Search NASA⌕ Search

SEARCH · Search NASA

Results for “HYDRODYNAMIC 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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

A procedure for computing surface wave trajectories on an inhomogeneous surface

Equations are derived for computing surface waves on smooth surfaces, including surfaces with a nonuniform wave speed. The prior literature dealt primarily with the theoretical development with little consideration given to computational methods, and examples were limited to waves on surfaces of simple analytic description, such as cones, spheres, and cylinders. The computational procedure presented is a relatively general method. Sample calculations illustrate the procedure for a class of practical shapes of the type that include aerodynamic and hydrodynamic surfaces. Equations are also included for computing the spreading of rays into a surrounding medium that will support waves.

Barger, Raymond L.↗
NASA NTRS1975

Relativistic astrophysics

The coordinate independence of gravitational radiation and the parameterized post-Newtonian approximation from which it is extended are described. The general consistency of the field equations with Bianchi identities, gauge conditions, and the Newtonian limit of the perfect fluid equations of hydrodynamics are studied. A technique of modification is indicated for application to vector-metric or double metric theories, as well as to scalar-tensor theories.

Smalley, L. L.↗
NASA NTRS1976

Face-seal lubrication: 1: Proposed and published models

The numerous published theories on the mechanism of hydrodynamic lubrication of face seals were reviewed. These theories employ either an inclined-slider-bearing macrogeometry or an inclined-slider-bearing microgeometry to produce hydrodynamic pressure that separates the surfaces of the primary seal. Secondary seal friction and primary ring inertia effects are not considered. Hypothetical seal operating models were devised to include secondary seal friction and primary ring inertia effects. It was hypothesized that these effects induce relative angular misalinement of the primary seal faces and that this misalinement is, in effect, an inclined slider macrogeometry. Stable running was postulated for some of these hypothetical operating models. In others, periodic loss of hydrodynamic lubrication was postulated to be possible with certain combinations of waviness and angular misalinement. Application of restrictions that apply to seal operation led to a hydrodynamic governing equation for the new model that is a two-dimensional, time-dependent Reynolds equation with the short-bearing approximation.

Ludwig, L. P.↗
NASA NTRS1985

A granular flow model for dense planetary rings

In the present study of the viscosity of a differentially rotating particle disk, in the limiting case where the particles are densely packed and their collective behavior resembles that of a liquid, the pressure tensor is derived from both the equations of hydrodynamics and a simple kinetic model of collisions due to Haff (1983). Density waves and narrow circular rings are unstable if the liquid approximation applies, and the consequent nonlinear perturbations may generate 'splashing' of the ring material in the vertical direction. These results are pertinent to the origin of the ellipticities of ringlets, the nonaxisymmetric features near the outer edge of the Saturn B ring, and unexplained residuals in kinematic models of the Saturn and Uranus rings.

Borderies, N.↗
NASA NTRS1986

EHD analysis of and experiments on pumping Leningrader seals

Analysis and design charts have been generated to provide design data for Pumping Leningrader Reciprocating Rod Seals. The analytical treatment divides the seal into three regions: an inlet zone, induced with the use of an expansion ring, a contact zone, and an exit zone. Complete solutions have been obtained by matching elasticity equations with hydrodynamic theory. Experiments, although of a limited nature, did demonstrate the ability of the seal design analysis to provide viable seals.

Eusepi, M. W.↗
NASA NTRS1987

Ion escape fluxes from the terrestrial high-latitude ionosphere

In this paper, the hydrodynamic transport equations for H(+) and O(+) are solved, including the important dynamic, collisional, and chemical effects that operate in the F region ionosphere below regions of ion acceleration. It is found that the most important parameter controlling the amount of O(+) in plasma outflows is the total ion flux demand imposed on the ionosphere by the higher-altitude acceleration region. The O(+) content is further modulated by the temperature of the exosphere and the resultant composition in the topside ionosphere, and by the location of the lower boundary of the ion acceleration region relative to the crossover altitude, where O and H have equal densities. As solar activity increases, the limiting O(+) escape flux increases, while the limiting H(+) escape flux decreases.

