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 487 records · Page 27

Liquid jet pumped by rising gas bubbles

A two-phase mathematical model is proposed for calculating the induced turbulent vertical liquid flow. Bubbles provide a large buoyancy force and the associated drag on the liquid moves the liquid upward. The liquid pumped upward consists of the bubble wakes and the liquid brought into the jet region by turbulent entrainment. The expansion of the gas bubbles as they rise through the liquid is taken into account. The continuity and momentum equations are solved numerically for an axisymmetric air jet submerged in water. Water pumping rates are obtained as a function of air flow rate and depth of submergence. Comparisons are made with limited experimental information in the literature.

Hussain, N. A.↗

Liquid jet pumped by rising gas bubbles

From observations of a stream of gas bubbles rising through a liquid, a two-phase mathematical model is proposed for calculating the induced turbulent vertical liquid flow. The bubbles provide a large buoyancy force and the associated drag on the liquid moves the liquid upward. The liquid pumped upward consists of the bubble wakes and the liquid brought into the jet region by turbulent entrainment. The expansion of the gas bubbles as they arise through the liquid is taken into account. The continuity and momentum equations are solved numerically for an axisymmetric air jet submerged in water. Water pumping rates are obtained as a function of air flow rate and depth of submergence. Comparisons are made with limited experimental information in the literature.

Hussain, N. A.↗

A transverse Kelvin-Helmholtz instability in a magnetized plasma

An analysis is conducted of the transverse Kelvin-Helmholtz instability in a magnetized plasma for unstable flute modes. The analysis makes use of a two-fluid model. Details regarding the instability calculation are discussed, taking into account the ion continuity and momentum equations, the solution of a zero-order and a first-order component, and the properties of the solution. It is expected that the linear calculation conducted will apply to situations in which the plasma has experienced no more than a few growth periods.

Kintner, P.↗

A time dependent difference theory for sound propagation in ducts with flow

A time dependent numerical solution of the linearized continuity and momentum equation was developed for sound propagation in a two dimensional straight hard or soft wall duct with a sheared mean flow. The time dependent governing acoustic difference equations and boundary conditions were developed along with a numerical determination of the maximum stable time increments. A harmonic noise source radiating into a quiescent duct was analyzed. This explicit iteration method then calculated stepwise in real time to obtain the transient as well as the steady state solution of the acoustic field. Example calculations were presented for sound propagation in hard and soft wall ducts, with no flow and plug flow. Although the problem with sheared flow was formulated and programmed, sample calculations were not examined. The time dependent finite difference analysis was found to be superior to the steady state finite difference and finite element techniques because of shorter solution times and the elimination of large matrix storage requirements.

Baumeister, K. J.↗

A time dependent difference theory for sound propagation in ducts with flow

A time dependent numerical solution of the linearized continuity and momentum equation is developed for sound propagation in a two-dimensional straight hard or soft wall duct with a sheared mean flow. The time dependent governing acoustic-difference equations and boundary conditions are developed along with a numerical determination of the maximum stable time increments. The analysis begins with a harmonic noise source radiating into a quiescent duct. This explicit iteration method then calculates stepwise in real time to obtain the transient as well as the 'steady' state solution of the acoustic field. Example calculations are presented for sound propagation in hard and soft wall ducts, with no flow and with plug flow. Although the problem with sheared flow has been formulated and programmed, sample calculations have not yet been examined. So far, the time dependent finite difference analysis has been found to be superior to the steady state finite difference and finite element techniques because of shorter solution times and the elimination of large matrix storage requirements.

Baumeister, K. J.↗

Model calculations of the dayside ionosphere of Venus - Ionic composition

Comprehensive model calculations of the dayside ion density distributions were carried out and compared with results from the Pioneer Venus ion mass spectrometer. The coupled continuity and momentum equations were solved for O2(+), O(+), CO2(+), C(+), N(+), He(+), and H(+) densities for altitudes well away from the ionopause, where the horizontal transport terms are negligible. Chemical equilibrium solutions, describing conditions below about 200 km, were also obtained for N2(+), NO(+), and CO(+). The agreement between the model calculations of ion density and the measurements is good for some species, such as O(+), and rather poor for others, such as CO(+), indicating that while a basic understanding of the major chemical and physical processes controlling the composition and vertical distribution of the dayside Venus ionosphere, well below the ionopause, has been achieved, there are many important details requiring further investigations.

