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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 253 records · Page 14
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

On the transport and propagation of relativistic electrons in galaxies

Analytic solutions to the time-dependent equation describing the transport of relativistic electrons that are being convected and diffused, and may be either gaining or losing energy, are described. The calculations yield a body of solutions from which specific ones can be chosen for the modelling of synchrotron radiation in the Galaxy and in other galaxies. The solutions allow for (1) spatially varying convection velocity; (2) an energy and spatially dependent diffusion coefficient; (3) adiabatic acceleration effects; (4) a term describing spatially dependent synchrotron loss and/or Fermi acceleration; (5) an injection source for the electrons that may be impulsive, steady-state, or variable-injection; (6) a spatial injection or spatially more diffuse source; (7) arbitrary energy dependence of the injection source; and (8) spatial and energy boundaries where the spatial or energy form of the convection, diffusion, and energy supply terms in the basic equation can change character.

Lerche, I.↗
NASA NTRS1977

Observations of galactic cosmic ray energy spectra between 1 and 9 AU

The variation of the 5 to 500 MeV/nuc cosmic ray helium component was studied between 1 and 9 A.U. using essentially identical detector systems on Pioneer 10 and 11 and Helios I. Between 100 and 200 MeV/nuc a radial gradient of 3.3?1.3%/A.U. is found. At 15 MeV/nuc this value increases to 20?4%/A.U. Between 4 and 9 A.U. a well defined intensity maximum is observed at approximately 17 MeV/nuc. The average adiabatic energy loss between 1 and 9 A.U. is approximately 4 MeV/nuc/A.U. The observed radial variation between 1 and 9 A.U. is well described by the Gleeson-Axford force field solution of the modulation equations over an energy range extending from 15 to 500 MeV/nuc and is in good agreement with the results reported by other Pioneer experiments. These values are much smaller than had been theoretically predicted.

Mcdonald, F. B.↗
NASA NTRS1988

Studies on pressure response of gas bubbles contributions of condensed droplets in bubbles generated by a uniform nucleation

The response of a tiny gas bubble under reduced pressure is investigated in its relation to cavitation. Equations of motion are formulated for gas mixtures inside the bubble and numerical calculations performed for several examples. The conclusions are as follows: (1) at the onset of bubble growth, the gas mixture inside it adiabatically expands and the temperature decreases. Condensed droplets appear inside the gas mixture due to a uniform nucleation and the temperature recovers, thus the motion of the bubble is apparently isothermal; (2) the evaporation and condensation coefficient largely affects bubble motions (maximum radius, period and rate of attenuation of the bubble oscillation) including the uniform contraction; (3) the oscillation period of the bubble is longer as the equilibrium bubble radius is larger when the surrounding pressure decreases stepwise. In this circumstance the temperature inside the bubble is kept constant due to condensation evaporation phenomena and is nearly isothermal; and (4) when the surrounding pressure decreases in a stepwise fashion, the critical pressure bubble radius relation becomes closer to that for the isothermal process if the bubble radius is larger than 8 microns.

Matsumoto, Y.↗
NASA NTRS1993

Collisionless parallel shocks

Consideration is given to a collisionless parallel shock based on solitary-type solutions of the modified derivative nonlinear Schroedinger equation (MDNLS) for parallel Alfven waves. The standard derivative nonlinear Schroedinger equation is generalized in order to include the possible anisotropy of the plasma distribution and higher-order Korteweg-de Vies-type dispersion. Stationary solutions of MDNLS are discussed. The anisotropic nature of 'adiabatic' reflections leads to the asymmetric particle distribution in the upstream as well as in the downstream regions of the shock. As a result, nonzero heat flux appears near the front of the shock. It is shown that this causes the stochastic behavior of the nonlinear waves, which can significantly contribute to the shock thermalization.

Khabibrakhmanov, I. KH.↗
NASA NTRS1995

Bounce-Averaged Hamiltonian for Charged Particles in an Axisymmetric but Nondipolar Model Magnetosphere

