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Results for “ADIABATIC 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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

An analytic solution to the steady-state double adiabatic equations

A set of 20 generalized moment-transport equations applicable to low-beta (low random energy density/magnetic energy density) plasmas of thermal origin in rotating planetary magnetospheres. An analytic solution is obtained for a set of simplified equations characterizing the steady-state transport of collisionless plasma; the novel element of this analytic solution is a closed-form solution for the parallel-flow velocity variation along magnetic field lines. It is shown that only T(perpendicular)/B remains constant along the field line, while density, parallel temperature, and parallel Mach number vary.

Gombosi, Tamas I.↗
NASA NTRS1947

Equations for Adiabatic but Rotational Steady Gas Flows without Friction

This paper makes the following assumptions: 1) The flowing gases are assumed to have uniform energy distribution. ("Isoenergetic gas flows," that is valid with the same constants for the the energy equation entire flow.) This is correct, for example, for gas flows issuing from a region of constant pressure, density, temperature, end velocity. This property is not destroyed by compression shocks because of the universal validity of the energy law. 2) The gas behaves adiabatically, not during the compression shock itself but both before and after the shock. However, the adiabatic equation (p/rho(sup kappa) = C) is not valid for the entire gas flow with the same constant C but rather with an appropriate individual constant for each portion of the gas. For steady flows, this means that the constant C of the adiabatic equation is a function of the stream function. Consequently, a gas that has been flowing "isentropically",that is, with the same constant C of the adiabatic equation throughout (for example, in origination from a region of constant density, temperature, and velocity) no longer remains isentropic after a compression shock if the compression shock is not extremely simple (wedge shaped in a two-dimensional flow or cone shaped in a rotationally symmetrical flow). The solution of nonisentropic flows is therefore an urgent necessity.

Schaefer, Manfred↗
NASA NTRS1947

Calculation of the Pressure Distribution on Bodies of Revolution in the Subsonic Flow of a Gas: Axially Symmetrical Flow - Part 1

The present report concerns a method of computing the velocity and pressure distributions on bodies of revolution in axially symmetrical flow in the subsonic range. The differential equation for the velocity potential Phi of a compressible fluid motion is linearized tn the conventional manner, and then put in the form Delta(Phi) = 0 by affine transformation. The quantity Phi represents the velocity potential of a fictitious incompressible flow, for which a constant superposition of sources by sections is secured by a method patterned after von Karman which must comply with the boundary condition delta(phi)/delta(n) = 0 at the originally specified contour. This requirement yields for the "pseudo-stream function" psi a differential equation which must be fulfilled for as many points on the contour as source lengths are assumed. In this manner, the problem of defining the still unknown source intensities is reduced to the solution of an inhomogeneous equation system. The pressure distribution is then determined with the aid of Bernoulli's equation and adiabatic equation of state. Lastly, the pressure distributions in compressible and incompressible medium are compared on a model problem.

Bilharz, Herbert↗
NASA NTRS1965

Atmospheric oscillations

Motion, continuity, and adiabatic equations for upper atmospheric oscillation

ADIABATIC EQUATION↗
NASA NTRS1990

Resonant Alfven wave heating of the plasma sheet boundary layer

The exchange of energy between the plasma mantle and the plasma sheet boundary layer (PSBL) is examined with a one-dimensional magnetotail model. The energy exchange occurs via Poynting flux generated by the localized mode conversion of a surface wave to an Alfven wave. This Poynting flux propagates through the lobe and into the PSBL where it is absorbed by two processes. The first arises from a gradient in the plasma beta causing a smooth absorption of Poynting flux. The second process results from the localized mode conversion of the decaying surface wave to an Alfven wave, causing a localized absorption of energy. A numerical solution of the linearized ideal MHD equations is obtained by assuming an adiabatic equation of state.

Harrold, B. G.↗
NASA NTRS1983

The adiabatic motion of charged dust grains in rotating magnetospheres

Adiabatic equations of motion are derived for the micrometer-sized dust grains detected in the Jovian and Saturn magnetospheres by the Pioneer 10 and 11 spacecraft. The adiabatic theory of charged particle motion is extended to the case of variable grain charge. Attention is focused on the innermost and outermost limits to the grain orbit evolution, with all orbits tending to become circular with time. The parameters such as the center equation of motion, the drift velocity, and the parallel equation of motion are obtained for grains in a rotating magnetosphere. Consideration is given to the effects of periodic grain charge-discharge, which are affected by the ambient plasma properties and the grain plasma velocity. The charge-discharge process at the gyrofrequency is determined to eliminate the invariance of the magnetic moment and cause the grain to exhibit radial movement. The magnetic moment increases or decreases as a function of the gyrophase of the charge variation.