Nagy, A. F.↗

Asymptotic freedom in solids - A theorem

A cusp theorem is proved that relates the zero-separation value and slope of two-particle position correlation functions in quantum many-body systems with Coulombic interactions. The theorem is independent of the particle type and symmetry of the wave function. Its proof uses only the integral form of the Schroedinger equation and the continuity and exponential decay of the wave function. It is used to derive a sum rule for the electron-gas structure factor and an exact statement about the screening of point charges. Applications to atomic-orbital-based calculations for H2 and metallic H are described.

Carlsson, A. E.↗

The chemistry of metastable species in the Venusian ionosphere

Reactions of metastable species are important in determining the densities of minor ions in the Venusian ionosphere. Calculations are carried out in which the coupled continuity and momentum equations are solved for twelve ions and four neutral species in the dayside ionosphere, including O(+)(2D), O(2P), N(2D), and N(2P). Altitude profiles of these metastable species are presented. Their reactions are shown to be a significant source of several minor ions, especially N2(+), CO(+), and N(+). The discrepancies which existed between model and measured densities of these ions are resolved.

Fox, J. L.↗

Numerical investigation of unsteady flow development in a nozzle-duct configuration

A computational approach has been used to resolve the transient phenomena caused by a rocket engine starting up and exhausting into a short duct. The results are obtained from the finite-difference Navier-Stokes, continuity, and energy equations for a single component gas. Using a recently developed numerical technique to account for the time-varying boundary conditions at the nozzle throat and the duct openings, the numerical simulation of the idealized ignition flow model has yielded some insight into the complex interactions between the wave patterns and the vortical flow. The present findings verify the hypothesis that a lateral expansion of the jetstream outside the nozzle will generate an over-pressure pulse on the duct wall if the jetstream is restricted within the nozzle by flow separation. The numerical simulations of this complex flow problem should be useful for improving simple correlation techniques used for engineering purposes.

Li, C. P.↗

An analytical investigation of shape control of large space structures by applied temperatures

An analytical procedure for the static shape control of flexible space structures subjected to thermal distortions is developed which is based on prescribing temperatures in control elements having much higher coefficients of thermal expansion than the main structure. The temperatures at the control elements are defined so as to minimize the overall thermal distortion of the structure from its ideal shape, and a matrix equation is obtained which can be solved for the set of optimum control temperatures. A formulation of the procedure for continuous structures governed by differential equations and a formulation for discrete (finite element modeled) structures governed by matrix equations are presented. The equations from the continuous formulation are employed for the shape control of a simple beam distorted by nonuniform heating, and the discrete formulation is applied in a general purpose finite-element structural analysis computer program for the shape control of a 750 m radiometer antenna reflector dish subjected to orbital heating. A reduction in thermal distortion by a factor of nearly 50 was obtained with the use of only seven control elements. Results for four different sets of control locations for the antenna are presented in which reductions in distortion of up to a factor of four were obtained.

Haftka, R. T.↗

A theoretical prediction of the acoustic pressure generated by turbulence-flame front interactions

The equations of momentum annd continuity are combined and linearized yielding the one dimensional nonhomogeneous acoustic wave equation. Three terms in the non-homogeneous equation act as acoustic sources and are taken to be forcing functions acting on the homogeneous wave equation. The three source terms are: fluctuating entropy, turbulence gradients, and turbulence-flame interactions. Each source term is discussed. The turbulence-flame interaction source is used as the basis for computing the source acoustic pressure from the Fourier transformed wave equation. Pressure fluctuations created in turbopump gas generators and turbines may act as a forcing function for turbine and propellant tube vibrations in Earth to orbit space propulsion systems and could reduce their life expectancy. A preliminary assessment of the acoustic pressure fluctuations in such systems is presented.

Huff, R. G.↗

The statistical theory of the fracture of fragile bodies. Part 2: The integral equation method

It is demonstrated how with the aid of a bending test, the Weibull fracture risk function can be determined - without postulating its analytical form - by resolving an integral equation. The respective solutions for rectangular and circular section beams are given. In the first case the function is expressed as an algorithm and in the second, in the form of series. Taking into account that the cumulative fracture probability appearing in the solution to the integral equation must be continuous and monotonically increasing, any case of fabrication or selection of samples can be treated.