In order to facilitate bounce-averaged guiding center simulations of geomagnetically trapped particles, we express the kinetic energy of a particle with magnetic coordinates (L,phi) as an analytic function of the first two adiabatic invariants (M, J) and the L value of the field line. The magnetic field model is axisymmetric, consisting of a dipolar B field plus a uniform southward magnetic field parallel to the dipole moment mu(sub E). This model magnetosphere is surrounded by a circular equatorial neutral line whose radius b is an adjustable parameter. The L value of a field line is (by definition) inversely proportional to the flux enclosed by the corresponding magnetic shell of equatorial radius r(sub 0), and the L value at the neutral line (r(sub 0) = b) is denoted L*. The azimuthal coordinate phi measures magnetic local time. The best functional representation found for the normalized difference (L(exp 3)a(exp 3)/mu(sub E))(B(sub m) - B(sub 0)) between mirror-point field B(sub m) and equatorial field B(sub 0) along any field line is a 5-term expansion in powers (2/3 through 6/3) of the quantity X equivalent to (La/mu(sub E))(exp 1/2)K, where K equivalent to (J(exp 2)/8m(sub 0)M)(exp 1/2) is an adiabatically conserved quantity independent of particle energy, m(sub 0) is the rest mass of the particle, and a is the radius of the Earth. This functional form is motivated by results for limiting cases in which particles mirror very near and very far from the magnetic equator. Expansion coefficients corresponding to various powers of X are obtained from least squares fits to numerically computed results for X as a function of L and B(sub m). These are accurately expressible as fourth-order polynomials in (r(sub 0)/b)(exp 3), hence indirectly as functions of L/L* = 3La/2b. This representation, which leads (except for a manageably small region of parameter space) to better than 1% accuracy in the specification of B(sub m) as a function of K and L, allows bounce-averaged guiding center simulations to be performed without actually tracing the bounce motions of individual particles. Bounce-averaged drifts L' (meridional) and phi' (azimuthal) are proportional to derivatives of the Hamiltonian H (sum of kinetic and potential energies) with respect to phi and L, respectively. Our formulation thus provides a computationally efficient method for tracing the bounce-averaged adiabatic motion (conserving all three invariants) and nonadiabatic transport (violating the third invariant while conserving the first two invariants) of geomagnetically trapped particles in the model magnetosphere.

Schulz, Michael↗
NASA NTRS1982

Charged particle motions in the distended magnetospheres of Jupiter and Saturn

Charged particle motion in the guiding center approximation is analyzed for models of the Jovian and Saturnian magnetospheric magnetic fields based on Voyager magnetometer observations. Field lines are traced and exhibit the distention which arises from azimuthally circulating magnetospheric currents. The spatial dependencies of the guiding center bounce period and azimuthal drift rate are investigated for the model fields. Non-dipolar effects in the gradient-curvature drift rate are most important at the equator and affect particles with all mirror latitudes. The effect is a factor of 10-15 for Jupiter with its strong magnetodisc current and 1-2 for Saturn with its more moderate ring current. Limits of adiabaticity, where particle gyroradii become comparable with magnetic scale lengths, are discussed and are shown to occur at quite modest kinetic energies for protons and heavier ions.

Birmingham, T. J.↗
NASA NTRS1985

Radial diffusion in magnetodiscs

The orbits of charged particles in magnetodiscs are considered. The bounce motion is assumed adiabatic except for transits of a small equatorial region of weak magnetic field strength and high field curvature. Previous theory and modeling have shown that particles scatter randomly in pitch angle with each passage through the equator. A peaked distribution thus diffuses in pitch angle on the time scale of many bounces. It is argued in this paper that spatial diffusion is a further consequence when the magnetodisc has a longitudinal asymmetry. A general expression for DLL, the diffusion of equatorial crossing radii, is derived. DLL is evaluated explicitly for ions in Jupiter's 20-35 radii magnetodisc, assumed to be represented by Connerney et al.'s (1982) Voyager model plus a small image dipole asymmetry. Rates are energy, species, and space dependent but can average as much as a few tenths of a planetary radius per bounce period.

Birmingham, T. J.↗
NASA NTRS1988

Nonradial oscillations of neutron stars

Linear, adiabatic, Newtonian, nonradial pulsation analyses have been performed for finite-temperature neutron star models with a fluid core, solid crust, and thin surface fluid 'ocean', including the effects of the neutron star crust. The pulsation equations are considered, including the spheroidal and toroidal modes. A local analysis is performed to provide information about the pulsation modes in the short-wavelength limit. Numerical calculations are made on the mode spectrum and systematic properties. Damping mechanisms are investigated, including gravitational radiation damping, neutrino emission damping, electromagnetic radiation from an oscillating stellar magnetic field, nonadiabatic effects, and internal friction and viscosity.