Northrop, T. G.↗
NASA NTRS1992

Nonadiabatic processes in the Earth's magnetotail

The challenge of the assumption of an adiabatic equation of state for the plasma sheet made in several studies of quiet time convection and expansive phase activity is addressed. The observed plasma pressures at distances of approximately 10 RE are less than that predicted by adiabatic convection by over an order of magnitude. Studies of the local plasma properties for individual events as well as an ensemble of all quiet time plasma sheet samples during two years of ISEE coverage show that the polytropic index is below 5/3, and on occasion may be less than unity. During substorm activity the main effect of the plasma sheet is an increase in plasma temperature. This is seen both in statistical and case studies of individual substorms. The nature of the heating process is nonadiabatic, as evidenced by the anticorrelation between changes in plasma density and temperature. These recent observations of nonadiabatic behavior emphasize thermodynamic processes in the magnetosphere, an area which has been largely ignored.

Huang, C. Y.↗
NASA NTRS1971

Collisionless solar wind. II - Variable electron temperature.

Examination of a two-component ?model' for the solar wind, in which the protons become collisionless beyond a distance from the solar center equal to or greater than 10 solar radii, where they are already highly supersonic. The proton temperatures are found from the double adiabatic equation of state. The electrons are highly subsonic, and their temperature profile is prescribed ad hoc. The momentum equations for the electrons and protons are solved subject to the conditions of quasi-neutrality and zero charge efflux from the sun. Some of the principal results are: (1) the proton thermal anisotropy is substantially reduced when solar rotation is considered; (2) solar rotation leads to significantly lower mean proton temperatures; and (3) the electron temperature profile in the supersonic region is the primary parameter determining flow acceleration there.

Hollweg, J. V.↗
NASA NTRS1978

Derivation and evaluation of an approximate analysis for three-dimensional viscous subsonic flow with large secondary velocities

An approximate analysis is presented for calculating three-dimensional, low Mach number, laminar viscous flows in curved passages with large secondary flows and corner boundary layers. The analysis is based on the decomposition of the overall velocity field into inviscid and viscous components with the overall velocity being determined from superposition. An incompressible vorticity transport equation is used to estimate inviscid secondary flow velocities to be used as corrections to the potential flow velocity field. A parabolized streamwise momentum equation coupled to an adiabatic energy equation and global continuity equation is used to obtain an approximate viscous correction to the pressure and longitudinal velocity fields. A collateral flow assumption is invoked to estimate the viscous correction to the transverse velocity fields. The approximate analysis is solved numerically using an implicit ADI solution for the viscous pressure and velocity fields. An iterative ADI procedure is used to solve for the inviscid secondary vorticity and velocity fields. This method was applied to computing the flow within a turbine vane passage with inlet flow conditions of M = 0.1 and M = 0.25, Re = 1000 and adiabatic walls, and for a constant radius curved rectangular duct with R/D = 12 and 14 and with inlet flow conditions of M = 0.1, Re = 1000, and adiabatic walls.

Anderson, O. L.↗
NASA NTRS1983

A new stream function formulation for the Euler equations

A new stream function formulation is developed for the solution of Euler's equations in the transonic flow region. The stream function and the density are the dependent variables in this method, while the governing equations for adiabatic flow are the momentum equations which are solved in the strong conservation law form. The application of this method does not require a knowledge of the vorticity. The algorithm is combined with the automatic grid solver (GRAPE) of Steger and Sorenson (1979) in order to study arbitrary geometries. Results of the application of this method are presented for the NACA 0012 airfoil at various Mach numbers and angles of attack, and cylinders. In addition, detailed comparisons are made with other solutions of the Euler equations.

Atkins, H. L.↗
NASA NTRS1989

Siphon flows in isolated magnetic flux tubes. II - Adiabatic flows

This paper extends the study of steady siphon flows in isolated magnetic flux tubes surrounded by field-free gas to the case of adiabatic flows. The basic equations governing steady adiabatic siphon flows in a thin, isolated magnetic flux tube are summarized, and qualitative features of adiabatic flows in elevated, arched flux tubes are discussed. The equations are then cast in nondimensional form and the results of numerical computations of adiabatic siphon flows in arched flux tubes are presented along with comparisons between isothermal and adiabatic flows. The effects of making the interior of the flux tube hotter or colder than the surrounding atmosphere at the upstream footpoint of the arch is considered. In this case, is it found that the adiabatic flows are qualitatively similar to the isothermal flows, with adiabatic cooling producing quantitative differences. Critical flows can produce a bulge point in the rising part of the arch and a concentration of magnetic flux above the bulge point.

Montesinos, Benjamin↗