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NASA NTRS1975

Isothermal blast wave model of supernova remnants

The validity of the 'adiabatic' assumption in supernova-remnant calculations is examined, and the alternative extreme of an isothermal blast wave is explored. It is concluded that, because of thermal conductivity, the large temperature gradients predicted by the adiabatic model probably are not maintained in nature. Self-similar solutions to the hydrodynamic equations for an isothermal blast wave have been found and studied. These solutions are then used to determine the relationship between X-ray observations and inferred parameters of supernova remnants. A comparison of the present results with those for the adiabatic model indicates differences which are less than present observational uncertainties. It is concluded that most parameters of supernova remnants inferred from X-ray measurements are relatively insensitive to the specifics of the blast-wave model.

Solinger, A.↗

NASA NTRS1975

Further investigations of Jupiter models

It is noted that previously calculated models of Jupiter, in which the H/He ratio is assumed to be solar, required the inclusion of considerable additional mass in the form of volatilized condensates in the atmosphere and excess mass in the central core. Several additional models are considered in this paper which take into account the stricter constraints imposed by Pioneer 10 measurements of Jupiter's gravitational moments. These measurements have indicated that the mass of the excess volatilized condensates (assumed to be water) relative to the core mass (assumed to be rock) exceeds the relevant solar ratio. The present models are tested for sensitivity to variations in the H/He ratio, in the softness of the equation of state for water, in the treatment of the internal adiabat, in departures from an internal adiabat, and in temperature at the one-bar level. The preliminary results indicate that the ratio of excess water to rock in Jupiter is considerably in excess of the solar value.

Podolak, M.↗

NASA NTRS1992

Two-equation turbulence modeling for 3-D hypersonic flows

An investigation to verify, incorporate and develop two-equation turbulence models for three-dimensional high speed flows is presented. The current design effort of hypersonic vehicles has led to an intensive study of turbulence models for compressible hypersonic flows. This research complements an extensive review of experimental data and the current development of 2D turbulence models. The review of experimental data on 2D and 3D flows includes complex hypersonic flows with pressure profiles, skin friction, wall heat transfer, and turbulence statistics data. In a parallel effort, turbulence models for high speed flows have been tested against flat plate boundary layers, and are being tested against the 2D database. In the present paper, we present the results of 3D Navier-Stokes numerical simulations with an improved k-omega two-equation turbulence model against experimental data and empirical correlations of an adiabatic flat plate boundary layer, a cold wall flat plate boundary layer, and a 3D database flow, the interaction of an oblique shock wave and a thick turbulent boundary layer with a free stream Mach number = 8.18 and Reynolds number = 5 x 10 to the 6th.

Bardina, J. E.↗

NASA NTRS2003

Slat Heater Boxes for Thermal Vacuum Testing

Slat heater boxes have been invented for controlling the sink temperatures of objects under test in a thermal vacuum chamber, the walls of which are cooled to the temperature of liquid nitrogen. A slat heater box (see Figure 1) includes a framework of struts that support electrically heated slats that are coated with a high-emissivity optically gray paint. The slats can be grouped together into heater zones for the purpose of maintaining an even temperature within each side. The sink temperature of an object under test is defined as the steady-state temperature of the object in the vacuum/ radiative environment during the absence of any internal heat source or sink. The slat heater box makes it possible to closely control the radiation environment to obtain a desired sink temperature. The slat heater box is placed inside the cold thermal vacuum chamber, and the object under test is placed inside (but not in contact with) the slat heater box. The slat heaters occupy about a third of the field of view from any point on the surface of the object under test, the remainder of the field of view being occupied by the cold chamber wall. Thus, the radiation environment is established by the combined effects of the slat heater box and the cold chamber wall. Given (1) the temperature of the chamber wall, (2) the fractions of the field of view occupied by the chamber wall and the slat heater box, and (3) the emissivities of the slats, chamber wall, and the surface of object under test, the slat temperature required to maintain a desired sink temperature can be calculated by solving the equations of gray-body radiation for the steady-state adiabatic case (equal absorption and emission by the object under test). Slat heater boxes offer an important advantage over the infrared lamps that have been previously used to obtain desired sink temperatures: In comparison with an infrared lamp, a slat heater box provides a greater degree of sink temperature uniformity for a test-object surface that includes multiple areas with differing optical properties.