Barakat, A. R.↗
NASA NTRS1988

O(+) and H(+) escape fluxes from the polar regions

The hydrodynamic transport equations are solved for H(+) and O(+) with allowance made for the important dynamic, collisional, and chemical effects that operate in the F region ionosphere below regions of ion acceleration. It is found that the total ion flux demand imposed on the ionosphere by the higher altitude acceleration region is an important parameter controlling the amount of O(+) in plasma outflows. As solar activity increases, there is an increase in the limiting O(+) escape flux and a decrease in the limiting H(+) escape flux.

Barakat, A. R.↗
NASA NTRS1989

Evolution of the solar nebula. I - Nonaxisymmetric structure during nebula formation

Numerical solutions of the equations of hydrodynamics, gravitation, and radiative transfer in three spatial dimensions are used to model the formation and time evolution of the early solar nebula in order to learn whether or not gravitational torques between nonaxisymmetric structures in the solar nebula can transport angular momentum rapidly enough to produce nebula clearing on astronomically indicated (10 to the 5 to 10 to the 7 yr) time scales. The models involve solutions for the collapse of spherical clouds with assumed initial density and rotation profiles onto protosuns of variable mass. Most of the models assume uniform initial density and rotation, and have variations in the initial parameters of cloud mass, cloud rotation rate, and protosun mass which are chosen to simulate a range of possible phases of early solar nebula evolution. The models show little tendency for directly forming small numbers of giant gaseous protoplanets through gaseous gravitational instability.

Boss, Alan P.↗
NASA NTRS1990

Reynolds stress closure in jet flows using wave models

A collection of papers is presented. The outline of this report is as follows. Chapter three contains a description of a weakly nonlinear turbulence model that was developed. An essential part of the application of such a closure scheme to general geometry jets is the solution of the local hydrodynamic stability equation for a given jet cross-section. Chapter four describes the conformal mapping schemes used to map such geometries onto a simple computational domain. Chapter five describes a solution of a stability problem for circular, elliptic, and rectangular geometries. In chapter six linear models for the shock shell structure in non-circular jets is given. The appendices contain reprints of papers also published during this study including the following topics: (1) instability of elliptic jets; (2) a technique for predicting the shock cell structure in non-circular jets using a vortex sheet model; and (3) the resonant interaction between twin supersonic jets.

Morris, Philip J.↗
NASA NTRS1990

Radiative shocks and nonequilibrium chemistry in the early universe - Galaxy and primordial star formation

The nonequilibrium radiative cooling, recombination, and molecule formation behind steady-state shock waves in primordial composition gas is studied. The hydrodynamical conservation equations are solved as well as equations for nonequilibrium ionization, recombination, and molecule formation and the equation of radiative transfer. The shocked gas is found to cool faster than it can recombine; as a result it is able to form an H2 concentration as high as 0.001 or higher via the formation of H(-) and H2(+) intermediaries due to the enhanced nonequilibrium ionization at 10,000 K. With such an H2 concentration, the gas cools by rotational-vibrational line excitation of H2 molecules to well below the canonical final temperature of 10,000 K for a molecule-free gas without metals. It is shown that, as the level of external ionizing and dissociating radiation flux is increased, the formation of and cooling by H2 molecules can be inhibited and delayed.

Shapiro, Paul R.↗
NASA NTRS1991

Formation of the protosolar nebula

Theoretical models are discussed of the collapse of a dense molecular cloud core to form the protosolar nebula that produce the sun and the planet. The theoretical models use the equations of hydrodynamics, gravitation, and radiative transfer to follow the time evolution of a cloud collapsing under its own self-gravity. Both semi-analytical and fully numerical solutions (in two and three spatial dimensions) were calculated by several workers, One challenge is to find a set of initial conditions that will lead to the formation of a suitable protosolar nebula. Detailed results are shown for 2-D models, both with and without turbulent viscosity for redistributing angular momentum, and for 3-D models investigating the strength of gravitational torques associated with nonaxisymmetry produced during the collapse phase.

Tscharnuter, Werner M.↗
NASA NTRS1993

A two-dimensional relativistic (Gamma = 3.25) jet simulation

A numerical simulation of a fully relativistic jet in slab geometry is presented. The simulation uses a covariant divergence formulation of the equations of hydrodynamics. A Mach disk familiar from nonrelativistic simulations is observed. We also find relativistically narrow streaks in the pressure distribution near the aperture.

Van Putten, Maurice H. P. M.↗