has been developed for the calculation of highly complex supersonic nozzle-exhaust flow fields. The difference equations have been developed for three coordinate systems. Local reference plane orientations are employed using the three coordinate systems concurrently thus catering to a wide class of flow geometries. Discontinuities such as the underexpansion shock and contact surfaces are computed explicitly for nonuniform vehicle external flows. The nozzles considered may have irregular cross-sections with swept throats and may be stacked in modules using the vehicle undersurface for additional expansion. Results are presented for several nozzle configurations.
Dash, S. M.↗
Buckling and vibration analysis for stiffened orthotropic shells of revolution.
Development of a numerical method, using the multistep integration approach, in which the buckling and vibration analyses are formulated as a succession of linear eigenvalue problems. The method does not require an estimate of the eigenvector, and once an eigenvalue has been converged good estimates for other eigenvalues are automatically available. This is accomplished through the use of an in-core Householder scheme for solution of the eigenvalue problem. Furthermore, since the method uses an eigenvalue solution, the possibility of missing modes is eliminated.
Svalbonas, V.↗
The radiative transfer equation and environmental effects in the upper atmosphere.
A highly effective approach to the solution of the radiative transfer equation, including the effects of emission, absorption, and multiply scattered radiation, is described. The transfer equation is cast in its unsteady hyperbolic form which is amenable to several different numerical methods of solution. Comparisons of solutions with emission, absorption, and scattering of radiation, are presented to demonstrate the validity of the present approach.
Callis, L. B.↗
Aeroelastic optimization of a panel in high Mach number supersonic flow.
Solution for a least-weight skin thickness distribution for a panel with a flutter parameter constraint. This panel weighs less than any similar constant thickness panel, but has the same critical supersonic panel flutter parameter. The panel rests on simple supports and is of sandwich construction. The span to chord ratio is large enough that the inertial, elastic, and aerodynamic behavior is one-dimensional. The Mach number is great enough that the aerodynamic forces acting on the upper panel surface may be accurately described by quasi-steady, linearized, supersonic aerodynamic theory. The final optimum design is obtained from theoretical and numerical methods adapted from optimal control theory. The results of this investigation show that the optimal panel thickness distribution is symmetric about the panel chord midpoint. Compared to a reference panel with constant thickness, optimum panels are found to be nearly 12% lighter.
Weisshaar, T. A.↗
Saturn systems holddown acoustic efficiency and normalized acoustic power spectrum.
Saturn systems field acoustic data are used to derive mid- and far-field prediction parameters for rocket engine noise. The data were obtained during Saturn vehicle launches at the Kennedy Space Center. The data base is a sorted set of acoustic data measured during the period 1961 through 1971 for Saturn system launches SA-1 through AS-509. The model assumes hemispherical radiation from a simple source located at the intersection of the longitudinal axis of each booster and the engine exit plane. The model parameters are evaluated only during vehicle holddown. The acoustic normalized power spectrum and efficiency for each system are isolated as a composite from the data using linear numerical methods. The specific definitions of each allows separation. The resulting power spectra are nondimensionalized as a function of rocket engine parameters. The nondimensional Saturn system acoustic spectrum and efficiencies are compared as a function of Strouhal number with power spectra from other systems.
Gilbert, D. W.↗
Theoretical and experimental investigations of antennas and waves in plasma
The near field characteristics of an antenna when it is covered by a plasma sheath were investigated. The areas of investigation were: (1) current distribution, (2) input admittance, and (3) radiation pattern as functions of the electrical length of the antenna. Diagnostic measurements were also made to determine the properties of the plasma. A numerical method was evolved to solve the problem of a finite cylindrical antenna in an infinite plasma column.
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Numerical calculations of flow fields
The solutions to the equations of motion for inviscid fluid flow around a pointed elliptic cone at incidence are presented. The numerical method used, MacCormack's second order preferential predictor-corrector finite difference approximation, is applied to the fluid flow equations derived in conservation-law form. The entropy boundary condition, hitherto unused for elliptic cone problems, is investigated and compared to reflection boundary condition solutions. The stagnation streamline movement of the inclined elliptic cone is noted and surface pressure coefficients are plotted. Also presented are solutions for an elliptic cone and a circular cone at zero incidence and a circular cone at a small angle of attack. Comparisons are made between these present solutions and previously published theory.
Anderson, D. M.↗
Tidal perturbations on the orbits of GEOS-1 and GEOS-2
Analysis of the luni-solar tidal perturbations of the inclination of GEOS-1 (1965-89A) and GEOS-2 (1968-002A) yielded the values k2 = 0.22 (sigma = 0.02) and 0.31 (sigma = 0.01) respectively for the second degree Love number. For GEOS-1 a new, purely numerical method involving osculating elements was employed. For GEOS-2 it was necessary to analyze the variations of the mean elements because of the very long period (450d) of the dominant solar tidal perturbation. An additional analysis of the variation of the mean elements of GEOS-1 confirmed the value of k2 obtained from the osculating elements.
Douglas, B. C.↗
Performance Analysis and Design Synthesis (PADS) computer program. Volume 2: Program description, part 2
The QL module of the Performance Analysis and Design Synthesis (PADS) computer program is described. Execution of this module is initiated when and if subroutine PADSI calls subroutine GROPE. Subroutine GROPE controls the high level logical flow of the QL module. The purpose of the module is to determine a trajectory that satisfies the necessary variational conditions for optimal performance. The module achieves this by solving a nonlinear multi-point boundary value problem. The numerical method employed is described. It is an iterative technique that converges quadratically when it does converge. The three basic steps of the module are: (1) initialization, (2) iteration, and (3) culmination. For Volume 1 see N73-13199.
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