Ungar, Eugene↗

NASA NTRS1983

On the equation of state of solar wind ions derived from Helios measurements

The radial evolution of such adiabatic invariants as the ion magnetic moments are studied on the basis of solar wind ion velocity distribution observations made by the Helios spacecraft between 0.3 and 1 AU. Significant differences between proton and alpha-particle parameters in wind velocity dependence are noted, and adiabaticity is on the average found to be violated. This violation is interpreted as evidence that protons are heated perpendicular to the field in fast streams. The contribution of the differential streaming energy to the total internal energy of the ions is also considered, and average heliocentric radial profiles for the ion heat fluxes are presented together with an examination of a possible ion heat flux role in the supply of thermal energy during the winds radial expansion. The present findings suggest that wave-particle interactions, and/or Coulomb collisions, are required to explain solar wind ion thermal energy states and radial temperature profiles.

Marsch, E.↗

NASA NTRS1986

Thermal structure of the Venus atmosphere in the middle cloud layer

Thermal structure measurements obtained by the two VEGA balloons show the Venus middle cloud layer to be generally adiabatic. Temperatures measured by the two balloons at locations roughly symmetric about the equator differed by about 6.5 kelvins at a given pressure. The VEGA-2 temperatures were about 2.5 kelvins cooler and those of VEGA-1 about 4 kelvins warmer than temperatures measured by the Pioneer Venus Large Probe at these levels. Data taken by the VEGA-2 lander as it passed through the middle cloud agreed with those of the VEGA-2 balloon. Study of individual frames of the balloon data suggests the presence of multiple discrete air masses that are internally adiabatic but lie on slightly different adiabats. These adiabats, for a given balloon, can differ in temperature by as much as 1 kelvin at a given pressure.

Linkin, V. M.↗

NASA NTRS1979

Phase change in liquid face seals. II - Isothermal and adiabatic bounds with real fluids

Analytical studies of phase change effects in parallel and tapered liquid face seals are presented. An isothermal and adiabatic model of low Reynolds number flow are considered by numerical integration of the descriptive equations for a real fluid, and its thermodynamic properties are calculated for each step, using a computer program for the steam tables or fluid thermodynamic properties. It was shown that for low leakage rate the isothermal model is more accurate and for high leakage rates the adiabatic model is more accurate; that both models yield the same conclusions regarding stability; and that the transient of collapse is described by the adiabatic model which predicts a catastrophic collapse and then either failure or explosive return to a larger film thickness value. Finally, it is shown that converging seals may become unstable and the mass leakage rate is reduced significantly below the all liquid value when boiling occurs.

Hughes, W. F.↗

NASA NTRS1980

The interplanetary transport of solar cosmic rays

Numerical solutions are presented for the propagation of solar cosmic rays in interplanetary space, including the effects of pitch-angle scattering and adiabatic focusing. The intensity-time profiles can be well fitted by a simple radial spatial diffusion equation with scattering mean-free path lambda(fit). The radial mean-free path so obtained is significantly larger than the true scattering mean-free path for low-rigidity particles due to both adiabatic focusing and the inapplicability of the diffusive approximation early in the event. The well-known discrepancy between lambda(fit) and the theoretical predictions may be resolved by these calculations.

