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At least 883 records · Page 49

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NASA NTRS1976

A scaling law for energy transfer by inelastic electron-molecule collisions in mixtures

The equation governing the electron energy distribution in the presence of a spatially uniform electric field in a weakly ionized gas was reformulated into an integral equation for the logarithmic slope of the distribution function. For gas mixtures in which the dominant electron energy loss mechanism is by vibrational excitation of the molecules, this equation is suitable for approximate analysis and exact numerical solution by iteration. Superelastic collisions are easily included in this formulation, and do not seriously effect the convergence of the numerical scheme. The approximate analytical results are only qualitatively correct, but suggest appropriate parameters which correlate the exact numerical results very well. The distribution function as well as certain gross properties such as net energy transfer into vibration, mean energy, and drift velocity depend primarily on a single nondimensional parameter involving only E/N and the cross sections.

Bienkowski, G. K.↗

NASA NTRS1980

Dynamic simulation of coronal mass ejections

A model is developed for the formation and propagation through the lower corona of the loop-like coronal transients in which mass is ejected from near the solar surface to the outer corona. It is assumed that the initial state for the transient is a coronal streamer. The initial state for the streamer is a polytropic, hydrodynamic solution to the steady-state radial equation of motion coupled with a force-free dipole magnetic field. The numerical solution of the complete time-dependent equations then gradually approaches a stationary coronal streamer configuration. The streamer configuration becomes the initial state for the coronal transient. The streamer and transient simulations are performed completely independent of each other. The transient is created by a sudden increase in the pressure at the base of the closed-field region in the streamer configuration. Both coronal streamers and coronal transients are calculated for values of the plasma beta (the ratio of thermal to magnetic pressure) varying from 0.1 to 100.

Steinolfson, R. S.↗

NASA NTRS1986

Arbitrarily laminated, anisotropic cylindrical shell under internal pressure

An arbitrarily laminated, anisotropic cylindrical shell of finite length, under uniform internal pressure, is analyzed using Love-Timoshenko's kinematic relations and under the framework of classical lamination theory. The previously obtained solutions for asymmetrically laminated orthotropic (cross-ply) as well as unbalanced-symmetric and balanced-unsymmetric (angle-ply) cylindrical shells under the same loading conditions have been shown to be special cases of the present closed-form solution. Numerical results have been presented for a two-layer cylindrical shell and compared with those obtained using finite element solutions based on the layerwise constant shear-angle theory. These are expected to serve as benchmark solutions for future comparisons and to facilitate the use of unsymmetric lamination in design.

Chaudhuri, Reaz Z.↗

NASA NTRS1989

The Hard X-rays and Gamma-rays from Solar Flares

Radiation of energies from 10 KeV to greater than 10 MeV has been observed during solar flares, and is interpreted to be due to bremsstrahlung by relativistic electrons. A complete treatment of this problem requires solution of the kinetic equation for relativistic electrons and inclusion of synchrotron energy losses. Using the electron distributions obtained from numerical solutions of this equation the bremsstrahlung spectra in the impulsive x ray and gamma-ray regimes are calculated, and the variation of these spectral indices and directivities with energy and observation angle are described. The dependences of these characteristics of the radiation of changes in the solar atmospheric model, including the convergence of the magnetic field, the injected electron spectral index, and most importantly, in the anisotropy of the injected electrons and of the convergence of the magnetic field are also described. The model results are compared with stereoscopic observations of individual flares and the constraints that this data sets on the models are discussed.

Mctiernan, James M.↗

NASA NTRS1990

The hard X-rays and gamma rays from solar flares

Radiation of energies from 10 KeV to greater than 10 MeV has been observed during solar flares, and is interpreted to be due to bremsstrahlung by relativistic electrons. A complete treatment of this problem requires solution of the kinetic equation for relativistic electrons and inclusion of synchrotron energy losses. Using the electron distributions obtained from numerical solutions of this equation the bremsstrahlung spectra in the impulsive X-ray and gamma ray regimes are calculated, and the variation of these spectral indices and directivities with energy and observation angle are described. The dependences of these characteristics of the radiation of changes in the solar atmospheric model, including the convergence of the magnetic field, the injected electron spectral index, and most importantly, in the anisotropy of the injected electrons and of the convergence of the magnetic field are also described. The model results are compared with stereoscopic observations of individual flares and the constraints that this data sets on the models are discussed.

