Search NASA⌕ Search

SEARCH · Search NASA

Results for “source terms”

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 757 records · Page 42

Computation of viscous flow in planar and axisymmetric ducts by an implicit marching procedure

A streamwise marching procedure, approximately 200 times faster than a full Navier-Stokes procedure with comparable accuracy, is presented for solving problems of compressible viscous subsonic flow. Results are presented and compared with experimental data for the cases of developing turbulent flow in a circular pipe; turbulent flow in a two-dimensional S-duct; and turbulent flow in a typical subsonic diffuser. Prior to each main marching step, a preliminary marching step is taken in which the integral continuity equation and an uncoupled form of the streamwise momentum equation are solved simultaneously to obtain the viscous pressure correction. During the main marching step the equations for continuity, streamwise momentum, cross-flow momentum, and energy are solved simultaneously as a coupled system using an implicit finite-difference method, with the viscous pressure correction treated as a source term. The analysis may be used for flows with both favorable and adverse pressure gradients and to predict the location of flow separation.

Towne, C. E.↗

Thermal electron heating rate - A derivation

The thermal electron heating rate is an important heat source term in the ionospheric electron energy balance equation, representing heating by photoelectrons or by precipitating higher energy electrons. A formula for the thermal electron heating rate is derived from the kinetic equation using the electron-electron collision operator as given by the unified theory of Kihara and Aono. This collision operator includes collective interactions to produce a finite collision operator with an exact Coulomb logarithm term. The derived heating rate O(e) is the sum of three terms, O(e) = O(P) + S + O(int), which are respectively: (1) primary electron production term giving the heating from newly created electrons that have not yet suffered collisions with the ambient electrons; (2) a heating term evaluated on the energy surface m(e)/2 = E(T) at the transition between Maxwellian and tail electrons at E(T); and (3) the integral term representing heating of Maxwellian electrons by eneegetic tail electrons at energies ET. Published ionospheric electron temperature studies used only the integral term O(int) with differing lower integration limits. Use of the incomplete heating rate could lead to erroneous conclusions regarding electron heat balance, since O(e) is greater than O(int) by as much as a factor of two. Previously announced in STAR as N84-15941

Hoegy, W. R.↗

A comparison of observed and numerically predicted eddy kinetic energy budgets for a developing extratropical cyclone

The eddy kinetic energy budget is calculated for a 48-hour forecast of an intense occluding winter cyclone associated with a strong well-developed jet stream. The model output consists of the initialized (1200 GMT January 9, 1975) and the 12, 24, 36, and 48 hour forecast fields from the Drexel/NCAR Limited Area Mesoscale Prediction System (LAMPS) model. The LAMPS forecast compares well with observations for the first 24 hours, but then overdevelops the low-level cyclone while inadequately developing the upper-air wave and jet. Eddy kinetic energy was found to be concentrated in the upper-troposphere with maxima flanking the primary trough. The increases in kinetic energy were found to be due to an excess of the primary source term of kinetic energy content, which is the horizontal flux of eddy kinetic energy over the primary sinks, and the generation and dissipation of eddy kinetic energy.

Dare, P. M.↗

Hot plasma composition results from the S3-3 spacecraft

The S3-3 satellite discovered the principal auroral acceleration region at altitudes of about 1 R(E) over the auroral zone. Intense fluxes of upward flowing O(+) and H(+) ions with keV energies were commonly observed in this region of the magnetosphere. The detailed morphology of these upflowing ions is described, including their latitude, local time, altitude, and magnetic activity dependences and their relationship to the trapped keV electron population. The first measurements of the composition of the trapped keV ions in the radiation belts are also described, showing the importance of the ionospheric source term to the storm time population of ions with energies equal to or less than 16 keV/e.

Sharp, R. D.↗

Development of a dynamically adaptive grid method for multidimensional problems

An approach to solution adaptive grid generation for use with finite difference techniques, previously demonstrated on model problems in one space dimension, has been extended to multidimensional problems. The method is based on the popular elliptic steady grid generators, but is 'dynamically' adaptive in the sense that a grid is maintained at all times satisfying the steady grid law driven by a solution-dependent source term. Testing has been carried out on Burgers' equation in one and two space dimensions. Results appear encouraging both for inviscid wave propagation cases and viscous boundary layer cases, suggesting that application to practical flow problems is now possible. In the course of the work, obstacles relating to grid correction, smoothing of the solution, and elliptic equation solvers have been largely overcome. Concern remains, however, about grid skewness, boundary layer resolution and the need for implicit integration methods. Also, the method in 3-D is expected to be very demanding of computer resources.