Gombosi, T. I.↗

NASA NTRS1999

A Multiphase Equation of State for Hydrazine and Monomethylhydrazine

The objective of this work was to obtain a validated equation of state for hydrazine and monomethylhydrazine (MMH) and use this equation to calculate thermodynamic properties. The approach was based on using both reliable critical property values and a value of the acentric factor in the Soave Redlich Kwong and the Peng Robinson model equations of state. These equations were validated by comparing calculated molar volumes for phase equilibrium with published experimental values and comparing calculated vapor pressures with published experimental values over the temperature range appropriate for the corresponding state equations. The equation of state giving the best results was used to calculate enthalpy and entropy departure functions and fugacity values. Additional thermodynamic property calculations were performed to produce partial Mollier diagrams and thermodynamic properties containing internal energy, enthalpy, and entropy values for hydrazine and MMH. The analyses of systems in which either adiabatic or near-adiabatic compression of liquid or vapor hydrazine or low velocity detonations occur require a validated equation of state for representing occurring molar volumes and for energy calculations. Other calculations for thermodynamic properties of hydrazine are available, but the values are for a strict ideal gas state. This work characterized destructive events using hydrazine by calculating for isentropic compression temperatures. The final temperatures were calculated and compared using the ideal and real gas fluid equations of state.

Barragan, Michelle↗

NASA NTRS1985

On the use of wall functions as boundary conditions for two-dimensional separated compressible flows

A new and improved wall function method for compressible turbulent flows has been developed and tested. This method is applicable to attached and separated flows, to both high- and low-Reynolds number flows, and to flows with adiabatic and nonadiabatic surfaces. This wall function method has been applied to the Launder-Spalding k-epsilon two-equation model of turbulence. The tests consist of comparisons of calculated and experimental results for: (1) an axisymmetrical transonic shock-wave/boundary-wave interaction flow at low Reynolds number in an adiabatic tube, (2) an axisymmetrical high-Reynolds number transonic flow over a nonadiabatic bump, and (3) a two-dimensional supersonic high-Reynolds number flow on a nonadiabatic deflected flap. Each of these experiments had significant regions of flow separation. The calculations are performed with an implicit algorithm that solves the Reynolds-averaged Navier-Stokes equations. It is shown that the results obtained agree very well with the data for the complex compressible flows tested.

Viegas, J. R.↗

NASA NTRS1974

Quasi-linear theory via the cumulant expansion approach

The cumulant expansion technique of Kubo was used to derive an intergro-differential equation for f , the average one particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the f equation degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory for this limited class of fluctuations. For more physically realistic fluctuations, however, quasi-linear theory is at best approximate.

Jones, F. C.↗

NASA NTRS1975

When is quasi-linear theory exact

We use the cumulant expansion technique of Kubo (1962, 1963) to derive an integrodifferential equation for the average one-particle distribution function for particles being accelerated by electric and magnetic fluctuations of a general nature. For a very restricted class of fluctuations, the equation for this function degenerates exactly to a differential equation of Fokker-Planck type. Quasi-linear theory, including the adiabatic assumption, is an exact theory only for this limited class of fluctuations.

Jones, F. C.↗

NASA NTRS1984

Acoustic-radiation stress in solids. I - Theory

The general case of acoustic-radiation stress associated with quasi-compressional and quasi-shear waves propagating in infinite and semiinfinite lossless solids of arbitrary crystalline symmetry is studied. The Boussinesq radiation stress is defined and found to depend directly on an acoustic nonlinearity parameter which characterizes the radiation-induced static strain, a stress-generalized nonlinearity parameter which characterizes the stress nonlinearity, and the energy density of the propagating wave. Application of the Boltzmann-Ehrenfest principle of adiabatic invariance to a self-constrained system described by the nonlinear equations of motion allows the acoustic-radiation-induced static strain to be identified with a self-constrained variation in the time-averaged product of the internal energy density and displacement gradient. The time-averaged product is scaled by the acoustic nonlinearity parameter and represents the first-order nonlinearity in the virial theorem. Finally, the relationship between the Boussinesq and the Cauchy radiation stress is obtained in a closed three-dimensional form.