Mcdermott, P. N.↗
NASA NTRS1980

A numerical investigation of thermal convection in a heat-generating fluid layer

Finite difference solutions of the equations governing thermal convection driven by uniform volumetric energy sources are presented for two-dimensional flows in a rectangular domain. The boundary conditions are a rigid (i.e, zero slip), zero heat-flux lower surface, rigid adiabatic sides, and either a rigid or free (i.e., zero shear) isothermal upper surface. Computations are carried out for Prandtl numbers from 0.05 to 20 and Rayleigh numbers from 5 x 10 to the 4th to 5 x 10 to the 8th. Nusselt numbers and average temperature profiles within the layer are in good agreement with experimental data for rigid-rigid boundaries. For rigid-free boundaries, Nusselt numbers are larger than in the former case. The structure of the flow and temperature fields in both cases is dominated by rolls, except at larger Rayleigh numbers where large-scale eddy transport occurs. Generally, low velocity upflows over broad regions of the layer are balanced by higher velocity downflows when the flow exhibits a cellular structure. The hydrodynamic constraint at the upper surface and the Prandtl number are found to influence only the detailed nature of flow and temperature fields. No truly steady velocity and temperature fields are found despite the fact that average Nusselt numbers reach steady values.

Emara, A. A.↗
NASA NTRS1986

Thermal shaft effects on load-carrying capacity of a fully coupled, variable-properties cryogenic journal bearing

The purpose of this work was to perform a rather complete analysis for a cryogenic (oxygen) journal bearing. The Reynolds equation required coupling and simultaneous solution with the fluid energy equation. To correctly account for the changes in the fluid viscosity, the fluid energy equation was coupled with the shaft and bearing heat conduction energy equations. The effects of pressure and temperature on the density, viscosity, and load-carrying capacity were further discussed as analysis parameters, with respect to relative eccentricity and the angular velocity. The isothermal fluid case and the adiabatic fluid case represented the limiting boundaries. The discussion was further extrapolated to study the Sommerfeld number dependency on the fluid Nusselt number and its consequence on possible total loss of load-carrying capacity and/or seizure (catastrophic failure).

Braun, M. J.↗
NASA NTRS1990

Titan's stratospheric temperatures - A case for dynamical inertia?

Voyager IRIS spectral radiances in the nu4-band of CH4 for the Titan atmosphere exhibit a hemispheric asymmetry. While asymmetry in the meridional distribution of opacity about the equator cannot be discounted, attention is given to the need for angular momentum transport concurrent with seasonally varying temperatures in the Titan stratosphere, which would maintain the cyclostrophic thermal wind relation between zonal winds and temperatures. The adiabatic heating and cooling associated with these motions can produce the observed temperature asymmetry.

Flasar, F. M.↗
NASA NTRS1982

Full-coverage film cooling

Transpiration cooling is treated and then full coverage discrete hole injection for three injection orientations. Spacings with pitch to diameter ratios of 5 and 10 are discussed. The array is staggered, with the transverse pitch and the streamwise pitch the same. Results are presented in terms of the Stanton number using the heat transfer coefficient defined in terms of the difference between the wall temperature and the free stream temperature. Two values of Stanton number are provided for each situation: one with the injectant at wall temperature, and the other with the injectant at free stream temperature. These two values are equivalent to knowing the heat transfer coefficient and the adiabatic effectiveness. The heat transfer coefficient thus defined is used with the actual wall temperature to and the actual gas temperature to calculate the heat load. The principle of superposition thus invoked is valid exactly when the governing equations are linear.

Moffat, R. J.↗
NASA NTRS2021

A Field-Particle Correlation Analysis of a Perpendicular Magnetized Collisionless Shock

Using the field-particle correlation technique, we examine the particle energization in a 1D-2V continuum Vlasov-Maxwell simulation of a perpendicular magnetized collisionless shock. The combination of the field-particle correlation technique with the high fidelity representation of the particle distribution function provided by a direct discretization of the Vlasov equation allows us to ascertain the details of the exchange of energy between the electromagnetic fields and the particles in phase space. We identify the velocity-space signatures of shock-drift acceleration of the ions and adiabatic heating of the electrons due to the perpendicular collisionless shock by constructing a simplified model with the minimum ingredients necessary to produce the observed energization signatures in the self-consistent Vlasov-Maxwell simulation. We are thus able to completely characterize the energy transfer in the perpendicular collisionless shock considered here and provide predictions for the application of the field-particle correlation technique to spacecraft measurements of collisionless shocks.

James Juno↗
NASA NTRS1988

Ion equation of state in quasi-parallel shocks - A simulation result

Ion equation of state in the quasi-parallel collisionless shock is deduced from simulation results. The simulations were performed for theta(bn) = 10 deg, beta = 0.5 and M sub A in the range from 1.2 to 8, where M sub A is the Alfven Mach number, beta is the upstream ratio of plasma pressure to magnetic pressure, and theta(bn) is the angle between the shock normal and the upstream magnetic field. The equation of state can be approximated by a power law with different exponents in the upstream and downstream sides of the shock transition region. The exponent in the upstream side of the transition region is much greater than the adiabatic value of 5/3 and increases with M sub A. The exponent in the downstream side of the transition region is slightly less than 5/3. The results show that ion heating in the quasi-parallel shock is highly nonadiabatic with a large increase in entropy and in temperature ratio in the upstream side of the transition region, while the heating is highly isentropic with a large increase in temperature difference across the principal density jump in the downstream side of the transition region.