Holcomb, J. E.↗

Solution of the wave equation for open surfaces involving a line integral over the edge

A simple mathematical model of a stationary source distribution for the supersonic-propeller noise-prediction formula of Farassat (1983) is developed to test the validity of the formula solutions. The conventional thickness source term is used in place of the Isom thickness formula; the relative importance of the line and surface integrals in the solutions is evaluated; and the numerical results are compared with those obtained with a conventional retarded-time solution in tables. Good agreement is obtained over elevation angles from 10 to 90 deg, and the line-integral contribution is found to be significant at all elevation angles and of the same order of magnitude as the surface-integral contribution at angles less than 30 deg. The amplitude-normalized directivity patterns for the four cases computed (x = 1.5 or 10; k = 5.0 or 50) are presented graphically.

Farassat, F.↗

On the relation between upwind-differencing schemes of Godunov, Engquist-Osher and Roe

The upwind differencing first order schemes of Godunov, Engquist-Osher and Roe are discussed on the basis of the inviscid Burgers equations. The differences between the schemes are interpreted as differences between the approximate Riemann solutions on which their numerical flux functions are based. Special attention is given to the proper formulation of these schemes when a source term is present. Second order two step schemes, based on the numerical flux functions of the first order schemes are also described. The schemes are compared in a numerical experiment, and recommendations on their use are included.

Vanleer, B.↗

A finite volume method for the calculation of compressible chemically reacting flows

Several efficient pseudo time techniques have been developed for calculating steady state chemically reacting flows. The techniques include the implicit treatment of the chemical source term, point implicit multiple grid accelerator and a constant CFL condition. It turns out that these methods can be viewed as ways of rescaling the equations in time such that all chemical and convective phenomena evolve at comparable pseudo time scales. Consequently the number of iterations needed to solve reacting problems is approximately the same as for non-reacting problems. The techniques are demonstrated for a simple dissociation model and a nontrivial H2 - Air combustion model.

Bussing, T. R. A.↗

Noniterative three-dimensional grid generation using parabolic partial differential equations

A new algorithm for generating three-dimensional grids has been developed and implemented which numerically solves a parabolic partial differential equation (PDE). The solution procedure marches outward in two coordinate directions, and requires inversion of a scalar tridiagonal system in the third. Source terms have been introduced to control the spacing and angle of grid lines near the grid boundaries, and to control the outer boundary point distribution. The method has been found to generate grids about 100 times faster than comparable grids generated via solution of elliptic PDEs, and produces smooth grids for finite-difference flow calculations.

Edwards, T. A.↗

Numerical solution of strong radiation gasdynamic interactions in a hydrogen-seedant mixture

Theoretical and experimental results are provided for the absorption of laser energy by a gas flow. A two-dimensional numerical model described the temperature field, fluid dynamics, variable absorptivity and gas dynamics. The model was tested using a hydrogen-seedant mixture injected with 10.6 micron laser radiation. The laser mix was selected to allow reduced temperature gradients and energy source terms. It was found possible, by varying parameters such as the laser power and flash pressure, to precisely position the peak absorptance region in higher speed flows. More refined models are being tested to achieve accurate absorptance predictions in flows below Mach 0.0001.

Merkle, C. L.↗

Solid waste treatment processes for space station

The purpose of this study was to evaluate the state-of-the-art of solid waste(s) treatment processes applicable to a Space Station. From the review of available information a source term model for solid wastes was determined. An overall system is proposed to treat solid wastes under constraints of zero-gravity and zero-leakage. This study contains discussion of more promising potential treatment processes, including supercritical water oxidation, wet air (oxygen) oxidation, and chemical oxidation. A low pressure, batch-type treament process is recommended. Processes needed for pretreatment and post-treatment are hardware already developed for space operations. The overall solid waste management system should minimize transfer of wastes from their collection point to treatment vessel.