Mctiernan, James M.↗

NASA NTRS1997

A Comparison of Soil Moisture Retrieval Models Using SIR-C Measurements over the Little Washita River Watershed

Six SIR-C L-band measurements over the Little Washita River watershed in Chickasha, Oklahoma during 11-17 April 1994 have been analyzed for studying the change of soil moisture in the region. Two algorithms developed recently for estimation of moisture content in bare soil were applied to these measurements and the results were compared with those sampled on the ground. There is a good agreement between the values of soil moisture estimated by either one of the algorithms and those measured from ground sampling for bare or sparsely vegetated fields. The standard error from this comparison is on the order of 0.05-0.06 cu cm/cu cm, which is comparable to that expected from a regression between backscattering coefficients and measured soil moisture. Both algorithms provide a poor estimation of soil moisture or fail to give solutions to areas covered with moderate or dense vegetation. Even for bare soils the number of pixels that bear no numerical solution from the application of either one of the two algorithms to the data is not negligible. Results from using one of these algorithms indicate that the fraction of these pixels becomes larger as the bare soils become drier. The other algorithm generally gives a larger fraction of these pixels when the fields are vegetation-covered. The implication and impact of these features are discussed in this article.

Wang, J. R.↗

NASA NTRS1987

Problem size, parallel architecture and optimal speedup

The communication and synchronization overhead inherent in parallel processing can lead to situations where adding processors to the solution method actually increases execution time. Problem type, problem size, and architecture type all affect the optimal number of processors to employ. The numerical solution of an elliptic partial differential equation is examined in order to study the relationship between problem size and architecture. The equation's domain is discretized into n sup 2 grid points which are divided into partitions and mapped onto the individual processor memories. The relationships between grid size, stencil type, partitioning strategy, processor execution time, and communication network type are analytically quantified. In so doing, the optimal number of processors was determined to assign to the solution, and identified (1) the smallest grid size which fully benefits from using all available processors, (2) the leverage on performance given by increasing processor speed or communication network speed, and (3) the suitability of various architectures for large numerical problems.

Nicol, David M.↗

NASA NTRS1988

Problem size, parallel architecture, and optimal speedup

Nicol, David M.↗

NASA NTRS1973

Unsteady subsonic compressible flow around finite thickness wings.

A general formulation for the unsteady subsonic compressible potential flow around aircraft having arbitrary configurations is presented. An integral representation of the velocity potential is obtained. From this a linear integral equation relating the perturbation potential and its normal derivative (which is known from the boundary conditions) is derived. For the numerical solution of the integral equation, the surface of the aircraft is divided into small elements and the potential is assumed to be constant within each element. Numerical results are obtained for an oscillating finite-thickness wing and indicate good convergence and excellent agreement with existing lifting surface solutions.

Morino, L.↗

NASA NTRS1992

Composite laminates with spatially varying fiber orientations - 'Variable stiffness panel concept'

A solution has been obtained to the plane elasticity problem for a symmetrically laminated composite panel with spatially varying fiber orientations. Since variation of the fiber angles along the length of a composite laminate results in stiffness properties that change as a function of location, the laminates are called variable stiffness panels. An analysis of the stiffness variation and its effect on the elastic response of the panel is presented here. A numerical solution has been obtained using an iterative collocation technique. Corresponding closed-form solutions are given for three different sets of boundary conditions. Two of the cases considered have exact solutions and thus serve to validate the numerical model.

Guerdal, Zafer↗

NASA NTRS2015

Toward a Nonlinear Acoustic Analogy: Turbulence as a Source of Sound and Nonlinear Propagation

An acoustic analogy is proposed that directly includes nonlinear propagation effects. We examine the Lighthill acoustic analogy and replace the Green's function of the wave equation with numerical solutions of the generalized Burgers' equation. This is justified mathematically by using similar arguments that are the basis of the solution of the Lighthill acoustic analogy. This approach is superior to alternatives because propagation is accounted for directly from the source to the far-field observer instead of from an arbitrary intermediate point. Validation of a numerical solver for the generalized Burgers' equation is performed by comparing solutions with the Blackstock bridging function and measurement data. Most importantly, the mathematical relationship between the Navier- Stokes equations, the acoustic analogy that describes the source, and canonical nonlinear propagation equations is shown. Example predictions are presented for nonlinear propagation of jet mixing noise at the sideline angle

Miller, Steven A. E.↗

NASA NTRS2015

Toward a Nonlinear Acoustic Analogy: Turbulence as a Source of Sound and Nonlinear Propagation

An acoustic analogy is proposed that directly includes nonlinear propagation effects. We examine the Lighthill acoustic analogy and replace the Green's function of the wave equation with numerical solutions of the generalized Burgers' equation. This is justified mathematically by using similar arguments that are the basis of the solution of the Lighthill acoustic analogy. This approach is superior to alternatives because propagation is accounted for directly from the source to the far-field observer instead of from an arbitrary intermediate point. Validation of a numerical solver for the generalized Burgers' equation is performed by comparing solutions with the Blackstock bridging function and measurement data. Most importantly, the mathematical relationship between the Navier-Stokes equations, the acoustic analogy that describes the source, and canonical nonlinear propagation equations is shown. Example predictions are presented for nonlinear propagation of jet mixing noise at the sideline angle.