Mandt, M. E.↗
NASA NTRS1972

Turbulent properties of a compressible boundary layer.

Turbulent shear-stress, eddy-viscosity, mixing-length, heat-flux and Prandtl number distributions across a hypersonic turbulent boundary layer have been determined from the 'time-averaged' conservation equations using experimental mean profile data obtained at several streamwise locations in a fully developed turbulent boundary layer with negligible pressure gradient. The eddy-viscosity, mixing-length and Prandtl number results show general agreement with previous incompressible and adiabatic compressible correlations. However, when the turbulent Prandtl number is defined using total enthalpy as opposed to static enthalpy no clear correlation of the results in the outer portion of the boundary layer could be obtained.

Horstman, C. C.↗
NASA NTRS1992

A diagnosis of the explosive development of two extratropical cyclones

This paper examines the 24-h explosive development periods of two extratropical cyclones, the first occurring over the Gulf Stream off the coast of New England from 18 to 19 January 1979 and the second occurring over the southeastern United States from 20 to 21 January 1979. The data used in this study are the First GARP (Global Atmospheric Research Program) Global Experiment (FGGE) level IIIb (SOP I) global analyses on a 4 deg latitude x 5 deg longitude grid. The parameter used to diagnose development is the geostrophic relative vorticity tendency calculated using an extended form of the Zwack-Okossi development equation. This development equation is similar to the Petterssen-Sutcliffe development equation, but is shown to be more complete by explicitly coupling surface development with forcing at all levels above the surface. Cyclonic-vorticity advection, warm-air advection, and latent heat release act to develop the two cyclones, while adiabatic cooling in the ascending air opposes development. Further, vertical profiles of the development quantities for these two cases reveal that vorticity and temperature advection maximize in the 200-300-mb layer, while the latent heat release maximum is typically below 500 mb.

Lupo, Anthony R.↗
NASA NTRS1992

Spin-up of a rapidly rotating star by angular momentum loss - Effects of general relativity

It has recently been shown that a rapidly rotating Newtonian star can spin up by radiating angular momentum. Extremely fast pulsars losing energy and angular momentum by magnetic dipole radiation or gravitational radiation may exhibit this behavior. Here, we show that this phenomenon is more widespread for rapidly rotating stars in general relativity. We construct and tabulate polytropic sequences of fully relativistic rotating stars of constant rest mass and entropy. We find that the range of adiabatic indices allowing spin-up extends somewhat above 4/3 because of the nonlinear effects of relativistic gravity. In addition, there is a new class of 'supramassive' stars which will inevitably spin up by losing angular momentum regardless of their equation of state. A supramassive star, spinning up via angular momentum loss, will ultimately evolve until it becomes unstable to catastrophic collapse to a black hole. Spin-up in a rapidly rotating star may thus be an observational precursor to such collapse.

Cook, Gregory B.↗
NASA NTRS2013

Modeling of Particle Acceleration at Multiple Shocks Via Diffusive Shock Acceleration: Preliminary Results

We present preliminary results from a model that diffusively accelerates particles at multiple shocks. Our basic approach is related to box models (Protheroe and Stanev, 1998; Moraal and Axford, 1983; Ball and Kirk, 1992; Drury et al., 1999) in which a distribution of particles is diffusively accelerated inside the box while simultaneously experiencing decompression through adiabatic expansion and losses from the convection and diffusion of particles outside the box (Melrose and Pope, 1993; Zank et al., 2000). We adiabatically decompress the accelerated particle distribution between each shock by either the method explored in Melrose and Pope (1993) and Pope and Melrose (1994) or by the approach set forth in Zank et al. (2000) where we solve the transport equation by a method analogous to operator splitting. The second method incorporates the additional loss terms of convection and diffusion and allows for the use of a variable time between shocks. We use a maximum injection energy (Emax) appropriate for quasi-parallel and quasi-perpendicular shocks (Zank et al., 2000, 2006; Dosch and Shalchi, 2010) and provide a preliminary application of the diffusive acceleration of particles by multiple shocks with frequencies appropriate for solar maximum (i.e., a non-Markovian process).

Parker, Linda Neergaard↗