Transport Coefficients of Partially Ionized Helium
Partially ionized He in chemical equilibrium at various pressures and temperatures, deriving transport coefficients with Chapman-Enskog- Burnett method
Devoto, R. S.↗
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A program for computing shock-tube gasdynamic properties
Computer program for calculating chemical equilibrium properties in shock tubes
Horton, T. E.↗
Calculation of complex chemical equilibria.
Complex chemical equilibrium calculation, analyzing thermodynamic principles and solution to nonlinear equations
Gordon, S.↗
Program to determine radiating, nonadiabatic, inviscid flow over a blunt body by the method of integral relations
Computer program performs the many calculations necessary for solving radiating, nonadiabatic flow of air in chemical equilibrium. Solution method provides accurate description of blunt body flow field in subsonic region.
Taylor, F. W.↗
A general stagnation-point convective heating equation for arbitrary gas mixtures
The stagnation-point convective heat transfer to an axisymmetric blunt body for arbitrary gases in chemical equilibrium was investigated. The gases considered were base gases of nitrogen, oxygen, hydrogen, helium, neon, argon, carbon dioxide, ammonia, and methane and 22 gas mixtures composed of the base gases. Enthalpies ranged from 2.3 to 116.2 MJ/kg, pressures ranged from 0.001 to 100 atmospheres, and the wall temperatures were 300 and 1111 K. A general equation for the stagnation-point convective heat transfer in base gases and gas mixtures was derived and is a function of the mass fraction, the molecular weight, and a transport parameter of the base gases. The relation compares well with present boundary-layer computer results and with other analytical and experimental results. In addition, the analysis verified that the convective heat transfer in gas mixtures can be determined from a summation relation involving the heat transfer coefficients of the base gases. The basic technique developed for the prediction of stagnation-point convective heating to an axisymmetric blunt body could be applied to other heat transfer problems.
Sutton, K.↗
An Implicit Finite Difference Solution to the Viscous Radiating Shock Layer with Strong Blowing
An implicit finite difference scheme is developed for the fully coupled solution of the viscous radiating stagnation line equations, including strong blowing. Solutions are presented for both air injection and carbon phenolic ablation products injection into air at conditions near the peak radiative heating point in an earth entry trajectory from interplanetary return missions. A detailed radiative transport code that accounts for the important radiative exchange processes for gaseous mixtures in local thermodynamic and chemical equilibrium is utilized.
Garrett, L. B.↗
Transpiration and film cooling boundary layer computer program. Volume 1: Numerical solutions of the turbulent boundary layer equations with equilibrium chemistry
A finite difference turbulent boundary layer computer program has been developed. The program is primarily oriented towards the calculation of boundary layer performance losses in rocket engines; however, the solution is general, and has much broader applicability. The effects of transpiration and film cooling as well as the effect of equilibrium chemical reactions (currently restricted to the H2-O2 system) can be calculated. The turbulent transport terms are evaluated using the phenomenological mixing length - eddy viscosity concept. The equations of motion are solved using the Crank-Nicolson implicit finite difference technique. The analysis and computer program have been checked out by solving a series of both laminar and turbulent test cases and comparing the results to data or other solutions. These comparisons have shown that the program is capable of producing very satisfactory results for a wide range of flows. Further refinements to the analysis and program, especially as applied to film cooling solutions, would be aided by the acquisition of a firm data base.
Levine, J. N.↗
Opacity of tungsten-seeded hydrogen to 2500 K and 115 atmospheres.
Experimental investigation and measurement of the radiant heat attenuation of an aerosol which may serve as a gas core nuclear-rocket propellant. The experiment uses a tungsten-hydrogen aerosol heated to temperatures as high as 2500 K under pressures up to 115 atmospheres. The hydrogen aerosol is produced by dispersion of submicron-sized particles of tungsten in hydrogen gas. A narrow beam of broad spectrum (visible and ultraviolet) light is passed through it with the attenuation being measured as a function of wavelength. Other aerosol characteristics examined include the nature and extent of chemical reactions between the seed material and the hydrogen and the degree of dispersion of the seed material obtained before and after heating. Chemical equilibrium calculations and vapor pressure data for the refractory metals indicate that tungsten is a prime candidate for the seed material in the gas core nuclear rocket.
Williams, J. R.↗
Metal/silicate fractionation in the solar system.
Fractionation between the metal and silicate components of objects in the inner solar system has long been recognized as a necessity in order to explain the observed density variations of the terrestrial planets and the H-group, L-group dichotomy of the ordinary chondrites. This paper discusses the densities of the terrestrial planets in light of current physical and chemical models of processes in the solar nebula. It is shown that the observed density trends in the inner solar system need not be the result of special fractionation processes, and that the densities of the planets may be direct results of simultaneous application of both physical and chemical restraints on the structure of the nebula, most notably the variation of temperature with heliocentric distance. The density of Mercury is easily attributed to accretion at temperatures so high that MgSiO3 is only partially retained but Fe metal is condensed. The densities of the other terrestrial planet are shown to be due to different degrees of retention of S, O and H as FeS, FeO and hydrous silicates produced in chemical equilibrium between condensates and solar-composition gases.
Lewis, J. S.↗
Computer program for calculation of thermodynamic and transport properties of complex chemical systems
Program performs calculations such as chemical equilibrium for assigned thermodynamic states, theoretical rocket performance for both equilibrium and frozen compositions during expansion, incident and reflected shock properties, and Chapman-Jouget detonation properties. Features include simplicity of input and storage of all thermodynamic and transport property data on master tape.