Miller, Steven A. E.↗

NASA NTRS1976

Incremental analysis of large elastic deformation of a rotating cylinder

The effect of finite deformation upon a rotating, orthotropic cylinder was investigated using a general incremental theory. The incremental equations of motion are developed using the variational principle. The governing equations are derived using the principle of virtual work for a body with initial stress. The governing equations are reduced to those for the title problem and a numerical solution is obtained using finite difference approximations. Since the problem is defined in terms of one independent space coordinate, the finite difference grid can be modified as the incremental deformation occurs without serious numerical difficulties. The nonlinear problem is solved incrementally by totaling a series of linear solutions.

Buchanan, G. R.↗

DOE OSTI2023

The neutron number probability distribution in coupled lumped assemblies

Here, the validity of the gamma distribution in describing the neutron number probability distribution function for both isolated and coupled multiplying assemblies when constrained to reproduce the true mean and variance is investigated in lumped geometry by numerical comparison with kinetic Monte Carlo simulations. The mean and variance are obtained from numerical solution of moment equations constructed from the relevant forward Master equation with assembly coupling coefficients obtained from a view factor method. Numerical results for a two-group, two coupled assemblies model, with static and dynamic reactivity insertion, show that except for subcritical assemblies, the gamma distribution well-approximates the number distribution. Differences in the fast and thermal neutron population shapes are explained in terms of effective source strengths due to downscatter and coupling.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS1982

Bubble shapes in steady axisymmetric flows at intermediate Reynolds number

The shape of a gas bubble which rises through a quiescent incompressible, Newtonian fluid at intermediate Reynolds numbers is considered. Exact numerical solutions for the velocity and pressure fields, as well as the bubble shape, are obtained using finite difference techniques and a numerically generated transformation to an orthogonal, boundary-fitted coordinate system. No restriction is placed on the allowable magnitude of deformation.

Ryskin, G.↗

NASA NTRS1983

Application of second-order-accurate Total Variation Diminishing (TVD) schemes to the Euler equations in general geometries

A one-parameter family of explicit and implicit second-order-accurate, entropy satisfying, total variation diminishing (TVD) schemes was developed by Harten. These TVD schemes were the property of not generating spurious oscillations for one-dimensional nonlinear scalar hyperbolic conservation laws and constant coefficient hyperbolic systems. Application of these methods to one- and two-dimensional fluid flows containing shocks (in Cartesian coordinates) yields highly accurate nonoscillatory numerical solutions. The goal of this work is to expand these methods to the multidimensional Euler equations in generalized coordinate systems. Some numerical results of shock waves impinging on cylindrical bodies are compared with MacCormack's method.

Yee, H. C.↗

NASA NTRS1988

Finite element solution of the Euler equations in two and three dimensions

The paper presents a finite element procedure for solving the equations of compressible flow over bodies of arbitrary geometry. The numerical solution algorithm employed is an explicit two-step version of a second order Taylor-Galerkin scheme. The discretization of the computational domain into unstructured meshes of triangles in two dimensions and tetrahedra in three dimensions is performed by an automatic mesh generator. In the approach, the mesh generator is coupled to the finite element solver to produce an adaptive remeshing procedure.

Peiro, J.↗

NASA NTRS1989

A Newton/upwind method and numerical study of shock wave/boundary layer interactions

The objective of the paper is two-fold. First, an upwind/central differencing method for solving the steady Navier-Stokes equations is described. The symmetric line relation method is used to solve the resulting algebraic system to achieve high computational efficiency. The grid spacings used in the calculations are determined from the triple-deck theory, in terms of Mach and Reynolds numbers and other flow parameters. Thus the accuracy of the numerical solutions is improved by comparing them with experimental, analytical, and other computational results. Secondly, the shock wave/boundary layer interactions are studied numerically, with special attention given to the flow separation. The concept of free interaction is confirmed. Although the separated region varies with Mach and Reynolds numbers, it is found that the transverse velocity component behind the incident shock, which has not been identified heretofore, is also an important parameter. A small change of this quantity is sufficient to eliminate the flow separation entirely.

Liou, Meng-Sing↗