Cantrell, J. H., Jr.↗

NASA NTRS2021

Constraining Cosmic Microwave Background Temperature Evolution With Sunyaev–Zel’Dovich Galaxy Clusters from the Atacama Cosmology Telescope

The Sunyaev–Zel’dovich (SZ) effect introduces a specific distortion of the blackbody spectrum of the cosmic microwave background(CMB) radiation when it scatters off hot gas in clusters of galaxies. The frequency dependence of the distortion is only independent of the cluster redshift when the evolution of the CMB radiation is adiabatic. Using 370 clusters within the redshift range 0.07z1.4 from the largest SZ-selected cluster sample to date from the Atacama Cosmology Telescope, we provide new constraints on the deviation of CMB temperature evolution from the standard model a=-+0.0170.0320.029, where()()=+a-TzTz101. This result is consistent with no deviation from the standard adiabatic model. Combining it with previous, independent data sets we obtain a joint constraint ofα=−0.001±0.012. Attributing deviation from adiabaticity to the decay of dark energy, this result constrains its effective equation of state=--+w0.998eff0.0100.008.

Yunyang Li↗

NASA NTRS1992

Nitric oxide formation in a lean, premixed-prevaporized jet A/air flame tube: An experimental and analytical study

An experimental and analytical study was performed on a lean, premixed-prevaporized Jet A/air flame tube. The NO(x) emissions were measured in a flame tube apparatus at inlet temperatures ranging from 755 to 866 K (900 to 1100 F), pressures from 10 to 15 atm, and equivalence ratios from 0.37 to 0.62. The data were then used in regressing an equation to predict the NO(x) production levels in combustors of similar design. Through an evaluation of parameters it was found that NO(x) is dependent on adiabatic flame temperature and combustion residence time, yet independent of pressure and inlet air temperature for the range of conditions studied. This equation was then applied to experimental data that were obtained from the literature, and a good correlation was achieved.

Lee, Chi-Ming↗

NASA NTRS1987

The effects of adiabatic and viscous heatings on plumes

The influences of viscous and adiabatic heatings on the transient development of plumes have been assessed by employing the time-dependent convection equations in the extended-Boussinesq limit. Both temperature-dependent and temperature- and pressure-dependent viscosities are employed. For constant thermal expansion of coefficient, the vigor of plume flows is diminished with larger magnitudes of the thermal expansivity. This effect is caused by the local domination of adiabatic decompression over viscous heating inside the developing plume for both the Cartesian and axisymmetric domains. For deep mantle flows a thermal expansivity decreasing with depth is required for thin plume structures to exist. Values of the thermal expansivity contrast, which can promote plume growth, are in accord with estimates from recent studies in seismic equation of state.

Zhao, Wuling↗

NASA NTRS1978

Equation of state fits to the lower mantle and outer core

The lower mantle and outer core are subjected to tests for homogeneity and adiabaticity. An earth model is used which is based on the inversion of body waves and Q-corrected normal-mode data. Homogeneous regions are found at radii between 5125 and 4825 km, 4600 and 3850 km, and 3200 and 2200 km. The lower mantle and outer core are inhomogeneous on the whole and are only homogeneous in the above local regions. Finite-strain and atomistic equations of state are fit to the homogeneous regions. The apparent convergence of the finite-strain relations is examined to judge their applicability to a given region. In some cases the observed pressure derivatives of the elastic moduli are used as additional constraints. The effect of minor deviations from adiabaticity on the extrapolations is also considered. An ensemble of zero-pressure values of the density and seismic velocities are found for these regions. The range of extrapolated values from these several approaches provides a measure of uncertainties involved.

Butler, R.↗

NASA NTRS1980

Interior structure of Saturn inferred from Pioneer 11 gravity data

The structure of Saturn is studied via a fourth-order theory for rotating planets and equations of state for the envelope which depend parametrically on the helium abundance, on the starting temperature for the adiabat, and on adopted forms of the pressure-density curve in the region of transition from molecular to metallic hydrogen. Models are constrained by the values of J2 and J4 obtained from the Pioneer-Saturn celestial mechanics experiment. Equations of state are tested by computing Jupiter models, which can now be subjected to a more stringent comparison with observed zonal harmonics. It is found that Saturn has a low-density hydrogen-helium envelope with no evidence for enhancement of H2O, CH4, or other abundant compounds. Such compounds are presumably located near the core. The helium mass abundance for Saturn's envelope appears to be in the range of approximately 0.12 to 0.19, but this result is very model-dependent. The helium abundance in the envelope of Jupiter is apparently very similar to that of Saturn.

Hubbard, W. B.↗