Svehla, R. A.↗
Analytical study of striated nozzle flow with small radius of curvature ratio throats
An analytical method was developed which is capable of estimating the chamber and throat conditions in a nozzle with a low radius of curvature throat. The method was programmed using standard FORTRAN 4 language and includes chemical equilibrium calculation subprograms (modified NASA Lewis program CEC71) as an integral part. The method determines detailed and gross rocket characteristics in the presence of striated flows and gives detailed results for the motor chamber and throat plane with as many as 20 discrete zones. The method employs a simultaneous solution of the mass, momentum, and energy equations and allows propellant types, 0/F ratios, propellant distribution, nozzle geometry, and injection schemes to be varied so to predict spatial velocity, density, pressure, and other thermodynamic variable distributions in the chamber as well as the throat. Results for small radius of curvature have shown good comparison to experimental results. Both gaseous and liquid injection may be considered with frozen or equilibrium flow calculations.
Norton, D. J.↗
An implicit finite-difference solution to the viscous shock layer, including the effects of radiation and strong blowing
An implicit finite-difference scheme is developed for the fully coupled solution of the viscous, radiating stagnation-streamline equations, including strong blowing. Solutions are presented for both air injection and injection of carbon-phenolic ablation products into air at conditions near the peak radiative heating point in an earth entry trajectory from interplanetary return missions. A detailed radiative-transport code that accounts for the important radiative exchange processes for gaseous mixtures in local thermodynamic and chemical equilibrium is utilized in the study. With minimum number of assumptions for the initially unknown parameters and profile distributions, convergent solutions to the full stagnation-line equations are rapidly obtained by a method of successive approximations. Damping of selected profiles is required to aid convergence of the solutions for massive blowing. It is shown that certain finite-difference approximations to the governing differential equations stabilize and improve the solutions. Detailed comparisons are made with the numerical results of previous investigations. Results of the present study indicate lower radiative heat fluxes at the wall for carbonphenolic ablation than previously predicted.
Garrett, L. B.↗
FORTRAN 4 computer program for calculation of thermodynamic and transport properties of complex chemical systems
A FORTRAN IV computer program for the calculation of the thermodynamic and transport properties of complex mixtures is described. The program has the capability of performing calculations such as:(1) chemical equilibrium for assigned thermodynamic states, (2) theoretical rocket performance for both equilibrium and frozen compositions during expansion, (3) incident and reflected shock properties, and (4) Chapman-Jouguet detonation properties. Condensed species, as well as gaseous species, are considered in the thermodynamic calculation; but only the gaseous species are considered in the transport calculations.
Svehla, R. A.↗
Calculated distributions of hydrogen and helium ions in the low-latitude ionosphere.
The simultaneous time-dependent continuity equations for O(+), H(+) and He(+) in the low latitude F-region are solved. Account is taken of E x B drift, a meridional neutral wind, and ion-ion and ion-neutral drag. The calculated profiles of O(+) and H(+) concentrations at 1630 LT are in fair agreement with the observations of Hanson et al. The He(+) field-aligned velocity is almost matched to the O(+) field-aligned velocity and, above the chemical equilibrium region and around the He(+) peak, the He(+) concentration is determined largely by production and transport. There is disagreement between the theoretical vertical He(+) profile and the profile observed by Hanson et al. Satisfactory agreement is obtained with Taylor's satellite results at fixed height for O(+) and H(+). It is found that the He(+) concentration is greater in the winter hemisphere than in the summer hemisphere, even if the neutral helium distribution is symmetrical about the Equator. The He(+) results are consistent with Taylor's results.
Moffett, R. J.↗
Deuterium in the early solar system.
An attempt is made to construct a self-consistent picture of the deuterium abundance in the early solar system based on the assumption of chemical equilibrium in the solar nebula. A recent determination of the D/H ratio for the atmosphere of Jupiter is consistent with a previous estimate of the D/H ratio for the protosun. The high (greater than .00015) D/H ratios determined from analyses of carbonaceous meteorites imply an equilibrium temperature less than 270 K, in marked disagreement with the equilibrium temperature determined for the same material by oxygen isotope cosmothermometry.
Black, D. C.↗
Equation of state and phase diagram of dense hydrogen
The equation of state of hydrogen was calculated for specific volumes ranging from 0.01 to 0.0001 cm3/mole and for temperatures ranging from 200 to 1 million K. Three phases are considered: the molecular solid, the metallic solid and the fluid. Chemical equilibrium between molecules, atoms, ions and electrons is considered in calculating the properties of the fluid phase. Transitions between the three phases will be discussed. The triple point, where the three phases coexist, is calculated to occur at 2.3 Mbar and 1679 K. At higher temperatures and pressures, the molecular solid is unstable.
Kerley, G. I.↗
Theoretical ion densities in the lower ionosphere
We have solved the coupled momentum and continuity equations for NO(+), O2(+), and O(+) ions in the E- and F-regions of the ionosphere. This theoretical model has enabled us to examine the relative importance of various processes that affect molecular ion densities. We find that transport processes are not important during the day; the molecular ions are in chemical equilibrium at all altitudes. At night, however, both diffusion and vertical drifts induced by winds or electric fields are important in determining molecular ion densities below about 200 km. Nitric oxide plays an important role in determining the NO(+) to O2(+) ratio in the E-region, particularly at night. Nocturnal sources of ionization are required to maintain the E-region through the night. Vertical velocities induced by expansion and contraction of the neutral atmosphere are too small to affect ion densities at any altitude.
Schunk, R. W.↗
Nonequilibrium flow calculations for the hydrogen constricted arc
A nonequilibrium flow model has been formulated and solved numerically for conditions in an atomic hydrogen cascade arc. Solutions show that although thermal nonequilibrium effects are minor, the departure from chemical equilibrium is significant. Comparisons with results obtained from an equilibrium flow model reveal the deficiencies associated with such a model and parametric calculations reveal the effect of current, pressure, and radius on arc behavior.
Scott, R. K.↗