Kittl, P.↗

The interplanetary electric field, cleft currents and plasma convection in the polar caps

The relationship between the pattern of plasma convection in the polar cleft and the dynamics of the interplanetary electric field (IEF) is examined theoretically. It is shown that owing to the geometrical properties of the magnetosphere, the East-West component of the IEF will drive field-aligned currents which connect to the ionosphere at points lying on either side of noon, while currents associated with the North-South component of the IEF will connect the two polar caps as sheet currents, also centered at 12 MLT. In order to describe the consequences of the Interplanetary Magnetic Field (IMF) effects upon high-latitude electric fields and convection patterns, a series of numerical simulations was carried out. The simulations were based on a solution to the steady-state equation of current continuity in a height-integrated ionospheric current. The simulations demonstrate that a simple hydrodynamical model can account for the narrow 'throats' of strong dayside antisunward convection observed during periods of southward interplanetary IMF drift, as well as the sunward convection observed during periods of strongly northward IMF drift.

Banks, P. M.↗

A theoretical prediction of the acoustic pressure generated by turbulence-flame front interactions

The equations of momentum and continuity are combined and linearized yielding the one dimensional nonhomogeneous acoustic wave equation. Three terms in the non-homogeneous equation act as acoustic sources and are taken to be forcing functions acting on the homogeneous wave equation. The three source terms are: fluctuating entropy, turbulence gradients, and turbulence-flame interactions. Each source term is discussed. The turbulence-flame interaction source is used as the basis for computing the source acoustic pressure from the Fourier transformed wave equation. Pressure fluctuations created in turbopump gas generators and turbines may act as a forcing function for turbine and propellant tube vibrations in earth to orbit space propulsion systems and could reduce their life expectancy. A preliminary assessment of the acoustic pressure fluctuations in such systems is presented.

Huff, R. G.↗

Temporal behavior of density perturbations in the polar wind

The time-dependent continuity and momentum equations for H(+) are solved in order to study the temporal evolution of density perturbations in the supersonic, collisionless polar wind. The results indicate that the sophisticated computer models of small-scale plasma expansions are indeed applicable to large-scale flow problems. The important prediction of the production of superthermal ions from small-scale simulations by the process of plasma expansion is borne out by the calculations in this paper. Energetic ions are produced for each type of density perturbation through the plasma expansion process. In the case of an extended density depletion, the forward-reverse shock pair forms when the depletion is very strong, but otherwise only the forward shock forms. In the case of localized density depletions, the density cavity evolves into two rarefaction waves joined by a forward-reverse shock pair. In the case of localized density enhancements, the shock pair evolves from compressive waves.

Singh, N.↗

A method for extracting meridonal winds from ionosonde measurements by using ionospheric models

There has been great progress in modelling and measuring the dynamics of the neutral upper atmosphere in recent years. However, future progress will depend on the availability of global measurements of neutral winds. Attention is drawn to a relatively cheap means of supplementing the data base of neutral winds provided by radar and optical measurements with data obtained by ionosondes. Rishbeth in his review of F-region dynamics, derived the relationship between the height of the F2 layer and the component of the neutral wind parallel to the magnetic field of the Earth. The sensitivity is examined of the height and density of the F2 layer over Boulder, Colorado on 30 July 1982 to changes in meridional wind speed using a comprehensive interhemispheric numerical model that solves the continuity and momentum equations for H+ and O+, the energy equations for Te and Ti, and the 2-stream photoelectron equations to obtain electron heating rates. For the neutral atmosphere temperature and densities, the mass spectrometer incoherent scatter radar model of Hedin was used.

Richards, P. G.↗

Interplanetary magnetic field effects on high latitude ionospheric convection

Relations between the electric field and the electric current in the ionosphere can be established on the basis of a system of mathematical and physical equations provided by the equations of current continuity and Ohm's law. For this reason, much of the synthesis of electric field and plasma velocity data in the F-region is made with the aid of similar data sets derived from field-aligned current and horizontal current measurements. During the past decade, the development of a self-consistent picture of the distribution and behavior of these measurements has proceeded almost in parallel. The present paper is concerned with the picture as it applies to the electric field and plasma drift velocity and its dependence on the interplanetary magnetic field. Attention is given to the southward interplanetary magnetic field and the northward interplanetary magnetic field.

Heelis, R. A.↗

Relating multitemporal meteorological satellite data to climatological data for Africa

The questions of surface-atmosphere interaction and effects of land surface changes have been investigated by studying the energy balance over Africa. The energy and mass balance model being developed is an adaptation of the Lettau climatonomy model. The climatonic approach is a systems approach which encompasses: (1) a process, (2) an input to the process (forcing function), (3) an output from the process (response function), (4) feedback, and (5) control or management of the system. Steady-state climate is described and parametrized using a series of one-dimensional differential continuity and balance equations for energy and mass.

Nicholson, Sharon E.↗