Search NASA⌕ Search

SEARCH · Search NASA

Results for “Continuity equation”

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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Modeling the dust size distribution in comets with dust fragmentation

A hydrodynamic model was developed of a spherically symmetric dusty gas flow in a cometary atmosphere assuming a single fluid, inviscid, perfect gas. The hydrodynamics for gas and dust, which involves the gas drag force (momentum transfer), heat exchange between gas and dust, photodissociation energy for H2O gas, and radiative heating and cooling terms for dust particles, are solved using the Gear method for stiff, coupled differential equations. Calculations were done with a dust size distribution for radii alpha = 0.01 micron to 10 cm with densities variable with the size. A nucleus size of 4.0 km radius with a density of 0.5 g/cu cm and a total dust-to-gas mass ratio chi = 1 was adopted. There are indications from in situ observations that dust particle fragment into smaller ones. Fragmentation of dust particles was incorporated into the model. This is done by adding source and sink terms in the continuity equations for the dust. Lifetimes for the decay of dust particles were assumed as a function of particle size. It is also assumed that dust particles always fragment only into the next smaller size.

Konno, Ichishiro↗
NASA NTRS1976

Time-asymptotic solutions of the Navier-Stokes equation for free shear flows using an alternating-direction implicit method

An uncoupled time asymptotic alternating direction implicit method for solving the Navier-Stokes equations was tested on two laminar parallel mixing flows. A constant total temperature was assumed in order to eliminate the need to solve the full energy equation; consequently, static temperature was evaluated by using algebraic relationship. For the mixing of two supersonic streams at a Reynolds number of 1,000, convergent solutions were obtained for a time step 5 times the maximum allowable size for an explicit method. The solution diverged for a time step 10 times the explicit limit. Improved convergence was obtained when upwind differencing was used for convective terms. Larger time steps were not possible with either upwind differencing or the diagonally dominant scheme. Artificial viscosity was added to the continuity equation in order to eliminate divergence for the mixing of a subsonic stream with a supersonic stream at a Reynolds number of 1,000.

Rudy, D. H.↗
NASA NTRS1981

Multivalued velocity field model of turbulence

The considered study is based on new theoretical concepts regarding a post-instability model of a fluid discussed by Zak (1980). The model permits the completion of the governing equations of turbulence by introducing multivalued fields of velocities. Attention is given to the mechanism of energy dissipation, the characteristic wave propagation, a simplified model, the formation of turbulence around stagnation points, the formulation of boundary conditions, and the mechanism of turbulence formation. The mechanism of turbulence formation can be understood as propagation of initial discontinuities from the boundaries into a flow with the characteristic velocity which is defined by the normal (to the boundary) velocity components. These components emerge at the boundary as a result of jumps in the tangential components due to the continuity equation.

Zak, M.↗
NASA NTRS1990

The role of high-speed plasma flows in plasmaspheric refilling

A model of time-dependent one-stream interhemispheric plasma flow is used to investigate plasmaspheric refilling. In the model the coupled time-dependent hydrodynamic equations (continuity, momentum and energy) of a two-ion, H(+) and O(+), quasi-neutral, currentless plasma are solved for a closed geomagnetic field line. For the present set of calculations an L = 2 field line was used. A steady state solution was found and used as the initial condition in subsequent simulations of the effect of density depletions. Density depletions were modeled by reducing the densities by an arbitrary factor above 2500 km altitude, while keeping the velocities and temperatures unchanged. Shock structures develop which move up the field line, meeting and reflecting at the equator. The reflected shocks are absorbed by the dense neutral atmosphere when they reach the model flux tube boundaries. After the upwelling streams collide, refilling occurs from the equator downward for 2 to 3 hours; thereafter there is steady refilling from the ionospheres upward.

Guiter, S. M.↗
NASA NTRS1999

Photochemistry of Pluto's Atmosphere

This work include studies of two problems: (1) Modeling thermal balance, structure. and escape processes in Pluto's upper atmosphere. This study has been completed in full. A new method, of analytic solution for the equation of hydrodynamic flow from in atmosphere been developed. It was found that the ultraviolet absorption by methane which was previously ignored is even more important in Pluto's thermal balance than the extreme ultraviolet absorption by nitrogen. Two basic models of the lower atmosphere have been suggested, with a tropopause and a planetary surface at the bottom of the stellar occultation lightcurve, respectively, Vertical profiles, of temperature, density, gas velocity, and the CH4 mixing ratio have been calculated for these two models at low, mean, and high solar activity (six models). We prove that Pluto' " s atmosphere is restricted to 3060-4500 km, which makes possible a close flyby of future spacecraft. Implication for Pluto's evolution have also been discussed. and (2) Modeling of Pluto's photochemistry. Based on the results of (1), we have made some changes in the basic continuity equation and in the boundary conditions which reflect a unique can of hydrodynamic escape and therefore have not been used in modeling of other planetary atmospheres. We model photochemistry of 44 neutral and 23 ion species. This work required solution of a set of 67 second-order nonlinear ordinary differential equations. Two models have been developed. Each model consists of the vertical profiles for 67 species, their escape and precipitation rates. These models predict the chemical structure and basic chemical processes in the current atmosphere and possible implication of these processes for evolution. This study has also been completed in full.