Marrero, T. R.↗

Remote sensing of atmospheric and surface parameters from HIRS2/MSU on TIROS-N

At the Goddard Laboratory for Atmospheric Sciences (GLAS) a physically based satellite temperature sounding retrieval system was developed, involving the simultaneous analysis of sounding data, for determining atmospheric and surface conditions that are consistent with the observed radiances. In addition to determining accurate atmospheric temperature profiles even in the presence of clouds, the system provides global estimates of day and night sea or land surface temperatures, snow and ice cover, cloud amounts, cloudtop heights and temperatures, and albedo. The characteristics of the atmospheric and surface parameters derived from the GLAS Physical Retrieval System are reviewed, results for the FGGE year are presented and, whenever possible, compared with other measurements of the same fields. Some of the model-derived diagnostic fields available from the GLAS Analysis/Forecast System are also discussed. These fields may lead to more accurate determination of the source terms of the atmospheric heat and moisture budgets.

Susskind, J.↗

Application of a computational model for vortex generators in subsonic internal flows

A model for the analysis of vortex generators in a fully viscous subsonic internal flow is evaluated. A vorticity source term is used in a modified form of the Parabolized Navier-Stokes equations to model the shed vortex. Computed results are compared with idealized flow vortex paths, and with experimental data for vortex generators embedded in a thick turbulent boundary layer. The analysis is also compared with experimental data for a separated diffusing S-duct and for a diffusing S-duct with vortex generators. Quantitative comparisons are shown for the latter three cases. Emphasis is placed on verifying the ability of the model to predict global distortions in the flow field.

Kunik, W. G.↗

Application of a computational model for vortex generators in subsonic internal flows

A model for the analysis of vortex generators in a fully viscous subsonic internal flow is evaluated. A vorticity source term is used in a modified form of the Parabolized Navier-Stokes equations to model the shed vortex. Computed results are compared with idealized flow vortex paths, and with experimental data for vortex generators embedded in a thick turbulent boundary layer. The analysis is also compared with experimental data for a separated diffusing S-duct and for a diffusing S-duct with vortex generators. Quantitative comparisons are shown for the latter three cases. Emphasis is placed on verifying the ability of the model to predict global distortions in the flow field.

Kunik, W. G.↗

Numerical study of hydrogen-air supersonic combustion by using elliptic and parabolized equations

The two-dimensional Navier-Stokes and species continuity equations are used to investigate supersonic chemically reacting flow problems which are related to scramjet-engine configurations. A global two-step finite-rate chemistry model is employed to represent the hydrogen-air combustion in the flow. An algebraic turbulent model is adopted for turbulent flow calculations. The explicit unsplit MacCormack finite-difference algorithm is used to develop a computer program suitable for a vector processing computer. The computer program developed is then used to integrate the system of the governing equations in time until convergence is attained. The chemistry source terms in the species continuity equations are evaluated implicitly to alleviate stiffness associated with fast chemical reactions. The problems solved by the elliptic code are re-investigated by using a set of two-dimensional parabolized Navier-Stokes and species equations. A linearized fully-coupled fully-implicit finite difference algorithm is used to develop a second computer code which solves the governing equations by marching in spce rather than time, resulting in a considerable saving in computer resources. Results obtained by using the parabolized formulation are compared with the results obtained by using the fully-elliptic equations. The comparisons indicate fairly good agreement of the results of the two formulations.

Chitsomboon, T.↗

The role and behavior of spin in gravitational physics

A self-consistent method of introducing spin into any Lagrangian based theory of gravitation was developed. The metric variation of the Lagrangian in the theory leads to an improved energy-momentum tensor which represents the source term in the gravitational field equations. The goal of the research is the construction of a theory general enough to be used to investigate spin effects in astrophysical objects and cosmology, and also to serve as a basis for discussion of the theoretical ideas tested by the NASA Gyroscope Experiment (aboard Gravity Probe B). Specific accomplishments in the following areas are summarized: the inclusion of electromagnetism into the variational principle for spinning matter, formulation of a self-consistent theory for the case of a fluid in which particle production processes occur, and the derivation of the Raychaudhuri equation in the case of spinning matter.

Ray, John R.↗

Investigation of chemically reacting and radiating supersonic internal flows

The two-dimensional spatially elliptic Navier-Stokes equations are used to investigate the chemically reacting and radiating supersonic flow of the hydrogen-air system between two parallel plates and in a channel with a ten degree compression-expansion ramp at the lower boundary. The explicit unsplit finite-difference technique of MacCormack is used to advance the governing equations in time until convergence is achieved. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The tangent slab approximation is employed in the radiative flux formation. Both pseudo-gray and nongray models are used to represent the absorption characteristics of the participating species. Results obtained for specific conditions indicate that the radiative interaction can have a significant influence on the flow field.

Mani, M.↗