Krasnopolsky, Vladimir A.↗
NASA NTRS1972

Diffusive and radiative effects on vaporization times of drops in film boiling

Diffusive and radiative effects are incorporated into an analysis for the vaporization time of drops in film boiling. The momentum, energy, and continuity equations are solved with some appropriate simplifications so as to obtain a simple closed form solution for the overall film boiling heat transfer coefficient. Next, a theoretical expression for the droplet vaporization time is developed and compared to the measured vaporization times of water droplets vaporizing into air, argon, nitrogen, and helium. The agreement between experiment and theory is good. Under the helium blanket, the diffusive evaporative component is significant in comparison to the film boiling component.

Baumeister, K. J.↗
NASA NTRS1971

On quasar evolution.

We examine the consequences for quasar statistics of a class of models describing the evolution of individual strong sources. The continuity equation for the change of density and luminosity with cosmological epoch determines the population, once a model for the evolution of an individual object is chosen. A dynamical model of spinning objects seems to agree satisfactorily with the present observational sample, both in density and in luminosity function; such a model requires that an individual object strongly brightens as time goes on. A genetic relationship between quasars and radio galaxies which qualitatively fits the observations is suggested by the model.

Cavaliere, A.↗
NASA NTRS1972

Synthesis of data obtained at Jicamarca, Peru, during the September 11, 1969, eclipse.

Results of continuous measurements of electron temperatures, electron concentrations, and vertical plasma drift made at Jicamarca during the Sept. 11, 1969, solar eclipse and of control measurements made on Sept. 13, 1969. Synthesis of the observed electron concentrations was made, using a model that solved the time-dependent electron-ion continuity equations. Ions O(-), NO(+), O2(+), and N2(+) were treated. Physical and chemical processes pertinent to the F region were considered in a realistic way. At noon, 300 km above Jicamarca, the values q = 290 per cu cm per sec for the O(+) production rate, beta = 1.94 x 0.0001 per sec for the loss coefficient, and H = 59 km for the atomic oxygen scale height were obtained. All large-scale features observed in the F2 region were synthesized by the model. This synthesis was not sensitive to a simultaneous 30% reduction of q and beta.

Sterling, D. L.↗
NASA NTRS1972

The electron heating rate and ion chemistry in the thermosphere above Wallops Island during the solar eclipse of 7 March 1970.

Measurement of the N2 concentration and temperature, the ion composition and concentrations, and the electron temperature up to 290 km about 30 and 5 min before totality during the Mar. 7, 1970, eclipse. The rockets traveled similar trajectories, thus permitting the purely temporal changes between flights to be resolved. The neutral temperature and N2 concentration changed little, but the electron temperature decreased by as much as 20% in the lower F region. The ion concentration decreased by about 30% in the F region and about 50% in the E region, with little change in relative ion composition. The electron cooling rates decreased by a factor of 6 in the lower F region, approximately in proportion to the change in the visible solar disk. A smaller than expected decrease in the cooling rate below 150 km between the two flights indicates a hardening of the solar spectrum and suggests a significant heat contribution from the solar corona near totality. The ion composition measurements were consistent with solutions of the ion continuity equations. A proper fit required a factor-of-three enhancement of the flux below 200 A, an amount also consistent with the electron heat balance analysis. Reactions involving the minor ions N(+) and N2(+) were found to be important for the ion chemistry of the major ions O2(+) and NO(+), especially at the time of eclipse.-

Brace, L. H.↗
NASA NTRS1972

Oxygen and hydrogen ion densities above Millstone Hill.

Measurements of the vertical flux of oxygen ions, when combined with simultaneous measurements of electron density and of electron and ion temperatures, present a unique opportunity to examine conditions in the topside ionosphere. The measured fluxes and densities may be used directly to evaluate terms in the O+ continuity equation without requiring any assumptions to be made about neutral winds, electric fields, or the ambipolar diffusion coefficient. From observations at Millstone Hill we have, in this way, derived the rate of loss of O+ in the charge-exchange reaction with hydrogen, the rate of photoionization of atomic oxygen, and the rate of loss of O+ in reactions with N2 and O2. In combination with laboratory and theoretical results, these rates can be interpreted to yield number densities of the corresponding neutral species. When the measured fluxes are examined for consistency with measured density gradients and temperature profiles, we find clear evidence of wind-induced or electrodynamic vertical drifts larger than 60 m/sec.

Schunk, R. W.↗
NASA NTRS1972

Synthesis of Jicamarca data during the great storm of March 8, 1970.

Continuous measurement of electron temperature and electron concentration during the great magnetic storm of Mar. 8, 1970, when the F2 peak rose as high as 800 km. Continuous measurements of the vertical component of E x B drift were made from 1130 to 1730 LT. A synthesis of the observed electron concentrations was made using a model that solved the time-dependent electron-ion continuity equation for O(+) and the molecular ions; the latter chemistry was included to improve the solutions at lower heights. It was found, using the observed values of vertical drift, that most of the observed features of the F2-region ionosphere were synthesized by the model. An interpretation of the synthesis that emphasizes the importance of horizontal diffusion at the equator is given. Observations are presented for Mar. 7, 8, and 9, 1970, including the Huancayo magnetograms, which display a close correlation with the drift measurements.

Woodman, R. F.↗